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ThA01 |
Orchid Main 4202-4306 |
Analysis and Design of Optimization Algorithms Using Tools from Control
Theory |
Tutorial Session |
Chair: Van Scoy, Bryan | Miami University |
Co-Chair: Lessard, Laurent | Northeastern University |
Organizer: Lessard, Laurent | Northeastern University |
Organizer: Van Scoy, Bryan | Miami University |
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10:00-10:20, Paper ThA01.1 | |
>Analysis and Design of Optimization Algorithms Using Tools from Control Theory (I) |
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Lessard, Laurent | Northeastern University |
Keywords: Optimization algorithms, LMIs, Robust control
Abstract: First-order methods provide robust and efficient solutions to large-scale optimization problems. Recent advances in the analysis and design of first-order methods have been fueled by tools from controls, including integral quadratic constraints and multipliers from robust control. Similar advances have been made in the optimization community through the (related) performance estimation framework. Together, these tools have transformed the way in which we analyze and design optimization methods. This talk will provide an overview of these tools and set the stage for the remainder of the session.
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10:20-10:40, Paper ThA01.2 | |
>Optimization Algorithm Synthesis Based on Integral Quadratic Constraints: A Tutorial (I) |
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Scherer, Carsten W. | University of Stuttgart |
Ebenbauer, Christian | RWTH Aachen University |
Holicki, Tobias | University of Stuttgart |
Keywords: Optimization algorithms, Robust control, LMIs
Abstract: We expose in a tutorial fashion the mechanisms which underlie the synthesis of optimization algorithms based on dynamic integral quadratic constraints. We reveal how these tools from robust control allow to design accelerated gradient descent algorithms with optimal guaranteed convergence rates by solving small-sized convex semi-definite programs. It is shown that this extends to the design of extremum controllers, with the goal to regulate the output of a general linear closed-loop system to the minimum of an objective function. Numerical experiments illustrate that we can not only recover gradient decent and the triple momentum variant of Nesterov's accelerated first order algorithm, but also automatically synthesize optimal algorithms even if the gradient information is passed through non-trivial dynamics, such as time-delays.
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10:40-11:00, Paper ThA01.3 | |
>A Tutorial on a Lyapunov-Based Approach to the Analysis of Iterative Optimization Algorithms (I) |
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Van Scoy, Bryan | Miami University |
Lessard, Laurent | Northeastern University |
Keywords: Optimization algorithms, Robust control, Lyapunov methods
Abstract: Iterative gradient-based optimization algorithms are widely used to solve difficult or large-scale optimization problems. There are many algorithms to choose from, such as gradient descent and its accelerated variants such as Polyak's Heavy Ball method or Nesterov's Fast Gradient method. It has long been observed that iterative algorithms can be viewed as dynamical systems, and more recently, as robust controllers. Here, the "uncertainty" in the dynamics is the gradient of the function being optimized. Therefore, worst-case or average-case performance can be analyzed using tools from robust control theory, such as integral quadratic constraints (IQCs). In this tutorial paper, we show how such an analysis can be carried out using an alternative Lyapunov-based approach. This approach recovers the same performance bounds as with IQCs, but with the added benefit of constructing a Lyapunov function.
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11:00-11:20, Paper ThA01.4 | |
>A Tutorial on the Structure of Distributed Optimization Algorithms (I) |
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Van Scoy, Bryan | Miami University |
Lessard, Laurent | Northeastern University |
Keywords: Optimization algorithms
Abstract: We consider the distributed optimization problem for a multi-agent system. Here, multiple agents cooperatively optimize an objective by sharing information through a communication network and performing computations. In this tutorial, we provide an overview of the problem, describe the structure of its algorithms, and use simulations to illustrate some algorithmic properties based on this structure.
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11:20-11:40, Paper ThA01.5 | |
>Interpolation Constraints for Computing Worst-Case Bounds in Performance Estimation Problems (I) |
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Rubbens, Anne | UCLouvain |
Bousselmi, Nizar | UCLouvain |
Colla, Sebastien | UCLouvain |
Hendrickx, Julien M. | UCLouvain |
Keywords: Optimization, Optimization algorithms, Computer-aided control design
Abstract: The Performance Estimation Problem (PEP) approach consists in computing worst-case performance bounds on optimization algorithms by solving an optimization problem: one maximizes an error criterion over all initial conditions allowed and all functions in a given class of interest. The maximal value is then a worst-case bound, and the maximizer provides an example reaching that worst case. This approach was introduced for optimization algorithms but could in principle be applied to many other contexts involving worst-case bounds. The key challenge is the representation of infinite-dimensional objects involved in these optimization problems such as functions, and complex or non-convex objects as linear operators and their powers, networks in decentralized optimization etc. This challenge can be resolved by interpolation constraints, which allow representing the effect of these objects on vectors of interest, rather than the whole object, leading to tractable finite dimensional problems. We review several recent interpolation results and their implications in obtaining of worst-case bounds via PEP.
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11:40-12:00, Paper ThA01.6 | |
>On Fundamental Proof Structures in First-Order Optimization (I) |
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Goujaud, Baptiste | Ecole Polytechnique |
Dieuleveut, Aymeric | Ecole Polytechnique |
Taylor, Adrien | Inria/Ecole Normale Supérieure |
Keywords: Optimization algorithms, Optimization, LMIs
Abstract: First-order optimization methods have attracted a lot of attention due to their practical success in many applications, including in machine learning. Obtaining convergence guarantees and worst-case performance certificates for first-order methods have become crucial for understanding ingredients underlying efficient methods and for developing new ones. However, obtaining, verifying, and proving such guarantees is often a tedious task. Therefore, a few approaches were proposed for rendering this task more systematic, and even partially automated. In addition to helping researchers finding convergence proofs, these tools provide insights on the general structures of such proofs. We aim at presenting those structures, showing how to build convergence guarantees for first-order optimization methods.
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ThA02 |
Melati Main 4001AB-4104 |
Learning-Based Control III: Model Learning, Analysis and Control |
Invited Session |
Chair: Schoellig, Angela P | University of Toronto |
Co-Chair: Müller, Matthias A. | Leibniz University Hannover |
Organizer: Trimpe, Sebastian | RWTH Aachen University |
Organizer: Müller, Matthias A. | Leibniz University Hannover |
Organizer: Schoellig, Angela P | Technical University of Munich & University of Toronto |
Organizer: Zeilinger, Melanie N. | ETH Zurich |
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10:00-10:20, Paper ThA02.1 | |
>Physically Consistent Multiple-Step Data-Driven Predictions Using Physics-Based Filters |
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Lian, Yingzhao | EPFL |
Shi, Jicheng | EPFL |
Jones, Colin N. | EPFL |
Keywords: Sampled-data control, Building and facility automation, Predictive control for linear systems
Abstract: Data-driven control can facilitate the rapid development of controllers, offering an alternative to conventional approaches. In order to maintain consistency between any known underlying physical laws and a data-driven decision-making process, preprocessing of raw data is necessary to account for measurement noise and any inconsistencies it may introduce. In this paper, we present a physics-based filter to achieve this and demonstrate its effectiveness through practical applications, using real-world datasets collected in a building on the École Polytechnique Fédérale de Lausanne (EPFL) campus. Two distinct use cases are explored: indoor temperature control and demand response bidding.
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10:20-10:40, Paper ThA02.2 | |
>Data-Driven Feedback Linearization with Complete Dictionaries (I) |
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De Persis, Claudio | University of Groningen |
Gadginmath, Darshan | University of California, Riverside |
Pasqualetti, Fabio | University of California, Riverside |
Tesi, Pietro | Università Degli Studi Di Firenze |
Keywords: Data driven control, Nonlinear systems, Feedback linearization
Abstract: We consider the feedback linearization problem, and contribute with a new method that can learn the linearizing controller from a library (a dictionary) of candidate functions. When the dynamics of the system is known, the method boils down to solving a set of linear equations. Remarkably, the same idea extends to the case in which the dynamics of the system is unknown and a linearizing controller must be found using experimental data. In particular, we derive a simple condition (checkable from data) to assess when the linearization property holds over the entire state space of interest and not just on the dataset used to determine the solution. We also discuss important research directions on this topic.
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10:40-11:00, Paper ThA02.3 | |
>Unconstrained Parametrization of Dissipative and Contracting Neural Ordinary Differential Equations (I) |
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Martinelli, Daniele | École Polytechnique Fédérale De Lausanne |
Galimberti, Clara Lucía | École Polytechnique Fédérale De Lausanne |
Manchester, Ian R. | University of Sydney |
Furieri, Luca | EPFL |
Ferrari-Trecate, Giancarlo | Ecole Polytechnique Fédérale De Lausanne |
Keywords: Neural networks, Stability of nonlinear systems, Machine learning
Abstract: In this work, we introduce and study a class of Deep Neural Networks (DNNs) in continuous-time. The proposed architecture stems from the combination of Neural Ordinary Differential Equations (Neural ODEs) with the model structure of recently introduced Recurrent Equilibrium Networks (RENs). We show how to endow our proposed NodeRENs with contractivity and dissipativity --- crucial properties for robust learning and control. Most importantly, as for RENs, we derive parametrizations of contractive and dissipative NodeRENs which are unconstrained, hence enabling their learning for a large number of parameters. We validate the properties of NodeRENs, including the possibility of handling irregularly sampled data, in a case study in nonlinear system identification.
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11:00-11:20, Paper ThA02.4 | |
>Abstracting Linear Stochastic Systems Via Knowledge Filtering (I) |
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Engelaar, Maico Hendrikus Wilhelmus | Eindhoven University of Technology |
Romao, Licio | University of Oxford |
Gao, Yulong | University of Oxford |
Lazar, Mircea | Eindhoven University of Technology |
Abate, Alessandro | University of Oxford |
Haesaert, Sofie | Eindhoven University of Technology |
Keywords: Formal Verification/Synthesis, Stochastic systems, Reduced order modeling
Abstract: In this paper, we propose a new model reduction technique for linear stochastic systems that builds upon knowledge filtering and utilizes optimal Kalman filtering techniques. This new technique will reduce the dimension of the noise disturbance and will allow any controller designed for the reduced model to be refined into a controller for the original stochastic system, while preserving any specification on the output. Although initially the reduced model will be time-varying, a method will be provided with which the reduced model can become time-invariant if it satisfies some minor technical conditions. We present our theoretical findings with an example that supports the proposed framework and illustrates how model reduction and controller refinement of stochastic systems can be achieved. We finish the paper by considering specific examples to analyze both completeness with respect to controller synthesis and model order reduction with respect to the state.
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11:20-11:40, Paper ThA02.5 | |
>Learning Control of Second-Order Systems Via Nonlinearity Cancellation (I) |
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Guo, Meichen | Delft University of Technology |
De Persis, Claudio | University of Groningen |
Tesi, Pietro | University of Florence |
Keywords: Data driven control, Stability of nonlinear systems, Learning
Abstract: A technique to design controllers for nonlinear systems from data consists of letting the controllers learn the nonlinearities, cancel them out and stabilize the closed-loop dynamics. When control and nonlinearities are unmatched, the technique leads to an approximate cancellation and local stability results are obtained. In this paper, we show that, if the system has some structure that the designer can exploit, an iterative use of the data leads to a globally stabilizing controller even when control and nonlinearities are unmatched.
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11:40-12:00, Paper ThA02.6 | |
>On the Impact of Regularization in Data-Driven Predictive Control (I) |
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Breschi, Valentina | Eindhoven University of Technology |
Chiuso, Alessandro | Univ. Di Padova |
Fabris, Marco | University of Padua |
Formentin, Simone | Politecnico Di Milano |
Keywords: Data driven control, Predictive control for linear systems, Uncertain systems
Abstract: Model predictive control (MPC) is a control strategy widely used in industrial applications. However, its implementation typically requires a mathematical model of the system being controlled, which can be a time-consuming and expensive task. Data-driven predictive control (DDPC) methods offer an alternative approach that does not require an explicit mathematical model, but instead optimize the control policy directly from data. In this paper, we study the impact of two different regularization penalties on the closed-loop performance of a recently introduced data-driven method called γ-DDPC. Moreover, we discuss the tuning of the related coefficients in different data and noise scenarios, to provide some guidelines for the end user.
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ThA03 |
Melati Junior 4010A-4111 |
Safe Planning and Control with Uncertainty Quantification II |
Invited Session |
Chair: Lindemann, Lars | University of Southern California |
Co-Chair: Gao, Yulong | University of Oxford |
Organizer: Gao, Yulong | University of Oxford |
Organizer: Lindemann, Lars | University of Southern California |
Organizer: Fan, Chuchu | Massachusetts Institute of Technology |
Organizer: Abate, Alessandro | University of Oxford |
Organizer: Pappas, George J. | University of Pennsylvania |
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10:00-10:20, Paper ThA03.1 | |
>Distributionally Robust Uncertainty Quantification Via Data-Driven Stochastic Optimal Control |
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Pan, Guanru | TU Dortmund University |
Faulwasser, Timm | TU Dortmund University |
Keywords: Stochastic optimal control, Predictive control for linear systems, Optimal control
Abstract: This paper studies optimal control problems of unknown linear systems subject to stochastic disturbances of uncertain distribution. Uncertainty about the stochastic disturbances is usually described via ambiguity sets of probability measures or distributions. Typically, stochastic optimal control requires knowledge of underlying dynamics and is as such challenging. Relying on a stochastic fundamental lemma from data-driven control and on the framework of polynomial chaos expansions, we propose an approach to reformulate distributionally robust optimal control problems with ambiguity sets as uncertain conic programs in a finite-dimensional vector space. We show how to construct these programs from previously recorded data and how to relax the uncertain conic program to numerically tractable convex programs via appropriate sampling of the underlying distributions. The efficacy of our method is illustrated via a numerical example.
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10:20-10:40, Paper ThA03.2 | |
>Inner Approximations of Stochastic Programs for Data-Driven Stochastic Barrier Function Design (I) |
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Mathiesen, Frederik Baymler | Delft University of Technology |
Romao, Licio | University of Oxford |
Abate, Alessandro | University of Oxford |
Calvert, Simeon Craig | Delft University of Technology |
Laurenti, Luca | TU Delft |
Keywords: Formal Verification/Synthesis, Stochastic systems, Lyapunov methods
Abstract: This paper proposes a new framework to compute finite-horizon safety guarantees for discrete-time piece-wise affine systems with stochastic noise of unknown distributions. The approach is based on a novel approach to synthesise a stochastic barrier function (SBF) from noisy data and rely on the scenario optimization theory. In particular, we show that the stochastic program to synthesize a SBF can be relaxed into a chance-constrained optimisation problem on which scenario approach theory applies. We further show that the resulting program can be reduced to a linear programming problem, thus guaranteeing efficiency. In contrast to existing approaches, this method is data efficient as it only requires the number of data to be proportional to the logarithm in the negative inverse of the confidence level and is computationally efficient due to its reduction to linear programming. The efficacy of the method is empirically evaluated on various verification benchmarks. Experiments show a significant improvement with respect to state-of-the-art, obtaining tighter certificates with a confidence that is several orders of magnitude higher.
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10:40-11:00, Paper ThA03.3 | |
>Capture, Propagate, and Control Distributional Uncertainty (I) |
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Aolaritei, Liviu | ETH Zurich |
Lanzetti, Nicolas | ETH Zürich |
Dörfler, Florian | Swiss Federal Institute of Technology (ETH) Zurich |
Keywords: Stochastic systems, Robust control, Optimization
Abstract: We study stochastic dynamical systems in settings where only partial statistical information about the noise is available, e.g., in the form of a limited number of noise realizations. Such systems are particularly challenging to analyze and control, primarily due to an absence of a distributional uncertainty model which: (1) is expressive enough to capture practically relevant scenarios; (2) can be easily propagated through system maps; (3) is invariant under propagation; and (4) allows for computationally tractable control actions. In this paper, we propose to model distributional uncertainty via Optimal Transport ambiguity sets and show that such modeling choice satisfies all of the above requirements. We then specialize our results to stochastic LTI systems, and start by showing that the distributional uncertainty can be efficiently captured, with high probability, within an Optimal Transport ambiguity set on the space of noise trajectories. Then, we show that such ambiguity sets propagate exactly through the system dynamics, giving rise to stochastic tubes that contain, with high probability, all trajectories of the stochastic system. Finally, we show that the control task is very interpretable, unveiling an interesting decomposition between the roles of the feedforward and the feedback control terms. Our results are actionable and successfully applied in stochastic reachability analysis and in trajectory planning under distributional uncertainty.
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11:00-11:20, Paper ThA03.4 | |
>Conformal Off-Policy Evaluation in Markov Decision Processes (I) |
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Foffano, Daniele | KTH Royal Institute of Technology |
Russo, Alessio | KTH Royal Institute of Technology |
Proutiere, Alexandre | KTH |
Keywords: Markov processes, Statistical learning, Estimation
Abstract: Reinforcement Learning aims at identifying and evaluating efficient control policies from data. In many real-world applications, the learner is not allowed to experiment and cannot gather data in an online manner (this is the case when experimenting is expensive, risky or unethical). For such applications, the reward of a given policy (the target policy) must be estimated using historical data gathered under a different policy (the behavior policy). Most methods for this learning task, referred to as Off-Policy Evaluation (OPE), do not come with accuracy and certainty guarantees. We present a novel OPE method based on Conformal Prediction that outputs an interval containing the true reward of the target policy with a prescribed level of certainty. The main challenge in OPE stems from the distribution shift due to the discrepancies between the target and the behavior policies. We propose and empirically evaluate different ways to deal with this shift. Some of these methods yield conformalized intervals with reduced length compared to existing approaches, while maintaining the same certainty level.
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11:20-11:40, Paper ThA03.5 | |
>Risk-Minimizing Two-Player Zero-Sum Stochastic Differential Game Via Path Integral Control (I) |
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Patil, Apurva | The University of Texas at Austin |
Zhou, Yujing | Princeton University |
Fridovich-Keil, David | The University of Texas at Austin |
Tanaka, Takashi | University of Texas at Austin |
Keywords: Game theory, Stochastic optimal control, Autonomous systems
Abstract: This paper addresses a continuous-time risk-minimizing two-player zero-sum stochastic differential game (SDG), in which each player aims to minimize its probability of failure. Failure occurs in the event when the state of the game enters into predefined undesirable domains, and one player's failure is the other's success. We derive a sufficient condition for this game to have a saddle-point equilibrium and show that it can be solved via a Hamilton-Jacobi-Isaacs (HJI) partial differential equation (PDE) with Dirichlet boundary condition. Under certain assumptions on the system dynamics and cost function, we establish the existence and uniqueness of the saddle-point of the game. We provide explicit expressions for the saddle-point policies which can be numerically evaluated using path integral control. This allows us to solve the game online via Monte Carlo sampling of system trajectories. We implement our control synthesis framework on two classes of risk-minimizing zero-sum SDGs: a disturbance attenuation problem and a pursuit-evasion game. Simulation studies are presented to validate the proposed control synthesis framework.
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11:40-12:00, Paper ThA03.6 | |
>Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference (I) |
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Hashemi, Navid | University of Southern California |
Qin, Xin | University of Southern California |
Lindemann, Lars | University of Southern California |
Deshmukh, Jyotirmoy | University of Southern California |
Keywords: Formal Verification/Synthesis, Neural networks, Statistical learning
Abstract: We consider data-driven reachability analysis of discrete-time stochastic dynamical systems using conformal inference. We assume that we are not provided with a symbolic representation of the stochastic dynamics, but instead have access to a dataset of K-step trajectories. The reachability problem is to construct a probabilistic flowpipe such that the probability that a K-step trajectory can violate the bounds of the flowpipe does not exceed a user-specified failure probability threshold. The key ideas in this paper are: (1) to learn a surrogate predictor model from data, (2) to perform reachability analysis using the surrogate model, and (3) to quantify the surrogate model’s incurred error using conformal inference in order to give probabilistic reachability guarantees. We focus on learning-enabled control systems with complex closed-loop dynamics that are difficult to model symbolically, but where state transition pairs can be queried, e.g., using a simulator. We demonstrate the applicability of our method on examples from the domain of learning-enabled cyber-physical systems.
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ThA04 |
Simpor Junior 4913 |
Electromobility: Transportation, Power Systems, and Markets |
Invited Session |
Chair: Cicic, Mladen | CNRS, GIPSA-Lab |
Co-Chair: Cenedese, Carlo | ETH Zurich |
Organizer: Cicic, Mladen | UC Berkeley |
Organizer: Cenedese, Carlo | ETH Zurich |
Organizer: Canudas de Wit, Carlos | CNRS, GIPSA-Lab |
Organizer: Lygeros, John | ETH Zurich |
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10:00-10:20, Paper ThA04.1 | |
>Electric Vehicle Charging Station Pricing Control under Balancing Reserve Capacity Commitments (I) |
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Cicic, Mladen | CNRS, GIPSA-Lab |
Gasnier, Guillaume | GIPSA-Lab, CNRS |
Canudas de Wit, Carlos | CNRS, GIPSA-Lab |
Keywords: Traffic control, Smart grid, Smart cities/houses
Abstract: Electric vehicle charging stations are expected to become key players in the future sustainable power system. We propose a framework for using them to provide balancing services to the grid, by implementing charging price control laws that ensure they are able to deliver their committed balancing capacity. The control laws are based on the Coupled Traffic, Energy, and Charging (CTEC) model, incorporating electric vehicle routing and charging decisions based on the charging price and EV state of charge. Charging stations compete with each other and must ensure a certain number of charging vehicles to maintain their role of frequency containment reserves. The results demonstrate the effectiveness of the proposed pricing control scheme in maximizing charging station profits, without violating their balancing reserve capacity commitments.
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10:20-10:40, Paper ThA04.2 | |
>Routing and Charging Game in Ride-Hailing Service with Electric Vehicles (I) |
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Zhang, Kenan | ETH Zurich |
Lygeros, John | ETH Zurich |
Keywords: Transportation networks, Mean field games, Markov processes
Abstract: This paper studies the routing and charging behaviors of electric vehicles in a competitive ride-hailing market. When the vehicles are idle, they can choose whether to continue cruising to search for passengers, or move a charging station to recharge. The behaviors of individual vehicles are then modeled by a Markov decision process (MDP). The state transitions in the MDP model, however, depend on the aggregate vehicle flows both in service zones and at charging stations. Accordingly, the value function of each vehicle is determined by the collective behaviors of all vehicles. With the assumption of the large population, we formulate the collective routing and charging behaviors as a mean-field Markov game. We characterize the equilibrium of such a game, prove its existence, and numerically show that the competition among vehicles leads to “inefficient congestion” both in service zones and at charging stations.
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10:40-11:00, Paper ThA04.3 | |
>Optimal Location of EVs Public Charging Stations Based on a Macroscopic Urban Electromobility Model (I) |
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Mourgues, Rémi | CNRS - Gipsa Lab |
Rodriguez-Vega, Martin | CNRS, GIPSA-Lab |
Canudas de Wit, Carlos | CNRS, GIPSA-Lab |
Keywords: Transportation networks, Modeling, Optimization
Abstract: This paper introduces a graph-based dynamic model for electric vehicle (EV) mobility in urban areas. The model tracks EV state-of-charge (SoC) changes over time and space, along with power inputs from public charging stations (PCS). It considers driver behavior when deciding when and where to charge, accounting for factors like current SoC, distance to PCS, and charging cost. The model helps identify optimal PCS locations to enhance convenience for EV users and profitability for PCS owners. Additionally, an averaged version of the model is presented to reduce computational overhead while aiding in optimal PCS placement. Simulation results affirm the effectiveness of our model and optimization approach in identifying ideal charging station locations and enhancing EV charging infrastructure accessibility.
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11:00-11:20, Paper ThA04.4 | |
>A Receding Horizon Scheme for EV Charging Stations in Demand Response Programs (I) |
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Zanvettor, Giovanni Gino | Universita' Di Siena |
Fochesato, Marta | ETH Zurich |
Casini, Marco | Universita' Di Siena |
Vicino, Antonio | Univ. Di Siena |
Keywords: Smart grid, Energy systems
Abstract: Demand response is expected to play a fundamental role in providing flexibility for balancing operations to the grid. On the other hand, the fast electrification of the transportation sector calls for new solutions to enforce safe and reliable grid operation. Here we consider an electric vehicle charging station that participates in demand response programs. The demand response program asks for a change of the charging station load profile in exchange for a monetary reward. A stochastic receding horizon scheme that exploits the charging flexibility is then designed to optimally coordinate vehicle charging. Numerical simulations show that the proposed approach ensures substantial cost reduction compared to simpler benchmarks while maintaining the computation time feasible for real-world applications.
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11:20-11:40, Paper ThA04.5 | |
>Learning How to Price Charging in Electric Ride-Hailing Markets (I) |
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Maljkovic, Marko | Ecole Polytechnique Fédérale De Lausanne (EPFL) |
Nilsson, Gustav | EPFL |
Geroliminis, Nikolas | Urban Transport Systems Laboratory, EPFL |
Keywords: Transportation networks, Game theory, Learning
Abstract: With the electrification of ride-hailing fleets, there will be a need to incentivize where and when the ride-hailing vehicles should charge. In this work, we assume that a central authority wants to control the distribution of the vehicles and can do so by selecting charging prices. Since there will likely be more than one ride-hailing company in the market, we model the problem as a single-leader multiple-follower Stackelberg game. The followers, i.e., the companies, then compete about the charging resources under given prices provided by the leader. We present a learning algorithm based on the concept of contextual bandits that allows the central authority to find an efficient pricing strategy. We also show how the exploratory phase of the learning can be improved if the leader has some partial knowledge about the companies’ objective functions. The efficiency of the proposed algorithm is demonstrated in a simulated case study for the city of Shenzhen, China.
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11:40-12:00, Paper ThA04.6 | |
>Designing Optimal Personalized Incentive for Traffic Routing Using BIG Hype (I) |
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Grontas, Panagiotis D | Swiss Federal Institute of Technology (ETH) Zürich |
Cenedese, Carlo | ETH Zurich |
Fochesato, Marta | ETH Zurich |
Belgioioso, Giuseppe | ETH Zürich |
Lygeros, John | ETH Zurich |
Dörfler, Florian | Swiss Federal Institute of Technology (ETH) Zurich |
Keywords: Traffic control, Game theory, Optimization algorithms
Abstract: We study the problem of routing plug-in electric and conventional fuel vehicles on a city scale using incentives. In our model, commuters selfishly aim to minimize a local cost that combines travel time and the financial expenses of using city facilities, i.e., parking and service stations. The traffic authority can influence the commuters' routing choice via personalized discounts on parking tickets and on the energy price at service stations. We formalize the problem of optimally designing these monetary incentives to induce traffic decongestion as a large-scale bilevel game, where constraints arise at both levels due to the finite capacities of city facilities and incentives budget. Then, we develop an efficient scalable solution scheme with convergence guarantees based on BIG Hype, a recently-proposed hypergradient-based algorithm for bilevel games. Finally, we validate our approach via numerical simulations over the Anaheim's traffic network, showcasing its advantages in terms of traffic decongestion and scalability.
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ThA05 |
Simpor Junior 4912 |
Recent Advances in Distributed Coordination of Intelligent Systems |
Invited Session |
Chair: Liu, Lu | City University of Hong Kong |
Co-Chair: Fang, Hao | Beijing Institute of Technology |
Organizer: Liu, Lu | City University of Hong Kong |
Organizer: Fang, Hao | Beijing Institute of Technology |
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10:00-10:20, Paper ThA05.1 | |
>Constructing a Virtual Leader for Sign Consensus of Heterogeneous Multi-Agent Systems (I) |
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Meng, Yihan | City University of Hong Kong |
Liu, Lu | City University of Hong Kong |
Zhang, Hongwei | Harbin Institute of Technology, Shenzhen |
Keywords: Distributed control, Observers for Linear systems, Adaptive control
Abstract: This paper studies output sign consensus problem for leaderless heterogeneous linear multi-agent systems (MASs) over switching signed graphs. Established on the assumption that the communication graph is jointly eventually positive, a distributed ‘sign observer’ is proposed to estimate a virtual leader. This virtual leader is not pre-determined, but induced from the topology of the graph, the initial conditions of the agents and the structure of the ‘observer’. Based on the distributed ‘sign observer’ and output regulation method, a state feedback controller is designed to drive the output signals of the MAS to have the same sign.
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10:20-10:40, Paper ThA05.2 | |
>Adaptive Coverage Control for Heterogeneous Mobile Sensor Networks in an Unknown Environment (I) |
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Zheng, Boyin | City University of HongKong, Hong Kong, P. R. China |
Liu, Lu | City University of Hong Kong |
Keywords: Cooperative control, Adaptive control, Distributed control
Abstract: This article addresses the coverage control problems for heterogeneous mobile sensor networks (MSNs) in an environment with unknown event density functions. In contrast to existing works, unknown heterogeneous sensing abilities of the mobile sensor network (MSN) are considered by leveraging a weighted Voronoi diagram, namely, the Power diagram. To guarantee that the time-varying Power diagram converges to that defined by the true sensing weights, an online weight learning law is designed. Moreover, to handle certain applications such as forest fire investigation or nuclear radiation leakage mapping where the density information for the events of interest is not known to the MSN, an adaptive law is presented so that the event density approximation of each sensor converges to the real one along its trajectory. In addition, a move-to-centroid control law is proposed to drive the MSN to a near-optimal coverage configuration as time goes to infinity. Finally, the effectiveness of the proposed approach is illustrated by an example.
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10:40-11:00, Paper ThA05.3 | |
>A Distributed Algorithm for Solving a Time-Varying Linear Equation (I) |
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Zhang, Xiaozhen | Beijing Institute of Technology |
Yang, Qingkai | Beijing Institute of Technology |
Wei, Haijiao | China North Vehicle Research Institute |
Chen, Wei | Beijing Institute of Technology Chongqing Innovation Center |
Peng, Zhihong | Beijing Institute of Technology |
Fang, Hao | Beijing Institute of Technology |
Keywords: Cooperative control, Distributed control, Time-varying systems
Abstract: This paper studies the problem of cooperatively solving a time-varying linear equation of the form textbf{A}(t)textbf{emph{x}}(t)=textbf{emph{b}}(t), which always has a unique solution. Each agent has access to only some rows of the time-varying augmented matrix [begin{matrix} textbf{A}(t) & textbf{emph{b}}(t) end{matrix}]. We propose a distributed algorithm for solving the time-varying linear equation.The proposed distributed algorithm enforces local solutions to track local time-varying manifolds corresponding to local linear sub-equations while simultaneously reaching a consensus. This enables all local solutions to converge to the solution of the original time-varying linear equation. Finally, the effectiveness of the proposed algorithm is demonstrated through its application in a cooperative monitoring task.
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11:00-11:20, Paper ThA05.4 | |
>Fully Distributed Dynamic Event-Triggering Formation Control of UAV Swarms under DoS Attacks (I) |
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Cao, Hui | Beihang University |
Han, Liang | Beihang University |
Li, Dongyu | BEIHANG UNIVERSITY |
Hu, Qinglei | Beihang University |
Hao, Pengkun | Beihang University |
Keywords: Cooperative control, Distributed control, Resilient Control Systems
Abstract: For large-scale unmanned aerial vehicle (UAV) swarms, the security of communication networks is critical. When subjected to cyberattacks, the performance of swarm systems will be significantly affected. This paper focuses on the fully distributed time-varying formation (TVF) control problem of UAV swarms under Denial-of-Service (DoS) attacks. First, the theoretical framework of the fully distributed dynamic eventtriggering TVF control protocol is introduced. Then, sufficient conditions and critical proofs are provided to demonstrate that the desired formation configuration can be achieved under the influence of DoS attacks, and Zeno behavior is eliminated. Finally, the framework of a mixed-reality swarm flight platform is presented, which includes virtual nodes and physical nodes and integrates the advantages of both simulation and physical experiments, enabling large-scale swarm experiments with less cost and higher efficiency. The formation experiment using this platform validates the efficacy of the proposed control protocol.
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11:20-11:40, Paper ThA05.5 | |
>Multi-Agent Coordination under Temporal Logic Tasks and Team-Wise Intermittent Communication (I) |
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Wang, Junjie | Peking University |
Guo, Meng | Peking University |
Li, Zhongkui | Peking University |
Keywords: Autonomous systems, Decentralized control, Formal Verification/Synthesis
Abstract: Multi-agent systems outperform single agent in complex collaborative tasks. However, in large-scale scenarios, ensuring timely information exchange during decentralized task execution remains a challenge. This work presents an online decentralized coordination scheme for multi-agent systems under complex local tasks and intermittent communication constraints. Unlike existing strategies that enforce all-time or intermittent connectivity, our approach allows agents to join or leave communication networks at aperiodic intervals, as deemed optimal by their online task execution. This scheme concurrently determines local plans and refines the commu- nication strategy, i.e., where and when to communicate as a team. A decentralized potential game is modeled among agents, for which a Nash equilibrium is generated iteratively through online local search. It guarantees local task completion and intermittent communication constraints. Extensive numerical simulations are conducted against several strong baselines.
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11:40-12:00, Paper ThA05.6 | |
>Combinatorial-Hybrid Optimization for Multi-Agent Systems under Collaborative Tasks (I) |
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Tang, Zili | Peking University |
Chen, Junfeng | Peking University |
Guo, Meng | Peking University |
Keywords: Autonomous systems, Hybrid systems, Optimization
Abstract: Multi-agent systems can be extremely efficient when working concurrently and collaboratively, e.g., for transportation, maintenance, search and rescue. Coordination of such teams often involves two aspects: (i) selecting appropriate sub-teams for different tasks; (ii) designing collaborative control strategies to execute these tasks. The former aspect can be combinatorial w.r.t. the team size, while the latter requires optimization over joint state-spaces under geometric and dynamic constraints. Existing work often tackles one aspect by assuming the other is given, while ignoring their close dependency. This work formulates such problems as combinatorial-hybrid optimizations (CHO), where both the discrete modes of collaboration and the continuous control parameters are optimized simultaneously and iteratively. The proposed framework consists of two interleaved layers: the dynamic formation of task coalitions and the hybrid optimization of collaborative behaviors. Overall feasibility and costs of different coalitions performing various tasks are approximated at different granularities to improve the computational efficiency. At last, a Nash-stable strategy for both task assignment and execution is derived with provable guarantee on the feasibility and quality.
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ThA06 |
Simpor Junior 4911 |
Estimation IV |
Regular Session |
Chair: Bonnabel, Silvere | Mines ParisTech |
Co-Chair: Xie, Junyao | University of Alberta |
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10:00-10:20, Paper ThA06.1 | |
>Adaptive Estimation of Time-Varying Parameters Using DREM |
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Diget, Emil Lykke | University of Southern Denmark |
Sloth, Christoffer | University of Southern Denmark |
Keywords: Estimation, Time-varying systems, Adaptive control
Abstract: In this paper we present a method for estimating time-varying parameters in a linear regression equation. We combine local polynomial regression with dynamic regressor extension and mixing to independently estimate the parameters. During local polynomial regression, a time-varying parameter is approximated by locally constant polynomial coefficients. We propose to use the Bernstein basis instead of the commonly used monomial basis to improve numerical conditioning. A simulation example shows that our proposed estimator has improved performance compared to a similar method and allows a higher polynomial order.
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10:20-10:40, Paper ThA06.2 | |
>Filtered High Gain Interval Observer for LPV Systems with Bounded Uncertainties |
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Hugo, Antoine | IRSEEM/ONERA |
Thabet, Rihab El Houda | IRSEEM ESIGELEC |
Meyer, Luc | ONERA, Univ Paris Saclay |
Ahmed Ali, Sofiane | IBISC, Evry-Val-d’Essonne University, Universite Paris-Saclay, E |
Piet-Lahanier, Helene | ONERA |
Keywords: Estimation, Uncertain systems, Linear parameter-varying systems
Abstract: In this paper, a new High-Gain Interval Observer (HGIO) structure and its filtered version, named Filtered High-Gain Interval Observer (FHGIO), are proposed for a class of Linear Parameter Varying (LPV) systems subject to additive disturbances and measurement noise. Those uncertainties are assumed to be unknown but bounded with known values. The HGIO is based on a high-gain observer structure from which an interval formulation is deduced taking into account the uncertainties bounds. Then, the proposed HGIO is extended to incorporate a filter for the output estimation error, leading to the FHGIO design whose goal is to reduce the measurement noise amplification. Usually, the design of such interval observers is based on monotone systems theory which is hard to satisfy in many cases. In this paper, suitable changes of coordinates are used to overcome this limitation. Moreover, a sufficient condition for the non-divergence of the radius dynamics and a procedure to design the observers gains ensuring the stability are given for each observer. The efficiency of the proposed observers is illustrated through a simulation on a numerical example.
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10:40-11:00, Paper ThA06.3 | |
>Velocity Estimation for Motorcycles Using Image-To-Road Mapping |
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Pryde, Martin | Université Paris-Saclay |
Nehaoua, Lamri | Evry Univeristy |
Hadj-Abdelkader, Hicham | University of Evry - Paris Saclay |
Arioui, Hichem | Evry Paris-Saclay University |
Keywords: Estimation, Vision-based control, Automotive systems
Abstract: The authors propose a visual-inertial approach to estimate the body-fixed lateral velocity of motorcycles traveling along extra-urban roads. The approach comprises the following steps: First, a monocular camera takes video of the road ahead. Key features from sequential images of the road surface are ex- tracted using the Harris corner detector and matching features are identified using the Fast retina keypoint descriptor. The locations of these features on the road surface are determined using a mapping based on an intuitive ray-casting approach. Next, the feature locations on the road, the angular velocity measurements and the optical flow of the feature projection locations on the image plane are used to formulate the ego- motion of the motorcycle as a system of linear equations from which a velocity estimate is solved for using the least-squares method. Finally, this estimate is fused with readings from an inertial navigation system using a Kalman filter to produce a filtered estimate and correct integrator drift. The approach is validated against simulation data generated using BikeSim and the results are compared against state observer approaches and previously published visual-inertial approaches from the authors.
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11:00-11:20, Paper ThA06.4 | |
>Estimation of Dynamic Gaussian Processes (I) |
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van Hulst, Jilles | Eindhoven University of Technology |
van Zuijlen, Roy | Eindhoven University of Technology |
Antunes, Duarte | Eindhoven University of Technology, the Netherlands |
Heemels, W.P.M.H. | Eindhoven University of Technology |
Keywords: Estimation, Kalman filtering, Statistical learning
Abstract: Gaussian processes provide a compact representation for modeling and estimating an unknown function, that can be updated as new measurements of the function are obtained. This paper extends this powerful framework to the case where the unknown function dynamically changes over time. Specifically, we assume that the function evolves according to an integro-difference equation and that the measurements are obtained locally in a spatial sense. In this setting, we will provide the expressions for the conditional mean and covariance of the process given the measurements, which results in a generalized estimation framework, for which we coined the term Dynamic Gaussian Process (DGP) estimation. This new framework generalizes both Gaussian process regression and Kalman filtering. For a broad class of kernels, described by a set of basis functions, fast implementations are provided. We illustrate the results on a numerical example, demonstrating that the method can accurately estimate an evolving continuous function, even in the presence of noisy measurements and disturbances.
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11:20-11:40, Paper ThA06.5 | |
>A Lie-Theoretic Approach to Propagating Uncertainty Jointly in Attitude and Angular Momentum |
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Jayaraman, Amitesh | Stanford University |
Ye, Jikai | National University of Singapore |
Chirikjian, Gregory | National University of Singapore |
Keywords: Estimation
Abstract: Dynamic state estimation, as opposed to kinematic state estimation, seeks to estimate not only the orientation of a rigid body but also its angular velocity, through Euler's equations of rotational motion. This paper demonstrates that the dynamic state estimation problem can be reformulated as estimating a probability distribution on a Lie group defined on phase space (the product space of rotation and angular momentum). The propagation equations are derived non-parametrically for the mean and covariance of the distribution. It is also shown that the equations can be approximately solved by ignoring the third and higher moments of the probability distribution. Numerical experiments show that the distribution constructed from the propagated mean and covariance fits the sample data better than an extended Kalman filter.
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11:40-12:00, Paper ThA06.6 | |
>Moving Horizon Estimation for Discrete-Time Linear Systems Using Transfer Learning (I) |
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Xie, Junyao | University of Alberta |
Huang, Biao | Univ. of Alberta |
Keywords: Estimation, Observers for Linear systems, Machine learning
Abstract: In this article, we propose a novel moving horizon estimation method for discrete-time linear systems through transfer learning. Most moving horizon estimation designs require data from the considered systems of interest. However, practical processes might suffer from data sparsity issues, especially in a new or early operating environment. Motivated by the idea of transfer learning, this manuscript proposes a moving horizon estimation design using data from a similar but different system (i.e., source system) instead of the considered system (i.e., target system). Based on the data from the source system, we propose a novel moving horizon state estimation method for the target system and provide convergence and stability analyses. The state estimation error is upper bounded by a time-dependent sequence that is related to three types of similarities/differences between target and source systems, including initial conditions, disturbance levels, and model parameters. The effectiveness of the proposed approach is demonstrated through a numerical example.
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ThA07 |
Simpor Junior 4813 |
Influence, Mechanism, and Information Design in Games |
Invited Session |
Chair: Eksin, Ceyhun | Texas A&M University |
Co-Chair: Brown, Philip N. | University of Colorado, Colorado Springs |
Organizer: Eksin, Ceyhun | Texas A&M University |
Organizer: Marden, Jason R. | University of California, Santa Barbara |
Organizer: Brown, Philip N. | University of Colorado Colorado Springs |
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10:00-10:20, Paper ThA07.1 | |
>Robust Social Welfare Maximization Via Information Design in Linear-Quadratic-Gaussian Games |
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Sezer, Furkan | Texas A&M University |
Eksin, Ceyhun | Texas A&M University |
Keywords: Game theory, Agents-based systems, Optimization
Abstract: Information design in an incomplete information game includes a designer with the goal of influencing players' actions through signals generated from a designed probability distribution so that its objective function is optimized. We consider a setting in which the designer has partial knowledge on agents' payoffs. We address the uncertainty about players' preferences by formulating a robust information design problem against the worst case payoffs. If the players have quadratic payoffs that depend on the players' actions and an unknown payoff-relevant state, and signals on the state that follow a Gaussian distribution conditional on the state realization, then the information design problem under quadratic design objectives is a semidefinite program (SDP). Specifically, we consider ellipsoid perturbations over payoff coefficients in linear-quadratic-Gaussian (LQG) games. We show that this leads to a SDP formulation. Numerical studies are carried out to identify the relation between the perturbation levels and the optimal information structures.
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10:20-10:40, Paper ThA07.2 | |
>Rationality and Behavior Feedback in a Model of Vehicle-To-Vehicle Communication (I) |
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Gould, Brendan | University of Colorado Colorado Springs |
Brown, Philip N. | University of Colorado Colorado Springs |
Keywords: Game theory, Transportation networks, Agents-based systems
Abstract: Vehicle-to-Vehicle (V2V) communication is intended to improve road safety through distributed information sharing; however, it is difficult to predict and optimize how human agents will respond to this information. In a Bayesian game, agents probabilistically adopt various types from a fixed, exogenous distribution. Agents in such models ostensibly perform Bayesian inference, which may not be a reasonable cognitive demand for most humans. To complicate matters, real-world information provided to agents is often implicitly dependent on agent behavior, meaning that the distribution of agent types is a function of the behavior of agents (i.e., the type distribution is endogenous). In this paper, we study an existing model of V2V communication, but relax it along two dimensions: first, we pose a behavior model which does not require human agents to perform Bayesian inference; second, an equilibrium model which avoids the challenging endogenous recursion. Surprisingly, we show that the simplified non-Bayesian behavior model yields the exact same equilibrium behavior as the original Bayesian model, which may lend credibility to Bayesian models. However, we also show that the endogenous type model is necessary to obtain certain informational paradoxes; these paradoxes do not appear in the simpler exogenous model. This suggests that standard Bayesian game models with fixed type distributions are not sufficient to express certain important phenomena.
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10:40-11:00, Paper ThA07.3 | |
>Collaborative Coalitions in Multi-Agent Systems: Quantifying the Strong Price of Anarchy for Resource Allocation Games (I) |
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Ferguson, Bryce L. | University of California, Santa Barbara |
Paccagnan, Dario | Imperial College London |
Pradelski, Bary S. R. | Centre National De La Recherche Scientifique, France |
Marden, Jason R. | University of California, Santa Barbara |
Keywords: Game theory, Agents-based systems, Cooperative control
Abstract: The emergence of new communication technologies allows us to expand our understanding of distributed control and consider collaborative decision-making paradigms. With collaborative algorithms, certain local decision-making entities (or agents) are enabled to communicate with one another and collaborate on their actions to attain better system behavior. By limiting the amount of communication, these algorithms exist somewhere between centralized and fully distributed approaches. To understand the possible benefits of this inter-agent collaboration, we model a multi-agent system as a common interest game in which groups of agents can collaborate on their actions to jointly increase the system welfare. We specifically consider k-strong Nash equilibria as the emergent behavior of these systems and address how well these states approximate the system optimal, formalized by the k-strong price of anarchy ratio. Our main contributions are in generating tight bounds on the k-strong price of anarchy in finite resource allocation games as the solution to a tractable linear program. By varying k –the maximum size of a collaborative coalition– we observe exactly how much performance is gained from inter-agent collaboration. To investigate further opportunities for improvement, we generate upper bounds on the maximum attainable k-strong price of anarchy when the agents’ utility function can be designed.
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11:00-11:20, Paper ThA07.4 | |
>Coordination in Markov Games with Asymmetric Information (I) |
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Wei, Xupeng | University of Michigan |
Anastasopoulos, Achilleas | University of Michigan |
Keywords: Game theory, Markov processes, Stochastic systems
Abstract: We study coordination in Markov games with asymmetric information. We consider a model where the state consists of different components, each representing the private type of each player. Players' actions depend on their private types and the public observation of past actions. The state components evolve as independent Markov processes conditioned on actions. We propose a solution concept called perfect correlated equilibrium (PCE), realized by a correlation device that observes only the public information of past actions. At time t, the device generates a prescription profile from a commonly known joint distribution, and sends each player a prescription privately before they act. Players are expected to take actions according to the prescriptions at equilibrium by evaluating the suggested prescription at the private types. We introduce "structured" PCE (sPCE), in which the correlation device generates prescriptions based on the common action history through a common belief on the state. We motivate sPCE by showing that any payoff profile induced by a general device can be induced by a structured one. We show that when the correlation device is using structured strategies, players' rationality constraints can be characterized through appropriate Markov decision processes (MDPs). Based on this characterization, we develop a backward dynamic approach, with which one can verify if a structured device is feasible, or even design a structured PCE in a backward recursive manner. Finally, we consider a specific example demonstrating how coordination can improve social welfare.
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11:20-11:40, Paper ThA07.5 | |
>Capacity Allocation and Pricing of High Occupancy Toll Lane Systems with Heterogeneous Travelers (I) |
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Pulyassary, Haripriya | Cornell University |
Yang, Ruifan | Cornell University |
Zhang, Zhanhao | Cornell University |
Wu, Manxi | Cornell University |
Keywords: Game theory, Transportation networks, Intelligent systems
Abstract: In this article, we study the optimal design of High Occupancy Toll (HOT) lanes. In our setup, the traffic authority determines road capacity allocation between HOT lanes and ordinary lanes, as well as the toll price charged for travelers who use the HOT lanes but do not meet the high-occupancy eligibility criteria. We build a game-theoretic model to analyze the decisions made by travelers with heterogeneous values of time and carpool disutilities, who must choose between paying or forming carpools to take the HOT lanes, or taking the ordinary lanes. Travelers' payoffs depend on the congestion cost of the lane that they take, the payment and the carpool disutilities. We provide a complete characterization of travelers' equilibrium strategies and resulting travel times for any capacity allocation and toll price. We also calibrate our model on the California Interstate highway 880 and compute the optimal capacity allocation and toll design.
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11:40-12:00, Paper ThA07.6 | |
>Information Asymmetry and Contract Design with Applications to Agriculture (I) |
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Bonatti, Alessandro | MIT |
Dahleh, Munther A. | Massachusetts Inst. of Tech |
Horel, Thibaut | MIT |
Roozbehani, Mardavij | Massachusetts Institute of Technology |
Keywords: Agents-based systems, Game theory, Emerging control applications
Abstract: We consider situations in which an intermediary facilitates the interactions of one or several players with a downstream market in a game of incomplete information. Our key assumption is the presence of information asymmetries: while the intermediary has in general better (less noisy) information about the observable parameters of the game, the players have better information about their own private parameters and preferences. The intermediary seeks to influence the actions of the agents by offering side information and/or certain guarantees regarding the outcomes. For instance, farmers aim to sell their produce in a downstream market. The intermediary has access to more accurate signals regarding the downstream market (e.g. demand, prices, etc.), while the farmers are aware of their own private cost structure. The central problem is then to understand how to design contracts for exchanging information and mediating the interaction between the players and the downstream market in such a way that generates value to the players and revenue to the intermediary. Prior work on information design with elicitation has shown that in the presence of competition between the players, the intermediary can generate value by coordinating the players' actions in such a way that reduces the negative externalities they exert on each other. In this work, we focus on the question of risk-aversion. Our first result is negative and shows that the intermediary cannot generate revenue when interacting with a single risk-neutral or risk-seeking player. We then explore how this result changes under various relaxations of the model which include altering the risk preference of the player or changing the timing of the game.
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ThA08 |
Simpor Junior 4812 |
Optimal Control IV |
Regular Session |
Chair: Richter, Rebecca | Bunderwehr University Munich |
Co-Chair: Oguri, Kenshiro | Purdue University |
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10:00-10:20, Paper ThA08.1 | |
>Optimization-Based Trajectory Generation and Receding Horizon Control for Systems with Convex Dynamics |
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Lishkova, Yana | University of Oxford |
Cannon, Mark | University of Oxford |
Keywords: Optimal control, Nonlinear systems, Modeling
Abstract: In this paper we propose an optimization-based control scheme, which can be used for trajectory generation or receding horizon control for system with nonlinear, but convex dynamics, and both explicit and implicit discrete time models. The scheme uses both the nonlinear model and its linearization to construct a tube containing all possible future system trajectories, and uses this tube to predict performance and ensure constraint satisfaction. The controls sequence and tube cross-sections are optimized online in a sequence of convex programs without the need of pre-computed error bounds. We prove feasibility, stability and non-conservativeness of the approach, with the series of convex programs converging to a point which is a local optimum for the original nonlinear optimal control problem. We further present how a structure-preserving model can be implemented within the approach and used to reduce the number of constraints and guarantee a structure-preserving discrete trajectory solution.
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10:20-10:40, Paper ThA08.2 | |
>Closed-Loop Neighboring Extremal Optimal Control Using HJ Equation |
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Rai, Ayush | Purdue University |
Mou, Shaoshuai | Purdue University |
Anderson, Brian D.O. | Australian National University |
Keywords: Optimal control, Nonlinear systems
Abstract: This study introduces a method to obtain a neighboring extremal optimal control (NEOC) solution for a broad class of nonlinear systems with nonquadratic performance indices by investigating the variation to a known closed-loop optimal control law caused by small, known variations in the system parameters or in the performance index. The NEOC solution can formally be obtained by solving a linear partial differential equation similar to those arising in an iterative solution procedure for a nonlinear Hamilton-Jacobi equation. Motivated by numerical procedures for solving such an equation, we also propose a numerical algorithm based on the Galerkin algorithm that uses basis functions to solve the underlying Hamilton-Jacobi equation. This approach allows the determination of the minimum performance index as a function of both the system state and parameters and extends to allow the determination of the adjustment to an optimal control law given a small adjustment of parameters in the system or the performance index, effectively by computing the derivative of the law with respect to those parameters. The validity of the claims and theory is supported by numerical simulations.
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10:40-11:00, Paper ThA08.3 | |
>Towards Continuous-Time MPC: A Novel Trajectory Optimization Algorithm |
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Das, Souvik | Indian Institute of Technology, Bombay |
Ganguly, Siddhartha | Indian Institute of Technology, Bombay |
Muthyala, Anjali | Indian Institute of Technology Bombay |
Chatterjee, Debasish | Indian Institute of Technology, Bombay |
Keywords: Optimal control, Numerical algorithms, Constrained control
Abstract: This article introduces a numerical algorithm that serves as a preliminary step toward solving continuous-time model predictive control (MPC) problems directly without explicit time-discretization. The chief ingredients of the underlying optimal control problem (OCP) are a linear time-invariant system, quadratic instantaneous and terminal cost functions, and convex path constraints. The thrust of the method involves finitely parameterizing the admissible space of control trajectories and solving the OCP satisfying the given constraints at every time instant in a tractable manner without explicit time-discretization. The ensuing OCP turns out to be a convex semi-infinite program (SIP), and some recently developed results are employed to obtain an optimal solution to this convex SIP. A numerical illustration on a benchmark model is included to show the efficacy of the algorithm.
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11:00-11:20, Paper ThA08.4 | |
>Dynamic and Nonlinear Programming for Trajectory Planning |
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Britzelmeier, Andreas | Bundeswehr University |
De Marchi, Alberto | Universität Der Bundeswehr München |
Richter, Rebecca | Bunderwehr University Munich |
Keywords: Optimal control, Numerical algorithms, Robotics
Abstract: Direct optimal control techniques, relying on numerical methods for constrained optimization, are typically used in trajectory planning tasks in high-dimensional spaces. However, general-purpose solvers often fail to find a feasible solution when facing cluttered environments. Sampling- or graph-based methods, instead, can explore complex configuration spaces but struggle with dynamic constraints. Here, we propose to combine dynamic programming (DP) and derivative-based methods to reliably solve trajectory planning problems. Specifically, we exploit DP to generate a sequence of waypoints in a low-dimensional space, which are then encoded as pointwise path constraints for a high-dimensional trajectory, whose constraint violations are then represented as a penalty within the Bellman equation to recompute the waypoints. This iterative approach, alternating path and trajectory optimization, avoids both the curse of dimensionality for DP and problematic nonconvexities (such as obstacles) for motion planning. We demonstrate our strategy using numerical experiments on a six-degree-of-freedom robotic manipulator moving in a confined space.
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11:20-11:40, Paper ThA08.5 | |
>Higher-Order Retraction Maps and Construction of Numerical Methods for Optimal Control of Mechanical Systems |
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Anahory Simões, Alexandre | IE University |
Barbero-Linan, Maria | Technical University of Madrid |
Colombo, Leonardo Jesus | Spanish National Research Council |
Martin de Diego, David | High Council for Scientific Research |
Keywords: Optimal control, Numerical algorithms, Variational methods
Abstract: Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to a higher-order tangent bundle to construct geometric integrators for the higher-order Euler-Lagrange equations. Given a cost function, an optimal control problem for fully actuated mechanical systems can be understood as a higher-order variational problem. In this paper we introduce the notion of a higher-order discretization map associated with a retraction map to construct geometric integrators for the optimal control of mechanical systems. In particular, we study applications to path planning for obstacle avoidance of a planar rigid body.
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11:40-12:00, Paper ThA08.6 | |
>Successive Convexification with Feasibility Guarantee Via Augmented Lagrangian for Non-Convex Optimal Control Problems |
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Oguri, Kenshiro | Purdue University |
Keywords: Optimal control, Optimization, Aerospace
Abstract: This paper proposes an algorithm that solves non-convex optimal control problems with a theoretical guarantee for global convergence to a feasible local solution of the original problem. The proposed algorithm extends the recently proposed successive convexification (SCvx) algorithm to address its key limitation: lack of feasibility guarantee to the original non-convex problem. The main idea of the proposed algorithm is to incorporate the SCvx iteration into an algorithmic framework based on the augmented Lagrangian method to enable the feasibility guarantee while retaining favorable properties of SCvx. Unlike the original SCvx, our approach iterates on both of the optimization variables and the Lagrange multipliers, which facilitates the feasibility guarantee as well as efficient convergence, in a spirit similar to the alternating direction method of multipliers (ADMM). Convergence analysis shows the proposed algorithm's strong global convergence to a feasible local optimum of the original problem and its convergence rate. These theoretical results are demonstrated via numerical examples with comparison against the original SCvx algorithm.
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ThA09 |
Simpor Junior 4811 |
Optimization Algorithms IV |
Regular Session |
Chair: Kalaimani, Rachel Kalpana | Indian Institute of Technology Madras |
Co-Chair: Sato, Hiroyuki | Kyoto University |
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10:00-10:20, Paper ThA09.1 | |
>PANTR: A Proximal Algorithm with Trust-Region Updates for Nonconvex Constrained Optimization |
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Bodard, Alexander | KU Leuven |
Pas, Pieter | KU Leuven |
Patrinos, Panagiotis | KU Leuven |
Keywords: Optimization algorithms, Optimal control
Abstract: This work presents PANTR, an efficient solver for nonconvex constrained optimization problems, that is well-suited as an inner solver for an augmented Lagrangian method.The proposed scheme combines forward-backward iterations with solutions to trust-region subproblems: the former ensures global convergence, whereas the latter enables fast update directions. We discuss how the algorithm is able to exploit exact Hessian information of the smooth objective term through a linear Newton approximation, while benefiting from the structure of box-constraints or L1-regularization. An open-source C++ implementation of PANTR is made available as part of the NLP solver library ALPAQA. Finally, the effectiveness of the proposed method is demonstrated in nonlinear model predictive control applications.
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10:20-10:40, Paper ThA09.2 | |
>Gradient Descent with Low-Rank Objective Functions |
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Cosson, Romain | INRIA |
Jadbabaie, Ali | Massachusetts Institute of Technology |
Makur, Anuran | Purdue University |
Reisizadeh, Amirhossein | Massachusetts Institute of Technology |
Shah, Devavrat | MIT |
Keywords: Optimization algorithms, Optimization, Machine learning
Abstract: Several recent empirical studies demonstrate that important machine learning tasks, e.g., training deep neural networks, exhibit low-rank structure, where the loss function varies significantly in only a few directions of the input space. In this paper, we leverage such low-rank structure to reduce the high computational cost of canonical gradient-based methods such as gradient descent (GD). Our proposed Low-Rank Gradient Descent (LRGD) algorithm finds an epsilon-minimizer of a p-dimensional function by first identifying r < p significant directions, and then estimating the true p-dimensional gradient at every iteration by computing directional derivatives only along those r directions. We establish that the "directional oracle complexity" of LRGD for strongly convex objective functions is O(r log(1/epsilon) + rp). Therefore, when r << p, LRGD provides significant improvement over the known complexity of O(p log(1/epsilon)) of GD in the strongly convex setting. Furthermore, using real and synthetic data, we empirically find that LRGD provides significant gains over GD when the data has low-rank structure, and in the absence of such structure, LRGD does not degrade performance compared to GD.
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10:40-11:00, Paper ThA09.3 | |
>Adaptive Low-Rank Gradient Descent |
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Jadbabaie, Ali | Massachusetts Institute of Technology |
Makur, Anuran | Purdue University |
Reisizadeh, Amirhossein | Massachusetts Institute of Technology |
Keywords: Optimization algorithms, Optimization, Machine learning
Abstract: Low-rank structures have been observed in several recent empirical studies in many machine and deep learning problems, where the loss function demonstrates significant variation only in a lower dimensional subspace. While traditional gradient-based optimization algorithms are computationally costly for high-dimensional parameter spaces, such low-rank structures provide an opportunity to mitigate this cost. In this paper, we aim to leverage low-rank structures to alleviate the computational cost of first-order methods and study Adaptive Low-Rank Gradient Descent (AdaLRGD). The main idea of this method is to begin the optimization procedure in a very small subspace and gradually and adaptively augment it by including more directions. We show that for smooth and strongly convex objectives and any target accuracy epsilon, AdaLRGD's complexity is O(r ln(r/epsilon)) for some rank r no more than dimension d. This significantly improves upon gradient descent's complexity of O(d ln(1/epsilon)) when r << d. We also propose a practical implementation of AdaLRGD and demonstrate its ability to leverage existing low-rank structures in data.
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11:00-11:20, Paper ThA09.4 | |
>Communication-Efficient Distributed Optimization with Adaptability to System Heterogeneity |
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Yu, Ziyi | University of Science and Technology of China |
Freris, Nikolaos M. | University of Science and Technology of China |
Keywords: Optimization algorithms, Optimization
Abstract: We consider the setting of agents cooperatively minimizing the sum of local objectives plus a regularizer on a graph. This paper proposes a primal-dual method in consideration of three distinctive attributes of real-life multi-agent systems, namely: (i) expensive communication, (ii) lack of synchronization, and (iii) system heterogeneity. In specific, we propose a distributed asynchronous algorithm with minimal communication cost, in which users commit variable amounts of local work on their respective sub-problems. We illustrate this both theoretically and experimentally in the machine learning setting, where the agents hold private data and use a stochastic Newton method as the local solver. Under standard assumptions on Lipschitz continuous gradients and strong convexity, our analysis establishes linear convergence in expectation and characterizes the dependency of the rate on the number of local iterations. We proceed a step further to propose a simple means for tuning agents’ hyperparameters locally, so as to adjust to heterogeneity and accelerate the overall convergence. Last, we validate our proposed method on a benchmark machine learning dataset to illustrate the merits in terms of computation, communication, and run-time saving as well as adaptability to heterogeneity.
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11:20-11:40, Paper ThA09.5 | |
>Robust Analysis of Almost Sure Convergence of Zeroth-Order Mirror Descent Algorithm |
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Paul, Anik Kumar | IIT Madras |
Mahindrakar, Arun D. | Indian Institute of Technology Madras |
Kalaimani, Rachel Kalpana | Indian Institute of Technology Madras |
Keywords: Optimization algorithms, Optimization
Abstract: This paper presents an almost sure convergence of the zeroth-order mirror descent algorithm. The algorithm admits non-smooth convex functions and a biased oracle which only provides noisy function value at any desired point. We approximate the subgradient of the objective function using Nesterov's Gaussian Approximation (NGA) with certain alternations suggested by some practical applications. We prove an almost sure convergence of the iterates' function value to the neighbourhood of optimal function value, which can not be made arbitrarily small, a manifestation of a biased oracle. This letter ends with a concentration inequality, which is a finite time analysis that predicts the likelihood that the function value of the iterates is in the neighbourhood of the optimal value at any finite iteration.
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11:40-12:00, Paper ThA09.6 | |
>Conjugate Gradient Methods for Optimization Problems on Symplectic Stiefel Manifold |
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Yamada, Mitsutaka | Kyoto University |
Sato, Hiroyuki | Kyoto University |
Keywords: Optimization algorithms, Optimization
Abstract: The symplectic Stiefel manifold is a Riemannian manifold that is a generalization of the symplectic group. In this study, we propose novel conjugate gradient methods on the symplectic Stiefel manifold and compare them with the steepest descent method proposed in existing studies through numerical experiments. Although the theoretical basis of the Riemannian conjugate gradient methods has already been established, special treatment is required to address specific manifolds since these methods utilize some mappings, such as a retraction and vector transport, on the manifold. Numerical experiments demonstrate that the proposed method outperforms existing methods and is efficient.
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ThA10 |
Roselle Junior 4713 |
Machine Learning IV |
Regular Session |
Chair: Bhatnagar, Shalabh | Indian Institute of Science |
Co-Chair: Coutinho, Daniel | Universidade Federal De Santa Catarina |
|
10:00-10:20, Paper ThA10.1 | |
>An ADMM Solver for the MKL-L_{0/1}-SVM |
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Shi, Yijie | School of Intelligent Systems Engineering, Sun Yat-Sen Universit |
Zhu, Bin | Sun Yat-Sen University |
Keywords: Machine learning, Optimization, Estimation
Abstract: We formulate the Multiple Kernel Learning (abbreviated as MKL) problem for the support vector machine with the infamous (0, 1)-loss function. Some first-order optimality conditions are given and then exploited to develop a fast ADMM solver for the nonconvex and nonsmooth optimization problem. A simple numerical experiment on synthetic planar data shows that our MKL-L_{0/1}-SVM framework could be promising.
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10:20-10:40, Paper ThA10.2 | |
>Combining Robust Control and Machine Learning for Uncertain Nonlinear Systems Subject to Persistent Disturbance |
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Banderchuk, Ana Cláudia | Universidade Federal De Santa Catarina |
Coutinho, Daniel | Universidade Federal De Santa Catarina |
Camponogara, Eduardo | Federal University of Santa Catarina |
Keywords: Machine learning, Robust control, Uncertain systems
Abstract: This paper proposes a control strategy consisting of a robust controller and an Echo State Network (ESN) based control law for stabilizing a class of uncertain nonlinear discrete-time systems subject to persistent disturbances. Firstly, the robust controller is designed to ensure that the closed-loop system is Input-to-State Stable (ISS) with a guaranteed stability region regardless of the ESN control action and exogenous disturbances. Then, the ESN based controller is trained in order to mitigate the effects of disturbances on the system output. A numerical example demonstrates the potentials of the proposed control design method.
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10:40-11:00, Paper ThA10.3 | |
>A Policy Gradient Approach for Finite Horizon Constrained Markov Decision Processes |
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Guin, Soumyajit | Indian Institute of Science, Bengaluru |
Bhatnagar, Shalabh | Indian Institute of Science |
Keywords: Machine learning, Stochastic optimal control, Stochastic systems
Abstract: The infinite horizon setting is widely adopted for problems of reinforcement learning (RL). These invariably result in stationary policies that are optimal. In many situations, finite horizon control problems are of interest and for such problems, the optimal policies are time-varying in general. Another setting that has become popular in recent times is of Constrained Reinforcement Learning, where the agent maximizes its rewards while it also aims to satisfy some given constraint criteria. However, this setting has only been studied in the context of infinite horizon MDPs where stationary policies are optimal. We present an algorithm for constrained RL in the Finite Horizon Setting where the horizon terminates after a fixed (finite) time. We use function approximation in our algorithm which is essential when the state and action spaces are large or continuous and use the policy gradient method to find the optimal policy. The optimal policy that we obtain depends on the stage and so is non-stationary in general. To the best of our knowledge, our paper presents the first policy gradient algorithm for the finite horizon setting with constraints. We show the convergence of our algorithm to an optimal policy. We also compare and analyze the performance of our algorithm through experiments and show that our algorithm performs better than other well known algorithms.
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11:00-11:20, Paper ThA10.4 | |
>A Multi-Fidelity Bayesian Approach to Safe Controller Design |
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Lau, Ethan | Michigan State University |
Srivastava, Vaibhav | Michigan State University |
Bopardikar, Shaunak D. | Michigan State University |
Keywords: Machine learning, Uncertain systems, Stochastic systems
Abstract: Safely controlling unknown dynamical systems is one of the biggest challenges in the field of control. Oftentimes, an approximate model of a system's dynamics exists which provides beneficial information for control design. However, differences between the approximate and true systems present challenges as well as safety concerns. We propose an algorithm called SAFESLOPE to safely evaluate points from a Gaussian process model of a function when its Lipschitz constant is unknown. We establish theoretical guarantees for the performance of SAFESLOPE and quantify how multi-fidelity modeling improves the algorithm's performance. Finally, we present a case where SAFESLOPE achieves lower cumulative regret than a naive sampling method by applying it to find the control gains of a linear time-invariant system.
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11:20-11:40, Paper ThA10.5 | |
>Safe Neural Control for Non-Affine Control Systems with Differentiable Control Barrier Functions |
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Xiao, Wei | Massachusetts Institute of Technology |
Allen, Ross | MITLL |
Rus, Daniela | MIT |
Keywords: Lyapunov methods, Machine learning, Constrained control
Abstract: This paper addresses the problem of safety-critical control for non-affine control systems. It has been shown that optimizing quadratic costs subject to state and control constraints can be sub-optimally reduced to a sequence of quadratic programs (QPs) by using Control Barrier Functions (CBFs). Our recently proposed High Order CBFs (HOCBFs) can accommodate constraints of arbitrary relative degree. The main challenges in this approach are that it requires affine control dynamics and the solution of the CBF-based QP is sub-optimal since it is solved point-wise. To address these challenges, we incorporate higher-order CBFs into neural ordinary differential equation-based learning models as differentiable CBFs to guarantee safety for non-affine control systems. The differentiable CBFs are trainable in terms of their parameters, and thus, they can address the conservativeness of CBFs such that the system state will not stay unnecessarily far away from safe set boundaries. Moreover, the imitation learning model is capable of learning complex and optimal control policies that are usually intractable online. We illustrate the effectiveness of the proposed framework on LiDAR-based autonomous driving and compare it with existing methods.
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11:40-12:00, Paper ThA10.6 | |
>Supervised Learning of Lyapunov Functions Using Laplace Averages of Approximate Koopman Eigenfunctions |
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Deka, Shankar | KTH Royal Institute of Technology, Sweden |
Dimarogonas, Dimos V. | KTH Royal Institute of Technology |
Keywords: Lyapunov methods, Machine learning, Stability of nonlinear systems
Abstract: Modern data-driven techniques have rapidly progressed beyond modelling and systems identification, with a growing interest in learning high-level dynamical properties of a system, such as safe-set invariance, reachability, input-to-state stability etc. In this paper, we propose a novel supervised Deep Learning technique for constructing Lyapunov certificates, by leveraging Koopman Operator theory-based numerical tools (Extended Dynamic Mode Decomposition and Generalized Laplace Analysis) to robustly and efficiently generate explicit ground truth data for training. This is in stark contrast to existing Deep Learning methods where the loss functions plainly penalize Lyapunov condition violation in the absence of labelled data for direct regression. Furthermore, our approach leads to a linear parameterization of Lyapunov candidate functions in terms of stable eigenfunctions of the Koopman operator, making them more interpretable compared to standard DNN-based architecture. We demonstrate and validate our approach numerically using 2-dimensional and 10-dimensional examples.
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ThA11 |
Roselle Junior 4712 |
Agent-Based Systems IV |
Regular Session |
Chair: Wang, Lin | Shanghai Jiao Tong University |
Co-Chair: Hespe, Christian | Hamburg University of Technology |
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10:00-10:20, Paper ThA11.1 | |
>Co-Evolution of Dual Opinions under Asynchronous Updating |
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Zhang, Qi | Shanghai Jiao Tong University |
Wang, Lin | Shanghai Jiao Tong University |
Wang, Xiaofan | Department of Automation, Shanghai Jiaotong University |
Chen, Guanrong | City University of Hong Kong |
Keywords: Agents-based systems, Network analysis and control, Decentralized control
Abstract: Inspired by the dual attitudes theory that implicit opinions are individuals' inner evaluations affected by experience while explicit opinions are external expressions of these evaluations, we propose an asynchronous co-evolution model of dual opinions, where individuals update explicit opinion at each time step but change their implicit opinion based on their own clock. Furthermore, we introduce the after-effect of observed opinion information in this model, which enables individuals to update implicit opinions not only based on the opinion information observed at the current time but also on the information received from the past period of time. We analyze the dynamics of dual opinions in two discussion scenarios: a group of individuals with similar and opposite initial opinions. In the former scenario, rigorous analysis suggests that dual opinions are polarized to extreme opinions, mathematically verifying the empirical finding that group discussion intensifies individuals' preferences, resulting in group polarization. In the latter scenario, our investigation shows that individuals with low bias show acceptance (inward conformity) while those with high bias exhibit compliance (outward conformity). We further analyze the influence of parameters on the co-evolution of dual opinions.
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10:20-10:40, Paper ThA11.2 | |
>On an Extension of the Friedkin-Johnsen Model: The Effects of a Homophily-Based Influence Matrix |
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Disarò, Giorgia | University of Padova |
Valcher, Maria Elena | Universita' Di Padova |
Keywords: Agents-based systems, Network analysis and control, Modeling
Abstract: In this paper we propose an extended version of the Friedkin-Johnsen (FJ) model that accounts for the effects of homophily mechanisms on the agents’ mutual appraisals. The proposed model consists of two difference equations. The first one describes the opinions’ evolution, namely how agents modify their opinions taking into account both their personal beliefs and the influences of other agents, as in the standard FJ model. Meanwhile, the second equation models how the influence matrix involved in the opinion formation process updates according to a homophily mechanism, by allowing both positive and negative appraisals. We derive necessary and sufficient conditions for the proposed time-varying version of the classical FJ model to asymptotically converge to a constant solution. In the case of a single discussion topic, asymptotic convergence is always ensured and the limit behavior of the system is derived in closed form.
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10:40-11:00, Paper ThA11.3 | |
>A Robustness Analysis to Structured Channel Tampering Over Secure-By-Design Consensus Networks |
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Fabris, Marco | University of Padua |
Zelazo, Daniel | Technion - Israel Institute of Technology |
Keywords: Agents-based systems, Network analysis and control
Abstract: This work addresses multi-agent consensus networks where adverse attackers affect the convergence performances of the protocol by manipulating the edge weights. We generalize [1] and provide guarantees on the agents’ agreement in the presence of attacks on multiple links in the network. A stability analysis is conducted to show the robustness to channel tampering in the scenario where part of the codeword, corresponding to the value of the edge weights, is corrupted. Exploiting the built-in objective coding, we show how to compensate the conservatism that may emerge because of multiple threats in exchange for higher encryption capabilities. Numerical examples related to semi-autonomous networks are provided.
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11:00-11:20, Paper ThA11.4 | |
>A Scalable Approach for Analysing Multi-Agent Systems with Heterogeneous Stochastic Packet Loss |
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Hespe, Christian | Hamburg University of Technology |
Werner, Herbert | Hamburg University of Technology |
Keywords: Agents-based systems, Networked control systems, Robust control
Abstract: An important aspect in jointly analysing networked control systems and their communication is to model the networking in a sufficiently rich but at the same time mathematically tractable way. As such, this paper improves on a recently proposed scalable approach for analysing multi-agent systems with stochastic packet loss by allowing for heterogeneous transmission probabilities and temporal correlation in the communication model. The key idea is to consider the transmission probabilities as uncertain, which facilitates the use of tools from robust control. Due to being formulated in terms of linear matrix inequalities that grow linearly with the number of agents, the result is applicable to very large multi-agent systems, which is demonstrated by numerical simulations with up to 10000 agents.
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11:20-11:40, Paper ThA11.5 | |
>Scalable Robust Multi-Agent Reinforcement Learning for Model Uncertainty |
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Jwa, Younkyung | Gwangju Institute of Science and Technology |
Gwak, Minseon | POSTECH |
Kwak, Jiin | Ulsan National Institute of Science and Technology |
Ahn, Chang Wook | Gwangju Institute of Science and Technology |
Park, PooGyeon | POSTECH (Pohang Univ. of Sci. & Tech.) |
Keywords: Agents-based systems, Machine learning, Cooperative control
Abstract: A robust multi-agent reinforcement learning (MARL) algorithm using a nature actor has been shown to be effective in finding a robust Nash equilibrium (NE) of a Markov game with model uncertainty. However, since a game-size scaling increases the search space and challenges reaching the NE, the robust property of the algorithm is reduced in environments with many agents. This paper proposes an evolutionary diversity-maintaining population curriculum (EDPC) framework with a robust attention-based multi-agent deep deterministic policy gradient (RA-MADDPG) algorithm, which enables an efficient robust NE search by a structured search space expansion. In the EDPC framework, the MARL divides into several stages, and when moving on to the next stage, a population consisting of larger games is made with two parent games from the previous stage. We introduce reward-proportionate parent selection and reward-guided mutation methods to continue reinforcing superior agents and maintain the diversity of the population. Furthermore, the RA-MADDPG is used to solve the robust Markov game at each stage with nature actors with attention-based architectures. The scalability and robustness of the proposed method are evaluated for different numbers of agents and levels of model uncertainty.
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11:40-12:00, Paper ThA11.6 | |
>Lexicographic Min-Max Fairness in Task Assignments |
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Ding, Geoffrey | Massachusetts Institute of Technology |
Balakrishnan, Hamsa | Massachusetts Institute of Technology |
Keywords: Agents-based systems, Optimization, Cooperative control
Abstract: Assignment problems and their variants are ubiquitous across resource allocation applications. While they traditionally focus on minimizing costs or maximizing utility, fairness is also an important consideration, especially for task assignment in multi-agent systems. We propose algorithms for assigning tasks to agents that consider lexicographic min-max fairness, a stronger notion of fairness than min-max fairness, which minimizes the maximum cost to any single agent. We apply our proposed approaches to both one-to-one and one-to-many assignment problems. Due to the computational challenges of one-to-many task assignments, we develop tractable approaches to achieve approximate fairness. Finally, we use the proposed methods to evaluate the trade-offs between efficiency and fairness through numerical experiments
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ThA12 |
Roselle Junior 4711 |
Cooperative Control IV |
Regular Session |
Chair: Hayashi, Naoki | Osaka University |
Co-Chair: Zhang, Hongwei | Harbin Institute of Technology, Shenzhen |
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10:00-10:20, Paper ThA12.1 | |
>Constrained Coverage of Unknown Environment Using Safe Reinforcement Learning |
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Zhang, Yunlin | University of Electronic Science and Technology of China |
You, JunJie | University of Electronic Science and Technology of China |
Shi, Lei | Henan University |
Shao, Jinliang | University of Electronic Science and Technology of China, Chengd |
Zheng, Wei Xing | Western Sydney University |
Keywords: Cooperative control, Learning, Agents-based systems
Abstract: Achieving a connected, collision-free and time-efficient coverage in unknown environments is challenging for multi-agent systems. Particularly, agents with second-order dynamics are supposed to efficiently search and reach the optimal deployment positions over targets whose distribution is unknown, while preserving the distributed connectivity and avoiding collision. In this paper, a safe reinforcement learning based shield method is proposed for unknown environment exploration while correcting actions of agents for safety guarantee and avoiding invalid samples into policy updating. The shield is achieved distributively by a control barrier function and its validity is proved in theory. Moreover, policies of the optimal coverage are centrally learned via reward engineering and executed distributively. Numerical results show that the proposed approach not only achieves zero safety violations during training, but also speeds up the convergence of learning.
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10:20-10:40, Paper ThA12.2 | |
>Minimally Disruptive Cooperative Lane-Change Maneuvers |
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Chalaki, Behdad | Honda Research Institute |
Tadiparthi, Vaishnav | Honda Research Institute |
Nourkhiz Mahjoub, Hossein | Honda Research Institute USA Inc |
D'sa, Jovin | Honda Research Institute USA Inc |
Moradi Pari, Ehsan | Honda Research Institute USA, Inc |
Chavez Armijos, Andres | Boston University |
Li, Anni | Boston University |
Cassandras, Christos G. | Boston University |
Keywords: Cooperative control, Optimization, Autonomous vehicles
Abstract: A lane-change maneuver on a congested highway could be severely disruptive or even infeasible without the cooperation of neighboring cars. However, cooperation with other vehicles does not guarantee that the performed maneuver will not have a negative impact on traffic flow unless it is explicitly considered in the cooperative controller design. In this letter, we present a socially compliant framework for cooperative lane-change maneuvers for an arbitrary number of CAVs on highways that aims to interrupt traffic flow as minimally as possible. Moreover, we explicitly impose feasibility constraints in the optimization formulation by using reachability set theory, leading to a unified design that removes the need for an iterative procedure used in prior work. We quantitatively evaluate the effectiveness of our framework and compare it against previously offered approaches in terms of maneuver time and incurred throughput disruption.
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10:40-11:00, Paper ThA12.3 | |
>Cooperative Learning for Adversarial Multi-Armed Bandit on Open Multi-Agent Systems |
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Nakamura, Tomoki | Osaka University |
Hayashi, Naoki | Osaka University |
Inuiguchi, Masahiro | Osaka University |
Keywords: Cooperative control, Optimization, Networked control systems
Abstract: This paper considers a cooperative decision-making method for an adversarial bandit problem on open multi-agent systems. In an open multi-agent system, the network configuration changes dynamically as agents freely enter and leave the network. We propose a distributed Exp3 policy in which a group of agents exchanges the estimation of the expected reward of each arm with active neighboring agents. Then, each agent updates the probability distribution of choosing arms by combining the estimated rewards of neighboring agents. We derive a sufficient condition for a sublinear bound of a pseudo regret. The numerical example shows that active agents can cooperatively find the optimal arm by the proposed Exp3 policy algorithm.
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11:00-11:20, Paper ThA12.4 | |
>Energy Efficient Optimization-Based Coordination of Electric Automated Vehicles in Confined Areas |
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Kojchev, Stefan | Chalmers University of Technology |
Hult, Robert | Chalmers University of Technology |
Fredriksson, Jonas | Chalmers University of Technology |
Keywords: Cooperative control, Optimization algorithms, Autonomous vehicles
Abstract: In this paper, we present an optimization-based control strategy for coordinating multiple electric automated vehicles (AVs) in confined sites. The approach focuses on obtaining and keeping energy-efficient driving profiles for the AVs while avoiding collisions in cross-intersections, narrow roads, and merge crossings. Specifically, the approach is composed of two optimization-based components. The first component obtains the energy-efficient profiles for each individual AV by solving a Nonlinear Program (NLP) for the vehicle's complete mission route. The conflict resolution, which is performed by the second component, is accomplished by solving a time-scheduling Mixed Integer Linear Programming (MILP) problem that exploits the application characteristics. We demonstrate the performance of the algorithm through a non-trivial comparative simulation example with an alternative optimization-based heuristic.
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11:20-11:40, Paper ThA12.5 | |
>Distributed Event-Triggered Dual Decomposition Method for Cooperative One-Way Car-Sharing Control |
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Ogawa, Gakuto | Osaka University |
Hayashi, Naoki | Osaka University |
Sakurama, Kazunori | Kyoto University |
Inuiguchi, Masahiro | Osaka University |
Keywords: Cooperative control, Optimization algorithms, Networked control systems
Abstract: In this paper, we present cooperative rebalancing control of a one-way car-sharing service, where several service providers operate vehicles independently while sharing the common rental stations. The objective of service providers is to reduce the number of deadhead vehicles considering limited parking slots at stations. To this end, we propose a rebalancing control method by a distributed dual decomposition algorithm. Each provider transmits the estimation of the dual optimizers to the neighboring providers in an event-triggered manner. A numerical example shows that all service providers can find an optimal rebalancing solution while effectively reducing the number of communications.
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11:40-12:00, Paper ThA12.6 | |
>Power Sharing and Voltage Deviation Restriction for Multi-Bus DC Microgrids |
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Bai, Handong | Yellow River Conservancy Technical Institute |
Liu, Zhancheng | Southwest Jiaotong University |
Zhang, Hongwei | Harbin Institute of Technology, Shenzhen |
Keywords: Cooperative control, Smart grid, Distributed control
Abstract: Power sharing and voltage regulation are fundamental but conflict control objectives of DC microgrids. This paper presents a distributed control strategy to achieve adjustment of the control objectives from accurate power sharing to accurate voltage regulation. At the same time, the bus voltage of critical node is regulated to reach the rated value of the DC microgrid. Based on this control strategy, steady state characteristics of the closed-loop system are analyzed. For a given DC microgrid, the proposed control method is verified experimentally.
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ThA13 |
Roselle Junior 4613 |
Networked Control Systems I |
Regular Session |
Chair: Lunze, Jan | Ruhr-Universität Bochum |
Co-Chair: Stursberg, Olaf | University of Kassel |
|
10:00-10:20, Paper ThA13.1 | |
>Phase Locking of Linear Oscillators with Individual Parameters |
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Lunze, Jan | Ruhr-Universität Bochum |
Keywords: Networked control systems, Agents-based systems, Cooperative control
Abstract: A recent paper has shown that linear oscillators can be synchronised only if their parameters are exactly the same. The main reason for this sensitivity lies in the fact that the oscillator network loses energy whenever the oscillators do not follow precisely the same output trajectory. This paper deals with the question how to extend oscillators to make them synchronisable in a practical sense. The oscillators are equipped with an energy source that replaces the energy lost during the synchronisation. It is shown that a power supply rate exists such that oscillators with different eigenfrequencies can phase lock, which means that they follow the same sinusoidal trajectory with some phase gap. For two coupled oscillators explicit relations for the frequency and the phase shift of the synchronous behaviour are derived.
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10:20-10:40, Paper ThA13.2 | |
>Uncorrelated Packet Loss Model for Networked Control Systems with H∞ Design Constraint |
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Villamil, Andres | TU Dresden |
González, Arturo | Vodafone Tech Innovation Center Dresden |
Fettweis, Gerhard | Technische Universität Dresden |
Keywords: Networked control systems, Communication networks, Optimization
Abstract: Networked Controlled Systems (NCS) are control systems that rely on the performance of the communications to ensure a desired Quality-of-Control (QoC). However, the wireless link is imperfect; the packet has an intrinsic latency, and packets can be lost due to its stochastic nature. Although the newest generation of wireless networks (5G and beyond) can provide Ultra-Reliable Low Latency Communications (URLLC) to attempt to remove the problems caused by the wireless network. This methodology is expensive regarding communications resources, and for NCS, the constant stream of data could be spared since some updates might contain similar information. Although there are multiple methodologies to design a NCS, not many methods attempt to develop the communications system based on reducing the consumption of communications resources. Therefore, this work finds the maximum transmission interval and delay to optimize the maximum peak Age-of-Information (AoI) while getting a model of the Maximum Allowable Packet Loss Probability (MAPLP) for the case that the H∞ norm of the control system must be maintained lower than a specified threshold. Finally, the model is validated in the case of platooning using Cooperative Adaptive Cruise Control(CACC), showing a high accuracy compared to the results of the solution of the optimization problem.
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10:40-11:00, Paper ThA13.3 | |
>Communication Demand Minimization for Perturbed Networked Control Systems with Coupled Constraints |
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Bahraini, Masoud | Chalmers University of Technology |
Zanon, Mario | IMT Institute for Advanced Studies Lucca |
Colombo, Alessandro | Politecnico Di Milano |
Falcone, Paolo | Chalmers University of Technology |
Keywords: Networked control systems, Constrained control, Optimization algorithms
Abstract: Communication scheduling is needed when control loops of several safety-critical systems are closed through a shared communication medium. To enable schedulability, control for each system is designed primarily to minimize its communication demand. In this paper, we study communication demand minimization for a class of perturbed multi-agent networked control systems with a shared communication medium and subject to input and coupled state constraints. First, a framework to design communication schedule and control is recalled such that state and input constraints are satisfied under no coupling assumption. Then, a heuristic method is proposed to decouple state constraints such that the overall communication demand of the systems is minimized. Effectiveness of the proposed results are illustrated through a numerical example.
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11:00-11:20, Paper ThA13.4 | |
>Resilience of Time-Varying Communication Graphs for Consensus of Changing Sets of Computing Agents |
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Schmidtke, Vincent | Universität Kassel |
Liu, Zonglin | University of Kassel |
Stursberg, Olaf | University of Kassel |
Keywords: Networked control systems, Control of networks, Resilient Control Systems
Abstract: System performance of distributed control systems and networked computing systems is strongly dependent of the underlying communication topology. This paper considers the rarely studied problem of how the topology can maintain resilience by reconfiguration in case that agents leave or join the network during online operation. Existing optimization-based approaches which reconfigure the entire network can typically not be used in this case, since the computational burden for online application is too high. Thus, this paper proposes a novel combined offline-online scheme which optimizes the topology for high convergence rate (of e.g. consensus problems) while providing guarantees for the robustness against agent failures. In the offline part, an optimization of the entire topology is carried out using novel constraints to prepare resilience of the online procedure. For the latter, the proposed scheme guarantees that robustness is maintained for joining agents and if a specified number of agents leave the network. In simulation, the proposed scheme is compared to existing approaches and the advantages of the online-offline procedure are demonstrated.
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11:20-11:40, Paper ThA13.5 | |
>Large Population Games on Constrained Unreliable Networks |
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Aggarwal, Shubham | University of Illinois, Urbana Champaign |
Zaman, Muhammad Aneeq uz | UIUC |
Bastopcu, Melih | University of Illinois Urbana Champaign |
Basar, Tamer | Univ of Illinois, Urbana-Champaign |
Keywords: Networked control systems, Control over communications, Constrained control
Abstract: This paper studies an N–agent cost-coupled game where the agents are connected via an unreliable capacity constrained network. Each agent receives state information over that network which loses packets with probability p. A Base station (BS) actively schedules agent communications over the network by minimizing a weighted Age of Information (WAoI) based cost function under a capacity limit C < N on the number of transmission attempts at each instant. Under a standard information structure, we show that the problem can be decoupled into a scheduling problem for the BS and a game problem for the N agents. Since the scheduling problem is an NP hard combinatorics problem, we propose an approximately optimal solution which approaches the optimal solution as N tends to infinity. In the process, we also provide some insights on the case without channel erasure. Next, to solve the large population game problem, we use the mean-field game framework to compute an approximate decentralized Nash equilibrium. Finally, we validate the theoretical results using a numerical example.
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11:40-12:00, Paper ThA13.6 | |
>Localized Privacy Preservation by Innovation Perturbation in a Cooperative LQG Control System |
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Sheng, Wenliang | East China University of Science and Technology |
Zhao, Zhiyun | East China University of Science and Technology |
Yang, Wen | East China University of Science and Technology |
Yang, Chao | East China University of Science and Technology |
Keywords: Networked control systems, Control Systems Privacy
Abstract: We consider a cooperative Linear Quadratic Gaussian (LQG) control system, in which an individual user owns a local plant whose control inputs are provided by a server. In the cooperation, the user takes the plant states as private information and desires to maximize the privacy preservation while ensuring that the server still provides a certain level of control performance. Moreover, the user requires a privacy scheme that is used locally and is unknown to the server, so that it can create a deviation in the server’s knowledge of the states from the true value. To achieve this, we propose two privacy schemes localized at the user side, which inject perturbations in the innovation data sent to the server. For both schemes, firstly, we analyze the privacy preservation quality provided by the scheme and the performance loss in the LQG control caused by it. Secondly, based on the trade-off between them, we propose an optimization problem. Thirdly, we propose a recovery procedure by which the control performance is recovered to the optimal one, i.e., the privacy preservation is achieved without any performance loss in control. Finally, simulations are provided, and we give discussions on the two schemes based on the simulation results.
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ThA14 |
Roselle Junior 4612 |
Identification III |
Regular Session |
Chair: Smith, Roy S. | ETH Zurich |
Co-Chair: Oomen, Tom | Eindhoven University of Technology |
|
10:00-10:20, Paper ThA14.1 | |
>Beyond Nyquist in Frequency Response Function Identification: Applied to Slow-Sampled Systems |
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van Haren, Max | Eindhoven University of Technology |
Mirkin, Leonid | Technion - IIT |
Blanken, Lennart | Eindhoven University of Technology |
Oomen, Tom | Eindhoven University of Technology |
Keywords: Identification, Sampled-data control
Abstract: Fast-sampled models are essential for control design, e.g., to address intersample behavior. The aim of this paper is to develop a non-parametric identification technique for fast-sampled models of systems that have relevant dynamics and actuation above the Nyquist frequency of the sensor, such as vision-in-the-loop systems. The developed method assumes smoothness of the frequency response function, which allows to disentangle aliased components through local models over multiple frequency bands. The method identifies fast-sampled models of slowly-sampled systems accurately in a single identification experiment. Finally, an experimental example demonstrates the effectiveness of the technique.
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10:20-10:40, Paper ThA14.2 | |
>Error Bounds for Kernel-Based Linear System Identification with Unknown Hyperparameters |
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Yin, Mingzhou | ETH Zurich |
Smith, Roy S. | ETH Zurich |
Keywords: Identification, Statistical learning, Machine learning
Abstract: Applying regularization in reproducing kernel Hilbert spaces has been successful in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the posterior covariance, which are useful in robust and stochastic control. However, the error bounds require knowledge of the true hyperparameters in the kernel design. They can be inaccurate with estimated hyperparameters for lightly damped systems or in the presence of high noise. In this work, we provide reliable quantification of the estimation error when the hyperparameters are unknown. The bounds are obtained by first constructing a high-probability set for the true hyperparameters from the marginal likelihood function. Then the worst-case posterior covariance is found within the set. The proposed bound is proven to contain the true model with a high probability and its validity is demonstrated in numerical simulation.
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10:40-11:00, Paper ThA14.3 | |
>On Concentration Bounds for Bayesian Identification of Linear Non-Gaussian Systems |
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Kim, Yeoneung | SeoulTech |
Kim, Gihun | Seoul National University |
Yang, Insoon | Seoul National University |
Keywords: Identification, Stochastic systems
Abstract: We adopt a Bayesian perspective to identify the unknown parameters of linear stochastic systems with possibly non-Gaussian disturbance distributions. The key idea of our algorithm is to alternately execute L randomly selected linear state-feedback controllers and keep track of a maximum a posteriori estimator. The proposed algorithm asymptotically achieves the concentration of posterior distributions around the true system parameters. We also derive probabilistic bounds for the concentration based on the classical results regarding the asymptotic properties of posterior distributions. An empirical demonstration is provided as well.
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11:00-11:20, Paper ThA14.4 | |
>SINDy-CRN: Sparse Identification of Chemical Reaction Networks from Data |
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Bhatt, Nirav | Indian Institute of Technology Madras |
Jayawardhana, Bayu | University of Groningen |
Sanchez-Escalonilla, Santiago | University of Groningen |
Keywords: Identification, Systems biology, Nonlinear systems identification
Abstract: This work considers an important problem of identifying the dynamics of chemical reaction networks from time-series data. We propose an approach to identify complex chemical reaction networks (CRN) from concentration data using the concept of sparse model identification. Particularly, we demonstrate challenges associated with the application of the sparse identification of nonlinear dynamics (SINDy) and its variants to data obtained from CRNs. We develop a SINDy-CRN algorithm based on the properties of CRNs for identifying governing equations of a CRN. The proposed algorithm is illustrated using a numerical simulation example.
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11:20-11:40, Paper ThA14.5 | |
>Fast Algorithms for Identification of Time-Varying Systems with Both Smooth and Discontinuous Parameter Changes |
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Niedzwiecki, Maciej | Gdansk University of Technology |
Gancza, Artur | Gdansk University of Technology |
Keywords: Identification, Time-varying systems, Stochastic systems
Abstract: The problem of noncausal identification of a time-varying linear system subject to both smooth and occasional jump-type changes is considered and solved using the preestimation technique combined with the basis function approach to modeling the variability of system parameters. The proposed estimation algorithms yield very good parameter tracking results and are computationally attractive.
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11:40-12:00, Paper ThA14.6 | |
>Identifying Single-Input Linear System Dynamics from Reachable Sets |
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Shafa, Taha | University of Illinois Urbana-Champaign |
Dong, Roy | University of Illinois at Urbana-Champaign |
Ornik, Melkior | University of Illinois Urbana-Champaign |
Keywords: Identification, Uncertain systems, Modeling
Abstract: This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the reachable sets are known from partially transparent manufacturer specifications or observations of the collective behavior of adversarial agents, we aim to utilize such sets to determine the unknown system's dynamics. This paper has two contributions. Firstly, we show that the sequence of the system's reachable sets can be used to uniquely determine the system's dynamics for asymmetric input sets under some generic assumptions, regardless of the system's dimensions. We also prove the same property holds up to a sign change for two-dimensional systems where the input set is symmetric around zero. Secondly, we present an algorithm to determine these dynamics. We apply and verify the developed theory and algorithms on an unknown band-pass filter circuit solely provided the unknown system's reachable sets over a finite observation period.
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ThA15 |
Roselle Junior 4611 |
Robust Adaptive Control |
Regular Session |
Chair: Ge, Shuzhi Sam | National University of Singapore |
Co-Chair: Miller, Daniel E. | University of Waterloo |
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10:00-10:20, Paper ThA15.1 | |
>Robust Adaptive Step-Tracking with Exponential Stability and Convolution Bounds Using Supervisory Control |
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Lalumiere, Craig | University of Waterloo |
Miller, Daniel E. | University of Waterloo |
Keywords: Robust adaptive control, Adaptive control, Switched systems
Abstract: Supervisory Control has been shown to be a very effective approach to adaptive control which ensures step-tracking, exponential stability, and a degree of robustness to unmodelled dynamics. Here we apply the technique in the discrete-time setting and prove a new linear-like convolution bound on the effect of the noise/disturbance. This property is then leveraged to prove robustness to slow time-variations.
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10:20-10:40, Paper ThA15.2 | |
>Adaptive Robust Control Contraction Metrics: Transient Bounds in Adaptive Control with Unmatched Uncertainties |
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Gessow, Samuel | University of California, Los Angeles |
Lopez, Brett | University of California - Los Angeles |
Keywords: Robust adaptive control, Indirect adaptive control, Adaptive control
Abstract: This work presents a new sufficient condition for synthesizing nonlinear controllers that yield bounded closed-loop tracking error transients despite the presence of unmatched uncertainties that are concurrently being learned online. The approach utilizes contraction theory and addresses fundamental limitations of existing approaches by allowing the contraction metric to depend on the unknown model parameters. This allows the controller to incorporate new model estimates generated online without sacrificing its strong convergence and bounded transients guarantees. The approach is specifically designed for trajectory tracking so the approach is more broadly applicable to adaptive model predictive control as well. Simulation results on a nonlinear system with unmatched uncertainties demonstrates the approach.
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10:40-11:00, Paper ThA15.3 | |
>Adaptive Output Regulation and the Use It or Lose It Principle |
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Mejia Uzeda, Erick | University of Toronto |
Broucke, Mireille E. | Univ. of Toronto |
Keywords: Robust adaptive control, Output regulation, Adaptive control
Abstract: It is well-known in adaptive control that when regressors are not persistently exciting (PE), then parameter adaptation is not robust. A number of adhoc modifications of parameter adaptation laws were developed to overcome this problem. In this paper we examine the PE subspace, a geometric characterization of a regressor’s excitation, which allows a more intrinsic modification of parameter adaptation laws. Our modular method, the mu-modification, is premised on the Use it or Lose it Principle of neuroplasticity, stating that parameters not excited by a regressor may be forgotten. This paper develops these ideas in the context of adaptive output regulation, with attention to the geometric properties of the PE subspace under linear filtering, such as when using augmented errors.
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11:00-11:20, Paper ThA15.4 | |
>Unmatched Uncertainty Mitigation through Neural Network Supported Model Predictive Control |
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Valverde Gasparino, Mateus | University of Illinois at Urbana Champaign |
Mishra, Prabhat Kumar | Massachusetts Institute of Technology |
Chowdhary, Girish | University of Illinois at Urbana Champaign |
Keywords: Robust adaptive control, Predictive control for linear systems, Neural networks
Abstract: This paper presents a deep learning based model predictive control (MPC) algorithm for systems with unmatched and bounded state-action dependent uncertainties of unknown structure. We utilize a deep neural network (DNN) as an oracle in the underlying optimization problem of learning based MPC (LBMPC) to estimate unmatched uncertainties. Generally, DNNs as oracle are considered difficult to employ with LBMPC due to the technical difficulties associated with the estimation of their coefficients in real time. We employ a dual-timescale adaptation mechanism, where the weights of the last layer of the neural network are updated in real time while the inner layers are trained on a slower timescale using the training data collected online and selectively stored in a buffer. Our results are validated through a numerical experiment on the compression system model of a jet engine. These results indicate that the proposed approach is implementable in real time and carries the theoretical guarantees of LBMPC.
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11:20-11:40, Paper ThA15.5 | |
>Adaptive Prescribed-Time Tracking Control for Fixed-Wing UAV with the Input Saturation and State Constraints (I) |
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Zheng, Jiayi | National University of Defense Technology |
Zhao, Shulong | National University of Defense Technology |
Wang, Qipeng | National University of Defense Technology |
Wang, Xiangke | National University of Defense Technology |
Zhou, Han | National University of Defense Technology |
Keywords: Adaptive control, Neural networks, Flight control
Abstract: In this paper, we propose an adaptive prescribed-time control algorithm for the fixed-wing unmanned aerial vehicle (UAV). How to follow the desired trajectory within a predetermined time is a problem worth investigating in fixed-wing UAV tracking missions. To this end, a novel method based on time-varying state feedback and segmented neural network (SNN) is proposed, using practice prescribed-time input-to-state stable to guarantee the convergence of all signals in the prescribed time. Considering the input saturation and state constraints, we give the basis for selecting the prescribed time with different initial conditions, rather than an arbitrary one. Finally, the simulation shows that the proposed method can realize prescribed-time tracking control with input saturation, despite large initial states, and the magnitude of the control changes moderately.
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11:40-12:00, Paper ThA15.6 | |
>Synchronized Optimization with Prescribed Performance for High-Order Strict-Feedback System (I) |
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Zhang, Yuxiang | National University of Singapore |
Liang, Xiaoling | National University of Singapore |
Li, Dongyu | BEIHANG UNIVERSITY |
Ge, Shuzhi Sam | National University of Singapore |
Lee, Tong Heng | National University of Singapore |
Keywords: Adaptive control, Automotive control, Learning
Abstract: This paper investigates synchronized optimization with prescribed performance for the strict-feedback system with time-synchronized convergence property, which is the highly essential performance desired in various real-world high-precision control applications. The prescribed performance is considered to keep the state-variables within a predefined region during the control period to meet the required system performance. To consider optimization performance while also concurrently attaining the time-synchronized properties simultaneously of each backstepping subsystem, optimized backstepping is utilized to establish the learning framework; wherein the norm-normalized sign function is appropriately incorporated in each backstepping subsystem, which generates the decomposition of the optimal system control and gradient term of the cost function with appropriate time-synchronized control items and unknown independently learning parts to be approximated with neural networks. With this decomposition design, the learning objective is transformed to adaptively explore the optimal control parameter in the admissible policy region. By additionally employing the adaptive dynamic programming technique, actor-critic method, and gradient-constrained method, the solution of the Hamilton-Jacobi-Bellman equation is iteratively approximated while the learnable parameter stays within the predefined region. The work here has the outcome of time-synchronized convergence which surpasses the usual typical developments in this class of problems considered. The proposed method is verified with the vehicle platoon problem to show its effectiveness in that the system preserves special properties of time-synchronized stability and control while optimizing the overall system control.
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ThA16 |
Peony Junior 4512 |
Power Systems I |
Regular Session |
Chair: Bosso, Alessandro | University of Bologna |
Co-Chair: Shi, Xiasheng | AnHui University |
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10:00-10:20, Paper ThA16.1 | |
>Nonlinear Stability Analysis of Distributed Self-Interleaving for Driving Signals in Multicellular Converters |
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Bosso, Alessandro | University of Bologna |
Mannes Hillesheim, Miguel | NXP Semiconductors |
Cousineau, Marc | LAPLACE, Université De Toulouse, CNRS, INPT, UPS, 31071, Toulous |
Zaccarian, Luca | LAAS-CNRS |
Keywords: Power electronics, Stability of hybrid systems, Distributed control
Abstract: We analyze a self-interleaving circuitry for driving signals in multicellular converters based on an interconnection graph with a ring topology that induces desirable fault-tolerant features. Using nonlinear hybrid dynamical tools, we show that the dynamics of this electronic solution can be formulated as a system with a sampled-data feedback law emulating a first-order Kuramoto-like model. For this Kuramoto model, under general conditions on the coupling functions, we provide a Lyapunov-based proof of local asymptotic stability of the splay-state (interleaved) configuration. We then illustrate the relation with the emulation-based sampled-data scenario via simulation results.
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10:20-10:40, Paper ThA16.2 | |
>Observer-Based Switched Control of the Three Level Neutral Point Clamped Rectifier |
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Doré, Manon | LAAS-CNRS |
Ariba, Yassine | INSA |
Garcia, Germain | LAAS-CNRS |
Keywords: Power electronics, Switched systems, Observers for nonlinear systems
Abstract: In this paper, an observer-based switched control law is proposed for the three level neutral point clamped (NPC) converter operating as a rectifier. Modeling the converter as a switched affine system, the proposed control is based on the well known argmin control law to track a varying state reference trajectory. A full-order observer is introduced to compute the control law with only the measure of the input and the output voltages. The control aims at tracking a state reference defined from a power analysis and three objectives are addressed: to stabilize the output at a given DC voltage, to ensure a unit power factor by having the input current and voltage on phase and to have balanced capacitor voltages on the output. Based on a unified modeling methodology, the control and the observer are easily derived from LMI conditions. An outer loop is added to regulate the output when constant perturbations are considered. The results are illustrated by simulations on MATLAB/Simulink.
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10:40-11:00, Paper ThA16.3 | |
>Model Predictive Control of Wind Turbines with Piecewise-Affine Power Coefficient Approximation |
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Sterle, Arnold | Technische Universität Berlin |
Grapentin, Aaron | Technical University Berlin |
Hans, Christian Andreas | TU Berlin |
Raisch, Joerg | Technical University Berlin |
Keywords: Power generation, Predictive control for nonlinear systems, Optimal control
Abstract: In this paper, an offset-free bilinear model predictive control approach for wind turbines is presented. State-of-the-art controllers employ different control loops for pitch angle and generator torque which switch depending on wind conditions. In contrast, the presented controller is based on one unified control law that works for all wind conditions. The inherent nonlinearity of wind turbines is addressed through a piecewise-affine approximation, which is modelled in a mixed-integer fashion. The presented controller is compared to a state-of-the-art baseline controller in a numerical case study using OpenFAST. Simulation results show that the presented controller ensures accurate reference power tracking. Additionally, damage equivalent loads are reduced for higher wind speeds.
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11:00-11:20, Paper ThA16.4 | |
>Initialization-Free Distributed Constrained Optimization Algorithms with a Pre-Specified Time |
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Shi, Xiasheng | AnHui University |
Mu, Chaoxu | Tianjin University |
Sun, Changyin | School of Automation, Southeast University |
Ren, Lu | Anhui University |
Su, Yanxu | Anhui University |
Keywords: Power generation
Abstract: The distributed constrained optimization problem over an undirected communication topology is investigated in this study. It focuses on addressing a global coupled equality constraint that applies to all agents. To tackle this problem, a distributed approach with arbitrary initialization is developed by virtue of the aperiodic sampling control idea and the consensus-based multi-agent system(MAS) technology. This approach is developed to address constrained optimization problems within a pre-specified time. In addition, this predefined time is freely defined by users and irrelevant to the initial states, control coefficients, and network structure of systems. The Lyapunov stability theory completes the convergence proof of the developed method. Then, the developed method is extended to handle distributed nonlinear constrained optimization problems. Finally, The availability of two developed methods is demonstrated through two simulation examples.
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11:20-11:40, Paper ThA16.5 | |
>Investigation of Sub-Synchronous Oscillation in HVDC-Connected PMSG-Based Offshore Wind Farm: Comprehensive Modeling and Analysis |
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Zhang, Zhihao | Xi'an Jiaotong University |
Kou, Peng | Xi’an Jiaotong University |
Mei, Mingyang | Xi'an Jiaotong Univercity |
Tian, Runze | Xi'an Jiaotong University |
Zhang, Yuanhang | Xi'an Jiaotong University |
Liang, Deliang | Xi'an Jiaotong University |
Keywords: Power systems, Electrical machine control, Power generation
Abstract: This paper investigates the sub-synchronous oscillation occurring in high voltage direct current (HVDC)-connected permanent magnet synchronous generator (PMSG)-based offshore wind farm. To do so, firstly, a comprehensive system model is developed, which incorporates the dynamics of the PMSG-based wind energy conversion system (WECS), the ac collection grid, and the HVDC transmission system. Subsequently, small signal model of the comprehensive system is derived. Based on the small signal model, the critical system mode is obtained using modal analysis. Special attention is paid to the influence of sub-synchronous mode on the onshore grid. Moreover, the influence of controller parameters on the sub-synchronous mode is investigated, which facilitates the design of converter controllers in HVDC-integrated PMSG-based offshore wind farm. Additionally, the modal analysis results are verified through time-domain simulations.
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11:40-12:00, Paper ThA16.6 | |
>Mean Field Game for Strategic Bidding of Energy Consumers in Congested Distribution Networks |
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Silani, Amirreza | Delft University of Technology |
Tindemans, Simon H. | TU Delft |
Keywords: Power systems, Game theory, Power generation
Abstract: The proliferation of batteries, photovoltaic cells and Electric Vehicles (EVs) in electric power networks can result in network congestion. A redispatch market that allows the Distribution System Operators (DSOs) to relieve congested networks by asking the energy consumers to adjust their scheduled consumption is an alternative to upgrading network capacity. However, energy consumers can strategically increase their bids on the day-ahead market in anticipation of payouts from the redispatch market. This behaviour, which is called increase-decrease gaming, can aggravate congestion and allow the energy consumers to extract windfall profits from the DSO. In this paper, we model the increase-decrease game for large populations of energy consumers in power networks using a mean field game approach. The agents (energy consumers) maximize their individual welfare on the day-ahead market with anticipation of the redispatch market, coupled via the electricity price. We show that there exists a Nash equilibrium for this game and use an algorithm that converges to the Nash equilibrium for the infinite population case.
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ThA17 |
Peony Junior 4511 |
Inverse Problems in Control, Estimation and Reinforcement Learning |
Invited Session |
Chair: Li, Yibei | Nanyang Technological University |
Co-Chair: Wahlberg, Bo | KTH Royal Institute of Technology |
Organizer: Li, Yibei | Nanyang Technological University |
Organizer: Wahlberg, Bo | KTH Royal Institute of Technology |
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10:00-10:20, Paper ThA17.1 | |
>Inverse Optimal Adaptive Prescribed Performance Control with Application to Compliant Actuator-Driven Robot Manipulators (I) |
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Lu, Kaixin | National University of Singapore |
Han, Shuaishuai | National University of Singapore |
Jia, Xinyu | National University of Singapore |
Yu, Haoyong | National University of Singapore |
Keywords: Adaptive control, Optimal control, Nonlinear systems
Abstract: In this work, we formulate and solve the problem of inverse optimal adaptive prescribed performance control and consider its application to compliant actuator-driven robot manipulators. A definition and sufficient conditions for this problem are introduced and derived based on adaptive control Lyapunov function method. An auxiliary system is constructed and incorporated with prescribed performance bounds so as to design a new class of inverse optimal adaptive controllers for the control system. By exploring the links between inverse optimality and stability, it is proved that the proposed controller ensures both inverse optimality and prescribed transient performance of the control system. Above developments are illustrated via an application to robot manipulators driven by compliant actuators. The inverse optimal adaptive control problem for robot manipulators with guaranteed transient performance has not been addressed in the literature.
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10:20-10:40, Paper ThA17.2 | |
>Finite-Sample Bounds for Adaptive Inverse Reinforcement Learning Using Passive Langevin Dynamics (I) |
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Snow, Luke | Cornell University |
Krishnamurthy, Vikram | Cornell University |
Keywords: Markov processes, Learning, Estimation
Abstract: Stochastic gradient Langevin dynamics (SGLD) are a useful methodology for sampling from probability distributions. This paper provides a finite sample analysis of a passive stochastic gradient Langevin dynamics algorithm (PSGLD) designed to achieve inverse reinforcement learning. By "passive", we mean that the noisy gradients available to the PSGLD algorithm (inverse learning process) are evaluated at randomly chosen points by an external stochastic gradient algorithm (forward learner). The PSGLD algorithm thus acts as a randomized sampler which recovers the cost function being optimized by this external process. Previous work has analyzed the asymptotic performance of this passive algorithm using stochastic approximation techniques; in this work we analyze the non-asymptotic performance. Specifically, we provide finite-time bounds on the 2-Wasserstein distance between the passive algorithm and its stationary measure, from which the reconstructed cost function is obtained.
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10:40-11:00, Paper ThA17.3 | |
>Inverse Kalman Filtering for Systems with Correlated Noises (I) |
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Li, Yibei | Nanyang Technological University |
Hu, Xiaoming | Royal Institute of Technology |
Wahlberg, Bo | KTH Royal Institute of Technology |
Xie, Lihua | Nanyang Tech. Univ |
Keywords: Kalman filtering, Identification, Optimal control
Abstract: This paper focuses on two inverse problems of the Kalman filter in which the process and measurement noises are correlated. The unknown covariance matrix in a stochastic system is reconstructed from observations of its posterior beliefs. For the standard inverse Kalman filtering problem, a novel duality-based formulation is proposed, where a well-defined inverse optimal control (IOC) problem is solved instead. Identifiability of the underlying model is proved, and a least squares estimator is designed that is statistically consistent. The time-invariant case using the steady-state Kalman gain is further studied. Since this inverse problem is ill-posed, a canonical class of covariance matrices is constructed, which can be uniquely identified from the dataset with asymptotic convergence. Finally, the performances of the proposed methods are illustrated by numerical examples.
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11:00-11:20, Paper ThA17.4 | |
>A Data-Driven Approach for Inverse Optimal Control (I) |
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Liang, Zihao | Purdue University |
Hao, Wenjian | Purdue University |
Mou, Shaoshuai | Purdue University |
Keywords: Optimal control, Autonomous systems
Abstract: This paper proposes a data-driven, iterative approach for inverse optimal control (IOC), which aims to learn the objective function of a nonlinear optimal control system given its states and inputs. The approach solves the IOC problem in a challenging situation when the system dynamics is unknown. The key idea of the proposed approach comes from the deep Koopman representation of the unknown system, which employs a deep neural network to represent observables for the Koopman operator. By assuming the objective function to be learned is parameterized as a linear combination of features with unknown weights, the proposed approach for IOC is able to achieve a Koopman representation of the unknown dynamics and the unknown weights in objective function together. Simulation is provided to verify the proposed approach.
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11:20-11:40, Paper ThA17.5 | |
>Diagnosing and Repairing Feature Representations under Distribution Shifts (I) |
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Lourenço, Inês | KTH Royal Institute of Technology |
Bobu, Andreea | University of California Berkeley |
Rojas, Cristian R. | KTH Royal Institute of Technology |
Wahlberg, Bo | KTH Royal Institute of Technology |
Keywords: Robotics, Learning, Human-in-the-loop control
Abstract: Robots have been increasingly better at doing tasks for humans by learning from their feedback, but still often suffer from model misalignment due to missing or incorrectly learned features. When the features the robot needs to learn to perform its task are missing or do not generalize well to new settings, the robot will not be able to learn the task the human wants and, even worse, may learn a completely different and undesired behavior. Prior work shows how the robot can detect when its representation is missing some feature and can, thus, ask the human to be taught about the new feature; however, these works do not differentiate between features that are completely missing and those that exist but o not generalize to new environments. In the latter case, the robot would detect misalignment and simply learn a new feature, leading to an arbitrarily growing feature representation that can, in turn, lead to spurious correlations and incorrect learning down the line. In this work, we propose separating the two sources of misalignment: we propose a framework for determining whether a feature the robot needs is incorrectly learned and does not generalize to new environment setups vs. is entirely missing from the robot’s representation. Once we diagnose the source of error, we show how the human can initiate the realignment process for the model: if the feature is missing, we follow prior work for learning new features; however, if the feature exists but does not generalize, we use data augmentation to expand its training and, thus, complete the repair process. We demonstrate the proposed approach in experiments with a simulated 7DoF robot manipulator and physical human corrections.
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11:40-12:00, Paper ThA17.6 | |
>Reinforcement Learning-Based Operational Decision-Making in the Process Industry Using Multi-View Data (I) |
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Liu, Chenliang | Central South University |
Wang, Yalin | Central South University |
Yang, Chunhua | Central South University |
Gui, Weihua | Central South University |
Keywords: Chemical process control, Control applications, Neural networks
Abstract: Owing to the frequent fluctuations encountered in raw material characteristics and operational conditions in the process industry, traditional data-driven approaches prove inadequate in adapting the adjustment of operational variables. Furthermore, the potential of multi-view data, including images, audio, and sensor data, remains underexploited in industrial processes. This study proposes an operational decision-making method based on feedstock-guided multi-view actor-critic (FMAC-ODM) using multi-view data to address these issues. This method utilizes the idea of reinforcement learning (RL) for enhanced decision-making. First, the problem of optimizing operational variables is reformulated into a continuous RL problem to acquire an improved decision-making policy aligned with the current operational conditions. Subsequently, the inclusion of feedstock properties in the state space is implemented to provide essential guidance for the decision-making process. Finally, in pursuit of a comprehensive understanding and bolstering the precision of the decision-making strategy, multi-view data sourced from the industrial site is harnessed as a surrogate for human observation. The effectiveness of the proposed decision-making method is substantiated through its practical application in the industrial flotation process.
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ThA18 |
Peony Junior 4412 |
Nonlinear Systems IV |
Regular Session |
Chair: Bollas, George | University of Connecticut |
Co-Chair: Como, Giacomo | Politecnico Di Torino |
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10:00-10:20, Paper ThA18.1 | |
>On the Existence and Uniqueness of Steady State Solutions of a Class of Dynamic Hydraulic Networks Via Actuator Placement |
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Jeeninga, Mark | Lund University |
Machado Martínez, Juan Eduardo | University of Groningen |
Cucuzzella, Michele | University of Pavia |
Como, Giacomo | Politecnico Di Torino |
Scherpen, Jacquelien M.A. | University of Groningen |
Keywords: Fluid flow systems, Network analysis and control, Nonlinear systems
Abstract: In this paper, using tools from graph theory we provide verifiable necessary and sufficient conditions for the existence of a unique hydraulic equilibrium in district heating systems of meshed topology and containing multiple heat sources. Even though numerous publications have addressed the design of efficient algorithms for numerically finding hydraulic equilibria in the general context of water distribution networks, this is not the case for the analysis of existence and uniqueness. Moreover, most of the existing work dealing with these aspects exploit the equivalence between the nonlinear algebraic equations describing the hydraulic equilibria and the KKT conditions of a suitably defined nonlinear convex optimization problem. Differently, this paper proposes necessary and sufficient graph-theoretic conditions on the actuator placement for the existence and uniqueness of a hydraulic equilibrium, independent of the actuators' control objective. An example based on a representative district heating network is considered to illustrate the key aspects of our contribution, and an explicit formulation of the steady state solution is given for the case in which pressure drops through pipes are linear with respect to the flow rate.
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10:20-10:40, Paper ThA18.2 | |
>The Stabilization Condition for Interval Type-2 Fuzzy Systems Via Relaxed Membership-Parameter Matrix Inequalities |
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Kim, Kyung Soo | POSTECH (Pohang Univ. of Sci. & Tech.) |
Park, PooGyeon | POSTECH (Pohang Univ. of Sci. & Tech.) |
Keywords: Fuzzy systems, Stability of nonlinear systems, LMIs
Abstract: This paper aims to investigate the relaxed stability condition for interval type-2 Takagi--Sugeno fuzzy systems via membership-parameter matrix inequalities. The membership framework of interval type-2 fuzzy sets is structured in convex polytopes with a straightforward method. The stabilization synthesis with a non-parallel distributed compensator controller incorporating lower and upper membership functions is achieved in the sense of a matrix. Moreover, this paper introduces the relaxation strategy for the orthogonal complement, effectively reducing the number of decision variables related to the linear matrix inequalities. In conclusion, examples are presented to demonstrate the effectiveness and applicability of the proposed methods.
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10:40-11:00, Paper ThA18.3 | |
>Bounded Extremum Seeking for Single-Variable Static Map with Large Measurement Delay Via Time-Delay Approach to Averaging |
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Yang, Xuefei | Harbin Institute of Technology |
Fridman, Emilia | Tel-Aviv Univ |
Zhao, Bowen | Harbin Institute of Technology |
Keywords: Extremum seeking, Delay systems, Constrained control
Abstract: In this paper, we present a time-delay approach to gradient-based bounded extremum seeking (ES) with large measurement constant delay, for an unknown single-input static quadratic map. We assume that the extremum point and the Hessian H belong to known intervals, whereas the sign of H is known. We apply a time-delay approach to the bounded ES system and arrive at the neutral type system with a nominal linear delayed system. We present the latter system as a retarded one and employ variation of constants formula for practical stability analysis. Explicit conditions in terms of simple scalar inequalities depending on tuning parameters and delay are established to guarantee the practical stability of the bounded ES control systems. Given any delay and neighborhood of the extremum point and through the solution of the constructed inequalities, we find lower bounds on the dither period that ensures the practical stability.
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11:00-11:20, Paper ThA18.4 | |
>Discovery of Partial Differential Equation Models Using Symbolic Regression Via Genetic Programming |
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Cohen, Benjamin | University of Connecticut |
Beykal, Burcu | University of Connecticut |
Bollas, George | University of Connecticut |
Keywords: Grey-box modeling, Machine learning, Nonlinear systems identification
Abstract: A framework for dynamic system model identification from scarce and noisy data is proposed. This framework uses symbolic regression via genetic programming with a gradient-based parameter estimation step to identify a differential equation model and its parameters from available system data. The effectiveness of the method is demonstrated by identifying four synthetic systems: an ideal plug flow reactor (PFR) with an irreversible chemical reaction, an ideal continuously stirred tank reactor (CSTR) with an irreversible chemical reaction, a system described by Burgers’ Equation, and an ideal PFR with a reversible chemical reaction. The results show that this framework can identify PDE models of systems from broadly spaced and noisy data. When the data was not sufficiently rich, the framework discovered a surrogate model that described the observations in equal or fewer terms than the true system model. Additionally, the method can select relevant physics terms to describe a system from a list of candidate arguments, providing valuable models for use in controls applications.
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11:20-11:40, Paper ThA18.5 | |
>Memory Saving State-Sharing Multi-Observer for a Class of Multi-Observer Based Algorithms |
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Chong, Michelle | Eindhoven University of Technology |
Wakaiki, Masashi | Kobe Univeristy |
Hespanha, Joao P. | Univ. of California, Santa Barbara |
Keywords: Observers for nonlinear systems
Abstract: A multi-observer is a bank of observers which is used for state estimation in various applications. However, it has an implementation bottleneck when a large number of observers are required for the desired estimation performance. To overcome this problem, we propose the design method of a state-sharing multi-observer for a class of nonlinear systems. The state-sharing multi-observer is a single observer that integrates a bank of observers, and its state size is independent of the number of observers. We analyze the error of the state obtained from the state-sharing multi-observer, and then show its applicability to multi-observer based algorithms such as supervisory observers and in secure state estimation.
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11:40-12:00, Paper ThA18.6 | |
>Robust Control of Cascaded H-Bridge Multilevel Inverters for Grid-Tied PV Systems Subject to Faulty Conditions |
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Katir, Hanane | ESE Laboratory, ENSEM of Casablanca, Hassan II University of Cas |
Abouloifa, Abdelmajid | ESE Lab, ENSEM of Casablanca, Hassan II University of Casablanc |
Elhoussin, Elbouchikhi | ISEN Yn Crea West |
Fekih, Afef | University of Louisiana at Lafayette |
Noussi, Karim | ESE Laboratory, ENSEM of Casablanca, University Hassan II of Cas |
El Aroudi, Abdelali | UNiversitat Rovira I Virgili |
Keywords: Energy systems, Fault tolerant systems, Robust control
Abstract: This paper deals with the design and implementation of a robust control approach for grid-tied PV systems. The main controller’s objectives are to inject the maximum available power to the grid, whilst guaranteeing power quality even under faulty conditions. To this end, a multi-loop regulator is designed for the Cascaded H-Bridge Multilevel Inverters (CHBMIs) by combining a sliding mode control strategy for maximum power point tracking and a Lyapunov approach for Power Factor Correction (PFC). Validation of the proposed approach using Matlab/ SimPowerSimscape environment confirmed the ability of the proposed approach to successfully accomplish its objectives in terms of references tracking and regulation under both matching and mismatching irradiation levels as well as faulty modes stemming from the photovoltaic (PV) panels and/or the dc-dc converters. Additionally, the proposed approach was shown to outperform conventional approaches and enable the continuous operation of the PV system under various failure modes affecting multiple PV panels and/or their associated dc-dc boost converters.
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ThA19 |
Peony Junior 4411 |
Linear Parameter-Varying Systems |
Regular Session |
Chair: Farhood, Mazen | Virginia Tech |
Co-Chair: Kon, Johan | Eindhoven University of Technology |
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10:00-10:20, Paper ThA19.1 | |
>Direct Data-Driven State-Feedback Control of General Nonlinear Systems |
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Verhoek, Chris | Eindhoven University of Technology |
Koelewijn, Patrick | Eindhoven University of Technology |
Haesaert, Sofie | Eindhoven University of Technology |
Tóth, Roland | Eindhoven University of Technology |
Keywords: Linear parameter-varying systems, Adaptive control
Abstract: Through the use of the Fundamental Lemma for linear systems, a direct data-driven state-feedback control synthesis method is presented for a rather general class of nonlinear (NL) systems. The core idea is to develop a data-driven representation of the so-called velocity-form, i.e., the time-difference dynamics, of the NL system, which is shown to admit a direct linear parameter-varying (LPV) representation. By applying the LPV extension of the Fundamental Lemma in this velocity domain, a state-feedback controller is directly synthesized to provide asymptotic stability and dissipativity of the velocity-form. By using realization theory, the synthesized controller is realized as a NL state-feedback law for the original unknown NL system with guarantees of universal shifted stability and dissipativity, i.e., stability and dissipativity w.r.t. any (forced) equilibrium point, of the closed-loop behavior. This is achieved by the use of a single sequence of data from the system and a predefined basis function set to span the scheduling map. The applicability of the results is demonstrated on a simulation example of an unbalanced disc.
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10:20-10:40, Paper ThA19.2 | |
>Minimal Realizations of Input-Output Behaviors by LPV State-Space Representations with Affine Dependency |
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Petreczky, Mihaly | UMR CNRS 9189, Ecole Centrale De Lille |
Tóth, Roland | Eindhoven University of Technology |
Mercère, Guillaume | University of Poitiers |
Keywords: Linear parameter-varying systems, Algebraic/geometric methods, Identification
Abstract: The paper makes the first steps towards a behavioral theory of LPV state-space representations with an affine dependency on scheduling, by characterizing minimality of such state-space representations. It is shown that minimality is equivalent to observability, and that minimal realizations of the same behavior are isomorphic. Moreover, this isomorphism does not depend on the scheduling variable. Furthermore, controllability of behaviors is equivalent to span-reachability of their minimal state-space representations. Finally, we establish a formal relationship between minimality of LPV state-space representations with an affine dependence on scheduling and minimality of LPV state-space representations with a dynamic and meromorphic dependence on scheduling.
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10:40-11:00, Paper ThA19.3 | |
>Parameter-Varying Koopman Operator for Nonlinear System Modeling and Control |
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Lee, Changyu | KAIST |
Park, Kiyong | KAIST |
Kim, Jinwhan | KAIST |
Keywords: Linear parameter-varying systems, Predictive control for nonlinear systems, Modeling
Abstract: This paper proposes a novel approach for modeling and controlling nonlinear systems with varying parameters. The approach introduces the use of a parameter-varying Koopman operator (PVKO) in a lifted space, which provides an efficient way to understand system behavior and design control algorithms that account for underlying dynamics and changing parameters. The PVKO builds on a conventional Koopman model by incorporating local time-invariant linear systems through interpolation within the lifted space. This paper outlines a procedure for identifying the PVKO and designing a model predictive control using the identified PVKO model. Simulation results demonstrate that the proposed approach improves model accuracy and enables predictions based on future parameter information. The feasibility and stability of the proposed control approach are analyzed, and their effectiveness is demonstrated through simulation.
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11:00-11:20, Paper ThA19.4 | |
>Robust Control of Discrete-Time Systems with Coefficient Matrices Given by Polytopic Martingales |
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Kitahiro, Tomoya | Kyoto Univ |
Hosoe, Yohei | Kyoto University |
Hagiwara, Tomomichi | Kyoto Univ |
Keywords: Linear parameter-varying systems, Stochastic systems, LMIs
Abstract: This paper is concerned with robust control of discrete-time linear stochastic systems with coefficient matrices given by polytopic martingales. To the best of our knowledge, this class of stochastic systems have not been dealt with as a target of control due to the absence of required theory. For such systems, we discuss the following two types of approaches for robust stabilization: One is the proposed stochastic control approach using the martingale property of the coefficient matrices, and the other is a deterministic control approach without using the information. Through theoretical and numerical comparisons of the two approaches, we demonstrate the effectiveness of the proposed stochastic control approach in the sense of conservativeness.
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11:20-11:40, Paper ThA19.5 | |
>Control of Polytopic LPV Systems with Uncertain Initial Conditions |
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Farhood, Mazen | Virginia Tech |
Keywords: Linear parameter-varying systems, Uncertain systems, Robust control
Abstract: This paper focuses on the control design and analysis for nonstationary linear parameter-varying systems with affine parameter dependence and uncertain initial conditions. The uncertain initial state and the disturbance input are allowed to reside in two separate norm balls. Convex analysis and synthesis conditions are derived, and a reachability analysis result for systems with pointwise-bounded inputs is developed, enabling the construction of ellipsoids in which the state or some output of interest lies at specified time instants. The usefulness of the proposed approach is demonstrated through an illustrative example involving a two-mass rotational system.
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11:40-12:00, Paper ThA19.6 | |
>Direct Learning for Parameter-Varying Feedforward Control: A Neural-Network Approach |
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Kon, Johan | Eindhoven University of Technology |
van de Wijdeven, Jeroen | ASML Netherlands B.V |
Bruijnen, Dennis | Philips Engineering Solutions |
Tóth, Roland | Eindhoven University of Technology |
Heertjes, Marcel | Eindhoven University of Technology |
Oomen, Tom | Eindhoven University of Technology |
Keywords: Mechatronics, Linear parameter-varying systems, Neural networks
Abstract: The performance of a feedforward controller is primarily determined by the extent to which it can capture the relevant dynamics of a system. The aim of this paper is to develop an input-output linear parameter-varying (LPV) feedforward parameterization and a corresponding data-driven estimation method in which the dependency of the coefficients on the scheduling signal are learned by a neural network. The use of a neural network enables the parameterization to compensate a wide class of constant relative degree LPV systems. Efficient optimization of the neural-network-based controller is achieved through a Levenberg-Marquardt approach with analytic gradients and a pseudolinear approach generalizing Sanathanan-Koerner to the LPV case. The performance of the developed feedforward learning method is validated in a simulation study of an LPV system showing excellent performance.
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ThA20 |
Orchid Junior 4312 |
Stochastic and Distributed Models in Systems and Synthetic Biology |
Invited Session |
Chair: Waldherr, Steffen | University of Vienna |
Co-Chair: Singh, Abhyudai | University of Delaware |
Organizer: Waldherr, Steffen | University of Vienna |
Organizer: Singh, Abhyudai | University of Delaware |
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10:00-10:20, Paper ThA20.1 | |
>Robust Microphase Separation through Chemical Reaction Networks |
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Blanchini, Franco | Univ. Degli Studi Di Udine |
Franco, Elisa | University of California a Los Angeles |
Giordano, Giulia | University of Trento |
Osmanovic, Dino | UCLA |
Keywords: Biological systems, Systems biology, Uncertain systems
Abstract: The interaction of phase-separating systems with chemical reactions is of great interest in various contexts, from biology to material science. In biology, phase separation is thought to be the driving force behind the formation of biomolecular condensates, i.e. organelles without a membrane that are associated with cellular metabolism, stress response, and development. RNA, proteins, and small molecules participating in the formation of condensates are also involved in a variety of biochemical reactions: how do the chemical reaction dynamics influence the process of phase separation? Here we are interested in finding chemical reactions that can arrest the growth of condensates, generating stable spatial patterns of finite size (microphase separation), in contrast with the otherwise spontaneous (unstable) growth of condensates. We consider a classical continuum model for phase separation coupled to a chemical reaction network (CRN), and we seek conditions for the emergence of stable oscillations of the solution in space. Given reaction dynamics with uncertain rate constants, but known structure, we derive easily computable conditions to assess whether microphase separation is impossible, possible for some parameter values, or robustly guaranteed for all parameter values within given bounds. Our results establish a framework to evaluate which classes of CRNs favor the emergence of condensates with finite size, a question that is broadly relevant to understanding and engineering life.
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10:20-10:40, Paper ThA20.2 | |
>Modeling Cell Size Distribution with Heterogeneous Flux Balance Analysis |
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Busschaert, Michiel | KU Leuven |
Vermeire, Florence H. | KU Leuven |
Waldherr, Steffen | University of Vienna |
Keywords: Systems biology, Biological systems, Cellular dynamics
Abstract: For over two decades, Flux Balance Analysis (FBA) has been successfully used for predicting growth rates and intracellular reaction rates in microbiological metabolism. An aspect that is often omitted from this analysis, is segregation or heterogeneity between different cells. In this work, we propose an extended FBA method to model cell size distributions in balanced growth conditions. Hereto, a mathematical description of the concept of balanced growth in terms of cell mass distribution is presented. The cell mass distribution, quantified by the Number Density Function (NDF), is affected by cell growth and cell division. An optimization program is formulated in which the NDF, average cell culture growth rate and reaction rates per cell mass are treated as optimization variables. As qualitative proof of concept, the methodology is illustrated on a core carbon model of Escherichia coli under aerobic growth conditions. This illustrates feasibility and applications of this method, while indicating some shortcomings intrinsic to the simplified biomass structuring and the time invariant approach.
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10:40-11:00, Paper ThA20.3 | |
>Multicellular PD Control in Microbial Consortia |
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Martinelli, Vittoria | Università Degli Studi Di Napoli Federico II |
Salzano, Davide | Scuola Superiore Meridionale |
Fiore, Davide | University of Naples Federico II |
di Bernardo, Mario | University of Naples Federico II |
Keywords: Biomolecular systems, Genetic regulatory systems, PID control
Abstract: We propose a multicellular implementation of a classical PD feedback controller to regulate gene expression in a microbial consortium. The implementation involves distributing the proportional and derivative control actions between two different cellular populations that can communicate with each other and regulate the output of a third target cellular population. We derive analytical conditions on biological parameters and control gains to adjust the system's static and dynamical properties. We then evaluate the strategy's performance and robustness through extensive in silico experiments in BSim, a realistic simulator of bacterial populations.
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11:00-11:20, Paper ThA20.4 | |
>Comparing Negative Feedback Mechanisms in Gene Expression: From Single Cells to Cell Populations (I) |
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Zhang, Zhanhao | University of Delaware |
Nieto, Cesar | University of Delaware |
Singh, Abhyudai | University of Delaware |
Keywords: Systems biology, Hybrid systems, Nonlinear systems
Abstract: Negative feedback regulation is a well-known motif for suppressing deleterious fluctuations in gene product levels. We systematically compare two scenarios where negative feedback is either implemented in the protein production rate (regulated synthesis) or in the protein degradation rate (regulated degradation). Our results show that while in low-noise regimes both schemes are identical, they begin to show remarkable differences in high-noise regimes. Analytically solving for the probability distributions of the protein levels reveals that regulated synthesis is a better strategy to suppress random fluctuations while also minimizing protein levels dipping below a threshold. In contrast, regulated degradation is preferred if the goal is to minimize protein levels going beyond a threshold. Finally, we compare and contrast these distributions not only in a single cell over time but also in an expanding cell population where these effects can be buffered or exacerbated due to the coupling between expression and cell growth.
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11:20-11:40, Paper ThA20.5 | |
>Out-Of-Equilibrium Fluctuations Drive Correlations between Enzyme and Metabolic Product Levels (I) |
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Borri, Alessandro | CNR-IASI |
Palumbo, Pasquale | University of Milano-Bicocca |
Singh, Abhyudai | University of Delaware |
Keywords: Systems biology, Biomolecular systems, Markov processes
Abstract: Enzyme-driven catalysis of a substrate into a product forms the fundamental backbone of cellular metabolic pathways. In the deterministic formulation of such a reaction scheme, the equilibrium level of the metabolic product is independent of the steady-state enzyme, so that any perturbation in enzyme levels causes a transient change in metabolic product levels that perfectly adapts to the original enzyme-independent steady state. In this work, we consider a stochastic formulation of the problem, where enzyme levels constantly fluctuate due to the inherently noisy gene expression process as well as to the extrinsic noise in substrate availability. Our results show that such out-of-equilibrium fluctuations can result in positive (or negative) enzyme-product and substrate-product correlations, whose behavior qualitatively and quantitatively changes in different scenarios characterized by perturbations of nominal parameters and variable noise levels.
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11:40-12:00, Paper ThA20.6 | |
>Error Bound for Hill-Function Approximations in a Class of Stochastic Transcriptional Network Models |
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Hirsch, Dylan | Massachusetts Institute of Technology |
Grunberg, Theodore W. | Massachusetts Institute of Technology |
Del Vecchio, Domitilla | Massachusetts Institute of Technology |
Keywords: Biomolecular systems, Systems biology, Genetic regulatory systems
Abstract: Hill functions are often used in stochastic models of gene regulation to approximate the dependence of gene activity on the concentration of the transcription factor (TF) that regulates the gene. However, it is generally unknown how much error one may incur from this approximation. We investigate this question in the context of transcriptional networks (TNs). Under the assumption of rapid binding and unbinding of TFs with their gene targets, we bound the approximation error (in terms of the total variation distance) between a mass-action stochastic model and a corresponding model with Hill function propensities. To do so, we use a combination of singular perturbation theory and moment analysis for stochastic chemical reaction networks. We assume throughout that TFs regulate genes in a one-to-one fashion, each regulated gene produces a single TF, TFs do not multimerize, and each gene only has a single TF binding site. These results are pertinent for the modeling of TNs and may also carry relevance for more general biological processes.
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ThA21 |
Orchid Junior 4311 |
Predictive Control for Nonlinear Systems I |
Regular Session |
Chair: Saccani, Danilo | École Polytechnique Fédérale De Lausanne (EPFL) |
Co-Chair: Mohammadpour Velni, Javad | Clemson University |
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10:00-10:20, Paper ThA21.1 | |
>Model Predictive Control for Multi-Agent Systems under Limited Communication and Time-Varying Network Topology |
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Saccani, Danilo | École Polytechnique Fédérale De Lausanne (EPFL) |
Fagiano, Lorenzo | Politecnico Di Milano |
Zeilinger, Melanie N. | ETH Zurich |
Carron, Andrea | ETH |
Keywords: Predictive control for nonlinear systems, Agents-based systems, Autonomous systems
Abstract: In control system networks, reconfiguration of the controller when agents are leaving or joining the network is still an open challenge, in particular when operation constraints that depend on each agent’s behavior must be met. Drawing our motivation from mobile robot swarms, in this paper, we address this problem by optimizing individual agent performance while guaranteeing persistent constraint satisfaction in presence of bounded communication range and time-varying network topology. The approach we propose is a model predictive control (MPC) formulation, building on multi-trajectory MPC (mt-MPC) concepts. To enable plug and play operations when the system is in closed-loop without the need of a request, the proposed MPC scheme predicts two different state trajectories in the same finite horizon optimal control problem. One trajectory drives the system to the desired target, assuming that the network topology will not change in the prediction horizon, while the second one ensures constraint satisfaction assuming a worst-case scenario in terms of new agents joining the network in the planning horizon. Recursive feasibility and stability of the closed-loop system during plug and play operations are shown. The approach effectiveness is illustrated with a numerical simulation.
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10:20-10:40, Paper ThA21.2 | |
>Nonlinear Data-Driven Predictive Control Using Deep Subspace Prediction Networks |
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Lazar, Mircea | Eindhoven University of Technology |
Popescu, Mihai-Serban | Eindhoven University of Technology |
Schoukens, Maarten | Eindhoven University of Technology |
Keywords: Predictive control for nonlinear systems, Data driven control, Nonlinear systems identification
Abstract: Indirect data-driven predictive control (DPC) algorithms for nonlinear systems typically employ multi-step predictors, which are identified from input-output data using neural networks. In this paper we put forward a unifying multi-step prediction network architecture, i.e., the deep subspace prediction network (DSPN). We then prove that the DSPN architecture specialized to multi-layer-perceptron neural networks recovers the linear predictor corresponding to subspace predictive control for a sufficient number of hidden layer neurons. Hence, we establish a well-posed generalization of subspace predictive control for nonlinear systems. Moreover, we develop a regularized DSPN architecture that embeds a linear subspace predictor to improve extrapolation properties for non-training data. Simulation results on a benchmark inverted pendulum show that nonlinear DPC based on DSPN achieves high control performance for both noiseless and noisy data.
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10:40-11:00, Paper ThA21.3 | |
>Discrete-Time Control Barrier Functions for Guaranteed Recursive Feasibility in Nonlinear MPC: An Application to Lane Merging |
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Katriniok, Alexander | Eindhoven University of Technology |
Shakhesi, Erfan | Eindhoven University of Technology |
Heemels, W.P.M.H. | Eindhoven University of Technology |
Keywords: Predictive control for nonlinear systems, Automotive systems, Optimal control
Abstract: In this paper, we present conditions under which the terminal ingredients, defined by discrete-time control barrier function (DTCBF) certificates, guarantee recursive feasibility in nonlinear MPC. Further, we introduce the notion of quasi-DTCBF (qDTCBF) certificates. Compared to DTCBFs, qDTCBF conditions can be satisfied with tighter control input bounds, which is highly advantageous if only limited actuation is possible. Both certificates encourage an earlier reaction of the control system and result in a lower cumulative MPC cost. The methodology is applied to a lane merging problem in automated driving, in which DTCBF and qDTCBF certificates subject to input constraints form the terminal ingredients to guarantee recursive feasibility of the nonlinear MPC scheme. A simulation study demonstrates the efficacy of the concept.
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11:00-11:20, Paper ThA21.4 | |
>Mixed-Integer MPC Strategies for Fueling and Density Control in Fusion Tokamaks |
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Orrico, Christopher Anthony | Eindhoven University of Technology |
van Berkel, Matthijs | Dutch Institute for Fundamental Energy Research |
Bosman, Thomas | DIFFER |
Heemels, W.P.M.H. | Eindhoven University of Technology |
Krishnamoorthy, Dinesh | TU Eindhoven |
Keywords: Predictive control for nonlinear systems, Hybrid systems, Constrained control
Abstract: Model predictive control (MPC) is promising for fueling and core density feedback control in nuclear fusion tokamaks, where the primary actuators, frozen hydrogen fuel pellets fired into the plasma, are discrete. Previous density feedback control approaches have only approximated pellet injection as a continuous input due to the complexity that it introduces. In this letter, we model plasma density and pellet injection as a hybrid system and propose two MPC strategies for density control: mixed-integer (MI) MPC using a conventional mixed-integer programming (MIP) solver and MPC utilizing our novel modification of the penalty term homotopy (PTH) algorithm. By relaxing the integer requirements, the PTH algorithm transforms the MIP problem into a series of continuous optimization problems, reducing computation complexity. By adding a logarithmic barrier term to the PTH algorithm, we prevent the concave penalty term and active path constraints from causing the optimization problem to yield non-integer solutions. Both strategies perform well with regards to reference tracking without violating path constraints and satisfy the computation time limit for real-time control of the pellet injection system. However, the computation time of the PTH-based MPC strategy consistently outpaces the conventional MI-MPC strategy and is especially beneficial for MPC formulations with longer prediction horizons.
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11:20-11:40, Paper ThA21.5 | |
>Relaxed Feasibility and Stability Criteria for Flexible-Step MPC |
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Fuernsinn, Annika | Queen's University |
Ebenbauer, Christian | RWTH Aachen University |
Gharesifard, Bahman | University of California, Los Angeles |
Keywords: Predictive control for nonlinear systems, Lyapunov methods, Stability of nonlinear systems
Abstract: We provide extensions to the new flexible-step model predictive control (MPC) scheme, which is based on the idea of generalized discrete-time control Lyapunov functions. These facilitate the implementation of a flexible number of control inputs in each iteration of the MPC scheme. We present relaxed recursive feasibility and stability results and provide a converse Lyapunov result. These results combined simplify the design of the flexible-step MPC scheme. We demonstrate the capabilities of the flexible-step MPC algorithm for a nonholonomic system, where the standard one-step implementation may suffer from lack of asymptotic convergence.
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11:40-12:00, Paper ThA21.6 | |
>A Hybrid Neural Network Approach for Adaptive Scenario-Based Model Predictive Control in the LPV Framework |
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Bao, Yajie | The University of Georgia |
Mohammadpour Velni, Javad | Clemson University |
Keywords: Predictive control for nonlinear systems, Machine learning, Linear parameter-varying systems
Abstract: This paper presents a hybrid neural network (NN) approach for adaptive scenario-based model predictive control (SMPC) design of nonlinear systems in the linear parameter-varying (LPV) framework. In particular, a deterministic artificial neural network (ANN)-based LPV model is learned from data as the nominal model. Then, a Bayesian NN (BNN) is used to describe the mismatch between the plant and the LPV-ANN model. Adaptive scenarios are generated online based on the BNN model to reduce the conservativeness of scenario generation. Moreover, a probabilistic safety certificate is incorporated into the scenario generation by ensuring that the trajectories of scenarios contain the trajectory of the system and that all the scenarios satisfy the constraints with a high probability. Furthermore, conditions for the recursive feasibility of the SMPC are given. Experiments on the closed-loop simulations of a two-tank system demonstrate that the proposed approach can better model the behaviors of nonlinear systems than sole ANN/BNN models can, and the SMPC based on the hybrid NN (HyNN) model can improve the control performance compared to the SMPC with a fixed scenario tree.
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ThA22 |
Orchid Junior 4212 |
Stochastic Systems I |
Regular Session |
Chair: Nesic, Dragan | University of Melbourne |
Co-Chair: Chertkov, Michael | University of Arizona |
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10:00-10:20, Paper ThA22.1 | |
>Stability Bounds for Learning-Based Adaptive Control of Discrete-Time Multi-Dimensional Stochastic Linear Systems with Input Constraints |
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Siriya, Seth | University of Melbourne |
Zhu, Jingge | University of Melbourne |
Nesic, Dragan | University of Melbourne |
Pu, Ye | The University of Melbourne |
Keywords: Stochastic systems, Adaptive control, Constrained control
Abstract: We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the system are unknown. To address this challenge, we propose a certainty-equivalent control scheme combining online parameter estimation with saturated linear control. We establish the existence of a high probability stability bound on the closed-loop system, under additional assumptions on the system and noise processes. Numerical examples are presented to illustrate our results.
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10:20-10:40, Paper ThA22.2 | |
>EVENT-DRIVEN L1-GAIN ASYNCHRONOUS FILTER of POSITIVE MARKOV JUMP SYSTEMS |
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Zhang, Junfeng | Hainan University |
Yang, Yahao | Hainan University |
Huang, Mengxing | Hainan University |
Deng, Xuanjin | South China University of Technology |
Keywords: Stochastic systems, Fault detection, Hybrid systems
Abstract: This paper proposes event-driven asynchronous filters for positive Markov jump systems by employing hidden Markov model. Based on the output of sensor measurement, a weighted event-driven threshold is established in the form of 1-norm. The stability of the corresponding augmented system can be guaranteed by transforming the error signal into interval uncertain form. Under the established triggering condition, an event-driven positive l1-gain asynchronous filter is constructed for positive Markov jump systems. Then, the asynchronous filter design for positive Markov jump systems with partial information of hidden Markov model is further addressed. All presented conditions are described in the linear programming form. Finally, one example is given to illustrate the effectiveness of the proposed design.
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10:40-11:00, Paper ThA22.3 | |
>Spectral Decomposition in Kalman Filter Algorithm for Homogeneous Atomic Clock Ensembles |
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Yan, Yuyue | Tokyo Institute of Technology |
Kawaguchi, Takahiro | Gunma University |
Yano, Yuichiro | National Institute of Information and Communications Technology |
Hanado, Yuko | National Institute of Information and Communications Technology |
Ishizaki, Takayuki | Tokyo Institute of Technology |
Keywords: Stochastic systems, Filtering, Computational methods
Abstract: Existing studies have pointed out numerical instability in the Kalman filter of atomic clocks, but the reasons for such instability have not been clarified mathematically. In this paper, we mathematically clarify the reason for the numerical instability by a new approach of spectral decomposition of the error covariance matrix in the Kalman filter. In particular, we reveal the fact that the error covariance matrix for homogeneous undetectable atomic clock ensembles can be decomposed into a diverging part and a converging part. Furthermore, the Kalman gain is solely influenced by the converging part, but not the diverging part, meaning that the Kalman gain converges to a steady-state value if ideal computation is possible without computation error. We present an alternative method to the conventional Kalman filter to avoid numerical instability and reduce computation cost where the covariance of Kalman filter can be computed rigorously only using three n-dimensional Riccati iterations instead of an nN-dimensional Riccati iterations for an n-order clock model with N clocks. A numerical example is provided to illustrate the efficacy of our approach.
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11:00-11:20, Paper ThA22.4 | |
>The First Achievement of a Given Level by a Random Process |
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Semakov, Sergei | Moscow Institute of Physics and Technology and Moscow Automobile |
Semakov, Aleksei | Moscow Institute of Physics and Technology |
Semakov, Ivan | Moscow Aviation Institute, Tinkoff Bank |
Keywords: Stochastic systems, Flight control
Abstract: We estimate the probability that the first achievement of a given level by the component y_1(x) of n-dimensional continuous process y(x)={y_1(x),..., y_n(x)} occurs at some moment x* from a given interval (x',x") and, at this moment x*, the condition (y_2(x*),...,y_n(x*)∈D holds, where D is a given domain of (n−1)-dimensional Euclidean space R^{n−1}. The need to calculate the above-mentioned probability arises in the problems of aircraft control during landing.
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11:20-11:40, Paper ThA22.5 | |
>Universality and Control of Fat Tails |
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Chertkov, Michael | University of Arizona |
Keywords: Stochastic systems, Fluid flow systems, Control of networks
Abstract: Motivated by applications in hydrodynamics and networks of thermostatically-control loads in buildings we study control of linear dynamical systems driven by additive and also multiplicative noise of a general position. Utilizing mathematical theory of stochastic multiplicative processes we present a universal way to estimate fat, algebraic tails of the state vector probability distributions. This prompts us to introduce and analyze mean-q-power stability criterion, generalizing the mean-square stability criterion, and then juxtapose it to other tools in control.
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11:40-12:00, Paper ThA22.6 | |
>Fraud Detection and Deterrence in Electronic Voting Machines: A Game-Theoretic Approach |
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Vora, Anuj | IIT Bombay |
Kulkarni, Ankur A. | Indian Institute of Technology Bombay |
Keywords: Stochastic systems, Game theory, Attack Detection
Abstract: We study a setting where a detector wishes to detect and deter adversarial manipulation in an electronic voting machine. An adversary tries to win the election by tampering the votes while obfuscating its manipulation. We pose this problem as a game between the detector and the adversary and characterize the equilibrium payoffs for the players and the asymptotic nature of these payoffs. We find that if the detector is too cautious, then in equilibrium the adversary wins with a probability higher than its prior probability of winning. We derive an expression for the deterrence threshold, i.e., the minimum level of false-alarm that the detector should endure so that the adversary is not any better off by the manipulation. With this, asymptotically, the detector can ensure that the probability of missed-detection becomes zero by appropriately adjusting the rate of decay of probability of false-alarm. But if this rate of decay is too `fast', then the adversary can get an arbitrarily high probability of winning in spite of having a vanishing prior probability of winning. We then extend the results to a setting where the detector has incomplete information about the adversary.
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ThA23 |
Orchid Junior 4211 |
Encrypted Control and Optimization |
Invited Session |
Chair: Schulze Darup, Moritz | TU Dortmund University |
Co-Chair: Kim, Junsoo | SEOULTECH |
Organizer: Schulze Darup, Moritz | TU Dortmund University |
Organizer: Alexandru, Andreea B. | Duality Technologies |
Organizer: Kim, Junsoo | Seoul National University of Science and Technology |
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10:00-10:20, Paper ThA23.1 | |
>Optimal Controller and Security Parameter for Encrypted Control Systems under Least Squares Identification |
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Teranishi, Kaoru | The University of Electro-Communications |
Kogiso, Kiminao | The University of Electro-Communications |
Keywords: Networked control systems, Information theory and control, Control over communications
Abstract: Encrypted control is a framework for the secure outsourcing of controller computation using homomorphic encryption that allows to perform arithmetic operations on encrypted data without decryption. In a previous study, the security level of encrypted control systems was quantified based on the difficulty and computation time of system identification. This study investigates an optimal design of encrypted control systems when facing an attack attempting to estimate a system parameter by the least squares method from the perspective of the security level. This study proposes an optimal H2 controller that maximizes the difficulty of estimation and an equation to determine the minimum security parameter that guarantee the security of an encrypted control system as a solution to the design problem. The proposed controller and security parameter are beneficial for reducing the computation costs of an encrypted control system, while achieving the desired security level. Furthermore, the proposed design method enables the systematic design of encrypted control systems.
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10:20-10:40, Paper ThA23.2 | |
>Homomorphically Encrypted Gradient Descent Algorithms for Quadratic Programming (I) |
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Bertolace, André | University of Oxford |
Gatsis, Konstantinos | University of Oxford |
Margellos, Kostas | University of Oxford |
Keywords: Optimization algorithms, Numerical algorithms, Computer/Network Security
Abstract: In this paper, we evaluate the different fully homomorphic encryption schemes, propose an implementation, and numerically analyze the applicability of gradient descent algorithms to solve quadratic programming in a homomorphic encryption setup. The limit on the multiplication depth of homomorphic encryption circuits is a major challenge for iterative procedures such as gradient descent algorithms. Our analysis not only quantifies these limitations on prototype examples, thus serving as a benchmark for future investigations, but also highlights additional trade-offs like the ones pertaining the choice of gradient descent or accelerated gradient descent methods, opening the road for the use of homomorphic encryption techniques in iterative procedures widely used in optimization based control. In addition, we argue that, among the available homomorphic encryption schemes, the one adopted in this work, namely CKKS, is the only suitable scheme for implementing gradient descent algorithms. The choice of the appropriate step size is crucial to the convergence of the procedure. The paper shows firsthand the feasibility of homomorphically encrypted gradient descent algorithms.
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10:40-11:00, Paper ThA23.3 | |
>Oblivious Markov Decision Processes: Planning and Policy Execution (I) |
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Alsayegh, Murtadha | Florida International University |
Fuentes, Jose | Florida International University |
Bobadilla, Leonardo | Florida International University |
Shell, Dylan | Texas A&M University |
Keywords: Control Systems Privacy, Markov processes, Robotics
Abstract: We examine a novel setting in which two parties have partial knowledge of the elements that make up a Markov Decision Process (MDP) and must cooperate to compute and execute an optimal policy for the problem constructed from those elements. This situation arises when one party wants to give a robot some task, but does not wish to divulge those details to a second party---while the second party possesses sensitive data about the robot's dynamics (information needed for planning). Both parties want the robot to perform the task successfully, but neither is willing to disclose any more information than is absolutely necessary. We utilize techniques from secure multi-party computation, combining primitives and algorithms to construct protocols that can compute an optimal policy while ensuring that the policy remains opaque by being split across both parties. To execute a split policy, we also give a protocol that enables the robot to determine what actions to trigger, while the second party guards against attempts to probe for information inconsistent with the policy's prescribed execution. In order to improve scalability, we find that basis functions and constraint sampling methods are useful in forming effective approximate MDPs. We report simulation results examining performance and precision, and assess the scaling properties of our Python implementation. We also describe a hardware proof-of-feasibility implementation using inexpensive physical robots, which, being a small-scale instance, can be solved directly.
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11:00-11:20, Paper ThA23.4 | |
>Hybrid Design of Multiplicative Watermarking for Defense against Malicious Parameter Identification (I) |
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Zhang, Jiaxuan | Delft University of Technology |
Gallo, Alexander J. | TU Delft |
Ferrari, Riccardo M.G. | Delft University of Technology |
Keywords: Attack Detection, Cyber-Physical Security, Resilient Control Systems
Abstract: Multiplicative watermarking (MWM) is an active diagnosis technique for the detection of highly sophisticated at- tacks, but is vulnerable to malicious agents that use eavesdropped data to identify and then remove or replicate the watermark. In this work, we propose a scheme to protect the parameters of MWM, by proposing a design strategy based on piecewise affine (PWA) hybrid dynamical systems, called hybrid multiplicative watermarking (HMWM). Due to the design decision to make certain states of the HMWM systems unobservable, we show that parameter reconstruction by an eavesdropper is infeasible, from both a computational and a system-theoretic perspective, while not altering the system’s closed-loop performance.
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11:20-11:40, Paper ThA23.5 | |
>Feedback Path Delay Attacks and Detection (I) |
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Wigren, Torbjorn | Uppsala University |
Teixeira, André M. H. | Uppsala University |
Keywords: Attack Detection, Identification, Cyber-Physical Security
Abstract: The paper discusses delay injection attacks on regulator loops and suggests joint recursive prediction error identification of delay and dynamics for supervision and attack detection. The control system is assumed to be operated either in open- or closed-loop mode. It is shown why delay insertion in the feedback path before the user switches to closed-loop operation is advantageous to disguise the attack. Delay attack monitoring is preferably performed continuously, allowing for early attack detection before closed-loop control is initiated. The detection performance is evaluated numerically for a linearized automotive cruise control feedback loop.
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11:40-12:00, Paper ThA23.6 | |
>On the Security of Randomly Transformed Quadratic Programs for Privacy-Preserving Cloud-Based Control (I) |
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Binfet, Philipp | TU Dortmund University |
Schlüter, Nils | TU Dortmund University |
Schulze Darup, Moritz | TU Dortmund University |
Keywords: Control Systems Privacy, Cyber-Physical Security, Optimization
Abstract: Control related data, such as system states and inputs or controller specifications, is often sensitive. Meanwhile, the increasing connectivity of cloud-based or networked control results in vast amounts of such data, which poses a privacy threat, especially when evaluation on external platforms is considered. In this context, a cipher based on a random affine transformation gained attention, which is supposed to enable privacy-preserving evaluations of quadratic programs (QPs) with little computational overhead compared to other methods. This paper deals with the security of such randomly transformed QPs in the context of model predictive control (MPC). In particular, we show how to construct attacks against this cipher and thereby underpin concerns regarding its security in a practical setting. To this end, we exploit invariants under the transformations and common specifications of MPC-related QPs. Our numerical examples then illustrate that these two ingredients suffice to extract information from ciphertexts.
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ThA24 |
Orchid Main 4201AB |
Event-Triggered and Self-Triggered Control II |
Invited Session |
Chair: Tallapragada, Pavankumar | Indian Institute of Science |
Co-Chair: Xie, Yijing | University of Texas at Arlington |
Organizer: Heemels, W.P.M.H. | Eindhoven University of Technology |
Organizer: Hirche, Sandra | Technische Universität München |
Organizer: Nowzari, Cameron | George Mason University |
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10:00-10:20, Paper ThA24.1 | |
>Performance Implications of Different P-Norms in Level-Triggered Sampling (I) |
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Meister, David | University of Stuttgart |
Allgöwer, Frank | University of Stuttgart |
Keywords: Networked control systems, Sampled-data control, Control over communications
Abstract: This work studies the performance of an event-based control approach, namely level-triggered sampling, in a standard multidimensional single-integrator setup. We falsify a conjecture from the literature that the deployed p-norm in the triggering condition supposedly has no impact on the performance of the sampling scheme in that setting. In particular, we show for the considered setup that the usage of the maximum norm instead of the Euclidean norm induces a performance deterioration of level-triggered sampling for sufficiently large system dimensions, when compared to periodic control at the same sampling rate. Moreover, we investigate the performance for other p-norms in simulation and observe that it degrades with increasing p. In addition, our findings reveal the previously unknown role of the triggering rule in the cause of a recently discovered phenomenon: Previous work has shown for a single-integrator consensus setup that the commonly observed performance advantage of event-based control over periodic control can be lost in distributed settings with a cooperative control goal. In our work, we obtain similar results for a non-cooperative setting only by adjusting the norm in the level-triggered sampling scheme. We therefore demonstrate that the performance degradation found in the distributed setting originates from the triggering rule and not from the considered cooperative control goal.
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10:20-10:40, Paper ThA24.2 | |
>Event-Triggered Distributed Optimization Algorithm Over Directed Networks: A Nonsingular Estimator Approach (I) |
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Xian, Chengxin | Northwestern Polytechnical University |
Tao, Qianle | Northwestern Polytechnical University |
Liu, Yongfang | Northwestern Polytechnical University |
Wang, Huimin | Northeastern University |
Zhao, Yu | Northwestern Polytechnical University |
Keywords: Distributed control, Control of networks, Optimization algorithms
Abstract: This paper investigates the event-triggered distributed optimization problems (ETDOPs) over strongly connected directed networks. By assigning an additional scalar state variable to each agent and utilizing diminishing time-varying gain/step-size, a class of modified event-triggered distributed optimization algorithms (ETDOAs) is proposed, which can address the ETDOPs well and can avoid the inverse operation of some estimators in the existing literature. Compared with the existing DOAs, this paper gives a new idea to solve the DOPs under weighted-unbalanced digraphs and continuous communication of agent networks is avoided. Finally, numerical simulations are given to illustrate the effectiveness of the proposed ETDOAs.
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10:40-11:00, Paper ThA24.3 | |
>Distributed Dynamic Event-Triggered Communication Mechanisms for Dynamic Average Consensus (I) |
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Qian, Yangyang | University of Virginia |
Xie, Yijing | University of Texas at Arlington |
Lin, Zongli | University of Virginia |
Wan, Yan | University of Texas at Arlington |
Shamash, Yacov | SUNY |
Keywords: Agents-based systems, Cooperative control, Distributed control
Abstract: This paper studies the dynamic average consensus problem of multi-agent systems under event-triggered communication. In this problem, each agent has access to a time-varying reference signal and aims to track the average of all reference signals. Distributed algorithms with event-triggered communication have been developed to achieve dynamic average consensus. Nevertheless, these existing event-triggered communication mechanisms cannot guarantee the existence of a designable positive minimum inter-event time (MIET), which is important in their practical implementation. Motivated by this observation, we propose a distributed dynamic event-triggered communication mechanism (ETCM) for each agent. It is shown that the proposed ETCM guarantees the existence of a positive MIET that is locally adjustable by tuning design parameters. It is also shown that the dynamic average consensus is achieved with any pre-specified level of accuracy. As an illustrative example, the theoretical results are applied to a networked battery energy storage system for state-of-charge balancing and desired total power tracking.
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11:00-11:20, Paper ThA24.4 | |
>Value of Information in Remote Estimation Subject to Delay and Packet Dropouts (I) |
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Wang, Siyi | Technical University of Munich |
Hirche, Sandra | Technische Universität München |
Keywords: Networked control systems, Network analysis and control, Estimation
Abstract: Emerging cyber-physical systems impel the development of advanced network scheduling schemes to utilize communication and computation resources efficiently. This paper investigates the event-based schedule for remote state estimation in networked control systems (NCSs) subject to delay and packet dropouts. The scheduler decides whether or not to send out a local estimate according to the Value of Information (VoI) metric, which measures the relative importance of an information update. In addition, we model the triggering intervals as a Markov chain and analyze the tradeoff between the estimation performance and communication cost under the proposed VoI-based scheduling for the first-order system.
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11:20-11:40, Paper ThA24.5 | |
>Event-Triggered Parameterized Control for Stabilization of Linear Systems (I) |
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Rajan, Anusree | Indian Institute of Science, Bangalore |
Tallapragada, Pavankumar | Indian Institute of Science |
Keywords: Control over communications, Networked control systems, Sampled-data control
Abstract: This paper proposes a new control method called event-triggered parameterized control (ETPC). We showcase this method by focusing on the specific problem of stabilization of linear systems. In this control method, between two consecutive events, each control input to the plant is a linear combination of a set of linearly independent scalar functions. At each event, the coefficients of the parameterized control input are chosen to minimize the error in approximating a model based control signal and then they are communicated to the actuator. We design two event-triggering rules that guarantee global asymptotic stability of the origin of the closed loop system under some conditions on the model uncertainty. We also show the existence of a uniform positive lower bound on the inter-event times. We illustrate our results through numerical examples. We compare the proposed control method with event-triggered zero-order-hold control and show a significant improvement in terms of the average inter-event times.
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11:40-12:00, Paper ThA24.6 | |
>Consistent Event-Triggered Consensus on Complete Graphs (I) |
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Antunes, Duarte | Eindhoven University of Technology, the Netherlands |
Meister, David | University of Stuttgart |
Namerikawa, Toru | Keio University |
Allgöwer, Frank | University of Stuttgart |
Heemels, W.P.M.H. | Eindhoven University of Technology |
Keywords: Agents-based systems, Stochastic optimal control, Networked control systems
Abstract: This paper starts by considering an optimal control formulation of the consensus problem on complete graphs with a cost capturing disagreement and agents modeled by integrators. An optimal control policy for this problem is shown to be the well-known consensus algorithm by which each agent resets its state to the average of its and other agents' state values received at every time step. The framework is extended to the case where agents can only exchange information periodically, with a period larger than one. Then an event-triggered control strategy is proposed that results in a better cost than that of the optimal periodic one with the same average transmission rate, that is, it is consistent. According to this strategy, each agent distributedly transmits its state if the error between its current state and a common consensus estimate based on previously transmitted agents' data exceeds a threshold.
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ThA25 |
Lotus Junior 4DE |
Informational Perspectives in Control |
Invited Session |
Chair: Ranade, Gireeja | Microsoft Research |
Co-Chair: Tanaka, Takashi | University of Texas at Austin |
Organizer: Ranade, Gireeja | University of California, Berkeley |
Organizer: Tanaka, Takashi | University of Texas at Austin |
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10:00-10:20, Paper ThA25.1 | |
>Online Variable-Length Source Coding for Minimum Bitrate LQG Control (I) |
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Cuvelier, Travis | University of Texas at Austin |
Tanaka, Takashi | University of Texas at Austin |
Heath Jr., Robert W. | North Carolina State University |
Keywords: Networked control systems, Information theory and control, Control over communications
Abstract: We propose an adaptive coding approach to achieve linear-quadratic-Gaussian (LQG) control with near-minimum bitrate prefix-free feedback. Our approach combines a recent analysis of a quantizer design for minimum rate LQG control with work on universal lossless source coding for sources on countable alphabets. It was recently demonstrated that the aforementioned quantizer's outputs are an asymptotically stationary, ergodic process. To enable LQG control with provably near-minimum bitrate, the quantizer outputs must be encoded into binary codewords efficiently. This is possible given knowledge of the quantizations' probability distributions, or of their limiting distribution. Obtaining such knowledge is challenging; the distributions do not readily admit closed form descriptions. This motivates the application of universal source coding. Our main theoretical contribution in this work is a proof that (after an invertible transformation), the quantizer outputs are random variables that fall within an exponential or power-law envelope class (depending on the plant dimension). Using ideas from universal coding on envelope classes, we develop a practical, zero-delay, fixed precision source code for the quantizer outputs. We evaluate the performance of this approach numerically, and demonstrate competitive results with respect to fundamental tradeoffs between bitrate and LQG control performance.
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10:20-10:40, Paper ThA25.2 | |
>Controllability with a Finite Data-Rate of Switched Linear Systems (I) |
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Scabin Vicinansa, Guilherme | The University of Melbourne |
Liberzon, Daniel | Univ of Illinois, Urbana-Champaign |
Keywords: Quantized systems, Switched systems, Information theory and control
Abstract: In this work, we argue that the usual notion of controllability is unfit for systems that operate with finite data-rate constraints. We deal with this issue by defining a new concept of controllability with finite data-rate. Then, we specialize our discussion to the case of switched linear systems. We state a necessary condition and a sufficient condition for our new controllability notion to hold. Next, we take advantage of the switched linear system's structure to present a simple sufficient condition for controllability with finite data-rate that only involves the controllable subspace of the individual modes and some mild assumptions about the switching signal that guarantee that our sufficient condition holds. We also present another sufficient condition for systems that activate some controllable mode often enough. In particular, we illustrate the power of this result by deriving relations between the sampling time and the Average Dwell-Time (ADT) of the switching signal that guarantee that the switched system is controllable with finite data-rate. Finally, we discuss the gap between the necessary and the sufficient conditions and show that the sufficient condition is not necessary.
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10:40-11:00, Paper ThA25.3 | |
>Experiment Design with Gaussian Process Regression with Applications to Chance-Constrained Control (I) |
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Anderson, Sean | University of California Santa Barbara |
Byl, Katie | University of California at Santa Barbara |
Hespanha, Joao P. | Univ. of California, Santa Barbara |
Keywords: Learning, Data driven control, Identification for control
Abstract: Learning for control in repeated tasks allows for well-designed experiments to gather the most useful data. We consider the setting in which we use a data-driven controller that does not have access to the true system dynamics. Rather, the controller uses inferred dynamics based on the available information. In order to acquire data that is beneficial for this controller, we present an experimental design approach that leverages the current data to improve expected control performance. We focus on the setting in which inference on the unknown dynamics is performed using Gaussian processes. Gaussian processes not only provide uncertainty quantification but also allow us to leverage structures inherit to Gaussian random variables. Through this structure, we design experiments via gradient descent on the expected control performance with respect to the experiment input. In particular, we focus on a chance-constrained minimum expected time control problem. Numerical demonstrations of our approach indicate our experimental design outperforms relevant benchmarks.
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11:00-11:20, Paper ThA25.4 | |
>Reinforcement Learning for Zero-Delay Coding Over a Noisy Channel with Feedback (I) |
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Cregg, Liam | Queen's University |
Alajaji, Fady | Queen's University |
Yuksel, Serdar | Queen's University |
Keywords: Information theory and control, Machine learning, Stochastic optimal control
Abstract: In Shannon’s classical information-theoretic lossy coding problem, one is allowed to encode long sequences of source symbols at once in order to achieve a lower distortion, which is optimal in the limit of unbounded block lengths. Such a block-coding approach is undesirable in many delay-sensitive applications, such as networked control, sensor networks and live-streaming, among others. Accordingly, we are interested in a variant of Shannon’s lossy coding problem, where one wishes to send an information source causally at a fixed rate with no delay over a channel with feedback, while minimizing the average distortion at the receiver. Thus, the classical block-coding approach is not viable. This problem has previously been studied using stochastic control techniques, leading to existence, structural, and general approximation results. However, these techniques do not provide closed-form solutions for either optimal performance or code designs, and they lead to algorithmic implementations that are computationally difficult. To address this problem, we propose a reinforcement learning approach by building on recent results on quantized Q-learning. We will consider the case of a finite-alphabet Markov source over a discrete memoryless channel. After developing some supporting technical results on regularity and stability properties of the associated Markov process, we rigorously justify convergence of a quantized Q-learning algorithm to a near-optimal policy for this problem. Finally, we illustrate our theoretical findings via simulations.
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11:20-11:40, Paper ThA25.5 | |
>Information Design in Bayesian Routing Games (I) |
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Cianfanelli, Leonardo | Politecnico Di Torino |
Ambrogio, Alexia | Politecnico Di Torino |
Como, Giacomo | Politecnico Di Torino |
Keywords: Transportation networks, Game theory
Abstract: We study optimal information provision in transportation networks when users are strategic and the network state is uncertain. An omniscient planner observes the network state and discloses information to the users with the goal of minimizing the expected travel time at the user equilibrium. Public signal policies, including full-information disclosure, are known to be inefficient in achieving optimality. For this reason, we focus on private signals and restrict without loss of generality the analysis to signals that coincide with path recommendations that satisfy obedience constraints, namely users have no incentive in deviating from the received recommendation according to their posterior belief. We first formulate the general problem and analyze its properties for arbitrary network topologies and delay functions. Then, we consider the case of two parallel links with affine delay functions, and provide sufficient conditions under which optimality can be achieved by information design. Interestingly, we observe that the system benefits from uncertainty, namely it is easier for the planner to achieve optimality when the variance of the uncertain parameters is large. We then provide an example where optimality can be achieved even if the sufficient conditions for optimality are not met.
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11:40-12:00, Paper ThA25.6 | |
>Control of Systems with Multiplicative Observation Noise (I) |
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Won, Moses | University of California, Berkeley |
Ranade, Gireeja | University of California, Berkeley |
Keywords: Information theory and control, Uncertain systems, Stability of linear systems
Abstract: We consider the control of a linear system observed over multiplicative-noise. Specifically, the controller must stabilize the system using a control action based on observations of the system state that have been multiplied by i.i.d. random variables. While there is a long history of work on this fundamental problem, much of it has focused on understanding the performance of linear controllers, and the optimal control strategy for such a system remains unknown. In this paper, we consider the case of uniform multiplicative observation noise, and provide a non-linear control strategy based on the maximum a-posteriori (MAP) estimator of the state. We explicitly compute the convergence rates of different moments of the system under this control strategy, and find that the MAP-based strategy outperforms the best memoryless linear strategy when the ``signal-to-noise'' ratio (SNR) of the multiplicative noise, i.e. the ratio of the mean to the standard deviation, is low. In the high SNR regime we see that the MAP strategy is also a linear memoryless strategy, however, it is suboptimal and is outperformed by the optimal linear controller.
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ThA26 |
Orchid Main 4301AB |
Modeling |
Regular Session |
Chair: Mironchenko, Andrii | University of Passau |
Co-Chair: Eising, Jaap | ETH Zurich |
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10:00-10:20, Paper ThA26.1 | |
>Live Systems of Varying Dimension: Modeling and Stability |
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Mironchenko, Andrii | University of Passau |
Keywords: Modeling, Hybrid systems, Nonlinear systems
Abstract: A major limitation of the classical control theory is the assumption that the state space remains stationary in time. This prevents analyzing and even formalizing the stability and control problems for open multi-agent systems whose agents may enter or leave the network, industrial processes where the sensors or actuators may be exchanged frequently, smart grids, etc. In this work, we propose a framework of live systems that covers a rather general class of systems with a time-varying state space. We argue that input-to-state stability is a proper stability notion for this class of systems, and many of the classic tools and results, such as Lyapunov methods and superposition theorems, can be extended to this setting.
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10:20-10:40, Paper ThA26.2 | |
>Design of Limit-Cycle Oscillators with Prescribed Trajectories and Phase-Response Properties Via Phase Reduction and Floquet Theory |
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Namura, Norihisa | Tokyo Institute of Technology |
Nakao, Hiroya | Tokyo Institute of Technology |
Keywords: Modeling, Model/Controller reduction
Abstract: We propose a method for designing stable limit-cycle oscillators with prescribed periodic trajectories and phase-response properties in general dimensions based on the phase reduction theory. The vector field of the oscillator is approximated by polynomials and their coefficients are optimized to satisfy required conditions. Linear stability of the periodic trajectory is ensured by imposing conditions on the eigenvalues of the monodromy matrix based on Floquet theory. We verify the validity of the proposed method by designing several types of oscillators with given properties. As an application, we design two oscillators with the same periodic trajectory but with different phase-response properties and show their distinct synchronization dynamics under the same periodic input.
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10:40-11:00, Paper ThA26.3 | |
>Interconnection Schemes in Modeling and Control |
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Borja, Pablo | University of Plymouth |
Ferguson, Joel | University of Newcastle |
van der Schaft, Arjan | Univ. of Groningen |
Keywords: Modeling, Nonlinear output feedback
Abstract: Interconnection schemes are ubiquitous in physical systems. For instance, in multi-domain systems consisting of interconnected subsystems from different physical domains. Furthermore, the interconnection of two or more systems has also been exploited to analyze and control dynamical systems, especially passive ones. To this end, the most common interconnection structure is the negative feedback interconnection. However, this approach is unsuitable to directly couple the states of the subsystems in the overall system's energy as customarily occurs in physical systems. This letter provides two interconnection approaches that overcome this issue. Notably, it is shown that these interconnection structures are suitable for decomposing passive systems into the interconnection of simpler passive subsystems. Moreover, these interconnections schemes allow the interpretation of some existing nonlinear control approaches as the interconnection of a passive plant with a passive controller. Additionally, the interpretation of the proposed interconnection structures is provided via bond graphs.
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11:00-11:20, Paper ThA26.4 | |
>Attitude Dynamics Modelling: Fractional Consensus Approach |
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Baranowski, Jerzy | AGH University of Science and Technology |
Bauer, Waldemar | AGH University of Science and Technology |
Dukała, Karolina | SWPS University of Social Sciences and Humanities |
Mozyrska, Dorota | Bialystok University of Technology |
Wyrwas, Malgorzata | Bialystok University of Technology |
Keywords: Modeling, Nonlinear systems, Stability of linear systems
Abstract: In this paper we propose a consensus model using fractional calculus, which is an emerging topic in multi-agent modeling. Fractional models have infinite memory and can be understood as a relatively simple extension of traditional calculus. We propose a model structure motivating it by psychological research. For such model we also provide a stability analysis allowing results on possibilities of consensus arising in the modelled group of agents. To achieve this, we use fractional difference equations, which illustrate our considerations for agent groups of increasing complexity.
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11:20-11:40, Paper ThA26.5 | |
>Synchronisation in Electrical Circuits with Memristors and Grounded Capacitors |
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Huijzer, Anne-Men | University of Groningen |
van der Schaft, Arjan | Univ. of Groningen |
Besselink, Bart | University of Groningen |
Keywords: Modeling, Stability of nonlinear systems, Network analysis and control
Abstract: Motivated by neuromorphic computing applications, this paper considers electrical circuits comprising memristors and grounded capacitors, connected to external sources. By using the flux-charge domain modelling approach, we will derive an initial value problem describing the dynamic behaviour of this circuit. Given an initial value and a fixed input, we will show that the fluxes in this circuit converge to an equilibrium. Furthermore, we show that when the fluxes reach this equilibrium, we achieve voltage synchronisation, i.e. no more currents are flowing through the circuit. These results are emphasised in an illustration.
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11:40-12:00, Paper ThA26.6 | |
>A Controlled Mean Field Model for Chiplet Population Dynamics |
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Nodozi, Iman | University of California, Santa Cruz |
Halder, Abhishek | Iowa State University |
Matei, Ion | Palo Alto Research Center |
Keywords: Modeling, Stochastic systems, Uncertain systems
Abstract: In micro-assembly applications, ensemble of chiplets immersed in a dielectric fluid are steered using dielectrophoretic forces induced by an array of electrode population. Generalizing the finite population deterministic models proposed in prior works for individual chiplet position dynamics, we derive a controlled mean field model for a continuum of chiplet population in the form of a nonlocal, nonlinear partial differential equation. The proposed model accounts for the stochastic forces as well as two different types of nonlocal interactions, viz. chiplet-to-chiplet and chiplet-to-electrode interactions. Both of these interactions are nonlinear functions of the electrode voltage input. We prove that the deduced mean field evolution can be expressed as the Wasserstein gradient flow of a Lyapunov-like energy functional. With respect to this functional, the resulting dynamics is a gradient descent on the manifold of joint population density functions with finite second moments that are supported on the position coordinates.
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ThB01 |
Orchid Main 4202-4306 |
Control and Optimization for Autonomous Energy Systems |
Tutorial Session |
Chair: Bernstein, Andrey | National Renewable Energy Lab (NREL) |
Co-Chair: Zhao, Changhong | The Chinese University of Hong Kong |
Organizer: Bernstein, Andrey | National Renewable Energy Lab (NREL) |
Organizer: Cavraro, Guido | National Renewable Energy Laboratory |
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13:30-13:50, Paper ThB01.1 | |
>Tutorial on Congestion Control in Multi-Area Transmission Grids Via Online Feedback Equilibrium Seeking (I) |
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Belgioioso, Giuseppe | ETH Zürich |
Bolognani, Saverio | ETH Zurich |
Pejrani, Giulia | ETHz |
Dörfler, Florian | Swiss Federal Institute of Technology (ETH) Zurich |
Keywords: Power systems, Game theory, Optimization
Abstract: Online feedback optimization (OFO) is an emerging control methodology for real-time optimal steady-state control of complex dynamical systems. This tutorial focuses on the application of OFO for the autonomous operation of large-scale transmission grids, with a specific goal of minimizing renewable generation curtailment and losses while satisfying voltage and current limits. When this control methodology is applied to multi-area transmission grids, where each area independently manages its congestion while being dynamically interconnected with the rest of the grid, a non-cooperative game arises. In this context, OFO must be interpreted as an online feedback equilibrium seeking (FES) scheme. Our analysis incorporates technical tools from game theory and monotone operator theory to evaluate the stability and robustness of multi-area grid operation. Through numerical simulations, we illustrate the key challenge of this non-cooperative setting: on the one hand, independent multi-area decisions are suboptimal compared to a centralized control scheme; on the other hand, some areas are heavily penalized by the centralized decision, which may discourage participation in the coordination mechanism.
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13:50-14:10, Paper ThB01.2 | |
>Time-Varying Feedback Optimization for Quadratic Programs with Heterogeneous Gradient Step Sizes (I) |
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Bernstein, Andrey | National Renewable Energy Lab (NREL) |
Comden, Joshua | National Renewable Energy Laboratory |
Chen, Yue | National Renewable Energy Laboratory |
Wang, Jing | National Renewable Energy Laboratory |
Keywords: Optimization algorithms, Adaptive control, Power systems
Abstract: Online feedback-based optimization has become a promising framework for real-time optimization and control of complex engineering systems. This paper surveys the recent advances in the field as well as provides novel convergence results for primal-dual online algorithms with heterogeneous step sizes for different elements of the gradient. The analysis is performed for quadratic programs and the approach is illustrated on applications for adaptive step-size and model-free online algorithms, in the context of optimal control of modern power systems.
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14:10-14:30, Paper ThB01.3 | |
>Balancing the Power Grid with Cheap Assets (I) |
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Meyn, Sean P. | Univ. of Florida |
Lu, Fan | University of Florida |
Mathias, Joel | Arizona State University |
Keywords: Power systems, Smart grid, Optimal control
Abstract: We have all heard that there is growing need to secure resources to obtain supply-demand balance in a power grid facing increasing volatility from renewable sources of energy. There are mandates for utility scale battery systems in regions all over the world, and there is a growing science of "demand dispatch" to obtain virtual energy storage from flexible electric loads such as water heaters, air conditioning, and pumps for irrigation. The question addressed in this tutorial is how to manage a large number of assets for balancing the grid. The focus is on variants of the economic dispatch problem, which may be regarded as the "feed-forward" component in an overall control architecture. 1) The resource allocation problem is identical to a finite horizon optimal control problem with degenerate cost---so called "cheap control". This implies a form of state space collapse, whose form is identified: the marginal cost for each load class evolves in a two-dimensional subspace, spanned by a scalar co-state process and its derivative. 2) The implication to distributed control is remarkable. Once the co-state process is synthesized, this common signal may be broadcast to each asset for optimal control. However, the optimal solution is extremely fragile, in a sense made clear through results from numerical studies. 3) Several remedies are proposed to address fragility. One is described through "robust training" in a particular Q-learning architecture (one approach to reinforcement learning). In numerical studies it is found that specialized training leads to more robust control solutions.
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14:30-14:50, Paper ThB01.4 | |
>Tutorial on Dynamics and Control of Grid-Connected Power Electronics and Renewable Generation (I) |
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Gross, Dominic | University of Wisconsin-Madison |
Keywords: Power systems, Power electronics, Power generation
Abstract: Electrical power systems are transitioning from fuel-based generation to renewable generation and transmission interfaced by power electronics. This transition challenges standard power system modeling, analysis, and control paradigms across timescales from milliseconds to seasons. This tutorial focuses on frequency stability on timescales of milliseconds to seconds. We first review basic results for grid-following (GFL) and grid-forming (GFM) control of voltage source converters (VSCs), typical renewable generation, and high voltage direct current (HVdc) transmission. In this context, it becomes apparent that GFL and GFM control functions are needed to operate emerging power systems. However, combining GFL resources, GFM resources, and legacy generation on the same system results in highly complex dynamics that are a significant obstacle to stability analysis. The remainder of the tutorial provides an overview of recent developments in universal GFM controls that bridge the gap between GFL and GFM control and provide a pathway to a coherent control and analysis framework accounting for power generation, power conversion, and power transmission.
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14:50-15:10, Paper ThB01.5 | |
>Modeling Unbalanced Power Flow with ∆-Connected Devices (I) |
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Low, Steven | California Institute of Technology |
Keywords: Power systems, Smart grid
Abstract: In this tutorial we present a simple approach to modeling unbalanced three-phase power flows. We allow general non-ideal models of voltage sources and ZIP loads. The basic idea is to explicitly separate a device/transformer model into an internal model, that depends on the characteristics of the single-phase devices or transformers, and a conversion rule, that depends on their configuration. This allows us to exploit common structures across different device/transformer variants and derive their external models that are general and unified. We illustrate the model by formulating a three-phase optimal power flow problem as a quadratically constrained quadratic program.
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15:10-15:30, Paper ThB01.6 | |
>Convergence of Backward/Forward Sweep for Power Flow Solution in Radial Networks (I) |
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Fang, Bohang | The Chinese University of Hong Kong |
Zhao, Changhong | The Chinese University of Hong Kong |
Low, Steven | California Institute of Technology |
Keywords: Power systems, Nonlinear systems
Abstract: Solving power flow is perhaps the most fundamental calculation related to the steady state behavior of alternating-current (AC) power systems. The normally radial (tree) topology of a distribution network induces a spatially recursive structure in power flow equations, which enables a class of efficient solution methods called backward/forward sweep (BFS). In this paper, we revisit BFS from a new perspective, focusing on its convergence. Specifically, we describe a general formulation of BFS, interpret it as a special Gauss-Seidel algorithm, and then illustrate it in a single-phase power flow model. We prove a sufficient condition under which the BFS is a contraction mapping on a closed set of safe voltages and thus converges geometrically to a unique power flow solution. We verify the convergence condition, as well as the accuracy and computational efficiency of BFS, through numerical experiments in IEEE test systems.
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ThB02 |
Melati Main 4001AB-4104 |
Learning-Based Control IV: Data-Driven Controller Design |
Invited Session |
Chair: Zeilinger, Melanie N. | ETH Zurich |
Co-Chair: Schoellig, Angela P | University of Toronto |
Organizer: Trimpe, Sebastian | RWTH Aachen University |
Organizer: Müller, Matthias A. | Leibniz University Hannover |
Organizer: Schoellig, Angela P | Technical University of Munich & University of Toronto |
Organizer: Zeilinger, Melanie N. | ETH Zurich |
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13:30-13:50, Paper ThB02.1 | |
>Data-Driven Model-Reference Control with Closed-Loop Stability: The Output-Feedback Case |
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de Jong, Thomas O. | Eindhoven University of Technology |
Breschi, Valentina | Eindhoven University of Technology |
Schoukens, Maarten | Eindhoven University of Technology |
Formentin, Simone | Politecnico Di Milano |
Keywords: Identification for control, Output regulation
Abstract: We generalize a recently introduced data-driven approach for model-reference control design with closed-loop stability guarantees to the case of single-input single-output systems with inaccessible state. By considering a dynamic controller with fixed structure and leveraging a data-based description of the closed-loop dynamics, we propose a two-stage strategy for the optimization of the controller's parameters to match the desired closed-loop behavior. By means of a benchmark simulation example, we show the potential of the proposed approach and the impact of a simple strategy to handle noisy measurements.
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13:50-14:10, Paper ThB02.2 | |
>Model-Free Data-Driven Predictive Control Using Reinforcement Learning (I) |
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Sawant, Shambhuraj | NTNU Trondheim |
Reinhardt, Dirk Peter | Norwegian University of Science and Technology |
Bahari Kordabad, Arash | Norwegian University of Science and Technology |
Gros, Sebastien | NTNU |
Keywords: Data driven control, Optimal control, Learning
Abstract: This paper proposes a novel approach for Predictive Control utilizing Reinforcement Learning (RL) and Data-Driven techniques to derive optimal control policies for real systems. Using pure input-output multi-step predictors based on Subspace Identification and RL techniques, the resulting predictive control scheme can approximate the optimal control policy of a system with high accuracy, even if the predictor cannot accurately capture the true system dynamics. One of the key contributions of the proposed approach is the extension of the framework connecting Model Predictive Control (MPC) and RL to one that does not require explicit state-space models, nor to define a notion of state at all. The paper demonstrates the efficacy of the proposed approach through an illustrative example, highlighting the ability of our approach to provide an optimal control policy for a real system without requiring any prior knowledge about its internal dynamics.
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14:10-14:30, Paper ThB02.3 | |
>The Fundamental Limitations of Learning Linear-Quadratic Regulators (I) |
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Lee, Bruce | University of Pennsylvania |
Ziemann, Ingvar | University of Pennsylvania |
Tsiamis, Anastasios | ETH Zurich |
Sandberg, Henrik | KTH Royal Institute of Technology |
Matni, Nikolai | University of Pennsylvania |
Keywords: Identification for control, Statistical learning, Linear systems
Abstract: We present a local minimax lower bound on the excess cost of designing a linear-quadratic controller from offline data. The bound is valid for any offline exploration policy that consists of a stabilizing controller and an energy bounded exploratory input. The derivation leverages a relaxation of the minimax estimation problem to Bayesian estimation, and an application of van Trees inequality. We show that the bound aligns with system-theoretic intuition. In particular, we demonstrate that the lower bound increases when the optimal control objective value increases. We also show that the lower bound increases when the system is poorly excitable, as characterized by the spectrum of the controllability gramian of the system mapping the noise to the state and the H-infinity norm of the system mapping the input to the state. We further show that for some classes of systems, the lower bound may be exponential in the state dimension, demonstrating exponential sample complexity for learning the linear-quadratic regulator.
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14:30-14:50, Paper ThB02.4 | |
>On the Design of Persistently Exciting Inputs for Data-Driven Control of Linear and Nonlinear Systems |
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Alsalti, Mohammad | Leibniz University Hannover |
Lopez, Victor G. | Leibniz University Hannover |
Müller, Matthias A. | Leibniz University Hannover |
Keywords: Identification for control
Abstract: In the context of data-driven control, persistence of excitation (PE) of an input sequence is defined in terms of a rank condition on the Hankel matrix of the input data. For nonlinear systems, recent results employed rank conditions involving collected input and state/output data, for which no guidelines are available on how to satisfy them a priori. In this paper, we first show that a set of discrete impulses is guaranteed to be persistently exciting for any controllable LTI system. Based on this result, for certain classes of nonlinear systems, we guarantee persistence of excitation of sequences of basis functions a priori, by design of the physical input only.
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14:50-15:10, Paper ThB02.5 | |
>Online Control for Adaptive Tapering of Medications (I) |
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Gradu, Paula | UC Berkeley |
Recht, Benjamin | University of California, Berkeley |
Keywords: Healthcare and medical systems, Optimal control, Statistical learning
Abstract: We investigate adaptive protocols for the elimination or reduction of the use of medications or addictive substances. We formalize this problem as online optimization, minimizing the cumulative dose subject to constraints on individual well-being. We adapt a model of addiction from the psychology literature and show how it can be described by a class of linear time-invariant systems. For such systems, the optimal policy amounts to taking the smallest dose that maintains well-being. We derive a simple protocol based on integral control that requires no system identification, only needing approximate knowledge of the instantaneous dose response. This protocol is robust to model misspecification and is able to maintain an individual's well-being during the tapering process. Numerical experiments demonstrate that the adaptive protocol outperforms non-adaptive methods in terms of both maintenance of well-being and rate of dose reduction.
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15:10-15:30, Paper ThB02.6 | |
>Differentially Flat Learning-Based Model Predictive Control Using a Stability, State, and Input Constraining Safety Filter |
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Hall, Adam W. | University of Toronto |
Greeff, Melissa | University of Toronto |
Schoellig, Angela P | University of Toronto |
Keywords: Predictive control for nonlinear systems, Machine learning, Robotics
Abstract: Learning-based optimal control algorithms control unknown systems using past trajectory data and a learned model of the system dynamics. These controllers use either a linear approximation of the learned dynamics, trading performance for faster computation, or nonlinear optimization methods, which typically perform better but can limit real-time applicability. In this work, we present a novel nonlinear controller that exploits differential flatness to achieve similar performance to state-of-the-art learning-based controllers but with significantly less computational effort. Differential flatness is a property of dynamical systems whereby nonlinear systems can be exactly linearized through a nonlinear input mapping. Here, the nonlinear transformation is learned as a Gaussian process and is used in a safety filter that guarantees, with high probability, stability as well as input and flat state constraint satisfaction. This safety filter is then used to refine inputs from a Flat Model Predictive Controller to perform constrained nonlinear learning-based optimal control through two successive convex optimizations. We compare our method to state-of-the-art learning-based control strategies and achieve similar performance, but with significantly better computational efficiency, while also respecting flat state and input constraints, and guaranteeing stability.
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ThB03 |
Melati Junior 4010A-4111 |
Gaussian Process Based Optimization and Control |
Invited Session |
Chair: Beckers, Thomas | Vanderbilt University |
Co-Chair: Bethge, Johanna | Otto-Von-Guericke University Magdeburg |
Organizer: Beckers, Thomas | Vanderbilt University |
Organizer: Bethge, Johanna | Otto-Von-Guericke University Magdeburg |
Organizer: Hirche, Sandra | Technische Universität München |
Organizer: Findeisen, Rolf | TU Darmstadt |
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13:30-13:50, Paper ThB03.1 | |
>Early Intention Prediction of Lane-Changing Based on Dual Gaussian-Mixed Hidden Markov Models (I) |
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Li, Zheng | Tianjin University |
Wang, Yijing | Tianjin University |
Zuo, Zhiqiang | Tianjin University |
Liu, Zhengxuan | Tianjin University |
Chen, Yining | Tianjin University |
Li, Hongchao | Hebei University of Technology |
Keywords: Learning, Pattern recognition and classification
Abstract: Adjacent lane-changing is one of the most dangerous maneuvers which may lead to rear-end crash, uncomfortable braking and sharp steering. If the autonomous driving system can predict the potential latent lane-changing intentions of surrounding vehicles in advance, the driver will have more time to make reasonable response. In this paper, we focus on how to give accurate and reliable prediction for latent lanechangings, especially before the vehicles merge into the target lanes. A prediction model based on dual Gaussian-mixed hidden Markov models is developed to exploit the advantages of different features more effectively. Since there is no comprehensive criteria to evaluate the accuracy and predictability performance simultaneously, we propose two new metrics for quantitative analysis as supplement to the classical indicators. Comparative validation on Next Generation Simulation (NGSIM) database shows that our model has a high recognition accuracy of 93.05% for lane-changing intention with earlier prediction over the existing homologous methods.
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13:50-14:10, Paper ThB03.2 | |
>Robust Stability of Gaussian Process Based Moving Horizon Estimation (I) |
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Wolff, Tobias M. | Leibniz University Hannover |
Lopez, Victor G. | Leibniz University Hannover |
Müller, Matthias A. | Leibniz University Hannover |
Keywords: Observers for nonlinear systems, Learning, Uncertain systems
Abstract: In this paper, we introduce a Gaussian process based moving horizon estimation (MHE) framework. The scheme is based on offline collected data and offline hyperparameter optimization. In particular, compared to standard MHE schemes, we replace the mathematical model of the system by the posterior mean of the Gaussian process. To account for the uncertainty of the learned model, we exploit the posterior variance of the learned Gaussian process in the weighting matrices of the cost function of the proposed MHE scheme. We prove practical robust exponential stability of the resulting estimator using a recently proposed Lyapunov-based proof technique. Finally, the performance of the Gaussian process based MHE scheme is illustrated via a nonlinear system.
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14:10-14:30, Paper ThB03.3 | |
>Learning a Gaussian Process Approximation of a Model Predictive Controller with Guarantees (I) |
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Rose, Alexander | Technical University of Darmstadt |
Pfefferkorn, Maik | Otto-Von-Guericke-Universität Magdeburg |
Nguyen, Hoang Hai | TU Darmstadt |
Findeisen, Rolf | TU Darmstadt |
Keywords: Predictive control for nonlinear systems, Learning, Optimization
Abstract: Model predictive control effectively handles complex dynamical systems with constraints, but its high computational demand often makes real-time application infeasible. We propose using Gaussian process regression to learn an approximation of the controller offline for online use. Our approach incorporates a robust predictive control scheme and provides bounds on approximation errors to ensure recursive feasibility and input-to-state stability. Exploiting a sampling-based scenario approach, we develop an efficient sampling strategy and guarantee that, with high probability, the approximation error remains within acceptable bounds. Our method demonstrates enhanced efficiency and reduced computational demand in an example application.
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14:30-14:50, Paper ThB03.4 | |
>Data-Driven Reachability Analysis for Gaussian Process State Space Models (I) |
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Griffioen, Paul | University of California, Berkeley |
Arcak, Murat | University of California, Berkeley |
Keywords: Data driven control, Uncertain systems, Statistical learning
Abstract: Gaussian process state space models are becoming common tools for the analysis and design of nonlinear systems with uncertain dynamics. When designing control policies for these systems, safety is an important property to consider. In this paper, we provide safety guarantees by computing finite-horizon forward reachable sets for Gaussian process state space models. We use data-driven reachability analysis to provide exact probability measures for state trajectories of arbitrary length, even when no data samples are available. We investigate two numerical examples to demonstrate the power of this approach, such as providing highly non-convex reachable sets and detecting holes in the reachable set.
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14:50-15:10, Paper ThB03.5 | |
>Safe Explorative Bayesian Optimization - towards Personalized Treatments in Plasma Medicine (I) |
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Chan, Kimberly J | University of California Berkeley |
Paulson, Joel | The Ohio State University |
Mesbah, Ali | University of California, Berkeley |
Keywords: Optimization, Process Control
Abstract: This paper considers the problem of Bayesian optimization (BO) for systems with safety-critical constraints. Recent work has shown that a theoretically consistent way to account for constraints in BO is to relax the constraint functions such that the feasible region has a high probability of containing the global solution. However, by construction, these approaches are unable to ensure safe/feasible operation at every query, which is unacceptable in safety-critical applications. Alternatively, safe BO methods force the query points to remain in the interior of a partially-revealed safety region, which may result in unacceptable (and unquantified) performance losses. This paper presents a new safe BO method that avoids these performance losses by systematically incorporating potential performance gains from enlargement of the safety region. The proposed method avoids getting stuck at suboptimal points based on a potentially small initial safety region due to limited initial exploration of the safety boundary. The performance of the proposed method is demonstrated for safe control of a cold atmospheric plasma jet towards personalized plasma medicine.
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15:10-15:30, Paper ThB03.6 | |
>Primal-Dual Contextual Bayesian Optimization for Control System Online Optimization with Time-Average Constraints (I) |
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Xu, Wenjie | EPFL |
Jiang, Yuning | EPFL |
Svetozarevic, Bratislav | University of Zurich |
Jones, Colin N. | EPFL |
Keywords: Machine learning, Optimization
Abstract: This paper studies the problem of online performance optimization of constrained closed-loop control systems, where both the objective and the constraints are unknown black-box functions affected by exogenous time-varying contextual disturbances. A primal-dual contextual Bayesian optimization algorithm is proposed that achieves sublinear cumulative regret with respect to the dynamic optimal solution under certain regularity conditions. Furthermore, the algorithm achieves zero time-average constraint violation, ensuring that the average value of the constraint function satisfies the desired constraint. The method is applied to both sampled instances from Gaussian processes and a continuous stirred tank reactor parameter tuning problem; simulation results show that the method simultaneously provides close-to-optimal performance and maintains constraint feasibility on average. This contrasts current state-of-the-art methods, which either suffer from large cumulative regret or severe constraint violations for the case studies presented.
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ThB04 |
Simpor Junior 4913 |
Learning and Control for Accessible, Safe, and Equitable Transportation |
Invited Session |
Chair: Malikopoulos, Andreas A. | University of Delaware |
Co-Chair: Salazar, Mauro | Eindhoven University of Technology |
Organizer: Malikopoulos, Andreas A. | Cornell University |
Organizer: Cassandras, Christos G. | Boston University |
Organizer: Wu, Cathy | UC Berkeley |
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13:30-13:50, Paper ThB04.1 | |
>A Time-Invariant Network Flow Model for Two-Person Ride-Pooling Mobility-On-Demand (I) |
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Paparella, Fabio | Eindhoven University of Technology |
Pedroso, Leonardo | Eindhoven University of Technology |
Hofman, Theo | Technische Universiteit Eindhoven |
Salazar, Mauro | Eindhoven University of Technology |
Keywords: Transportation networks, Traffic control, Optimization
Abstract: This paper presents a time-invariant network flow model capturing two-person ride-pooling that can be integrated within design and planning frameworks for Mobility-on-Demand systems. In these type of models, the arrival process of travel requests is described by a Poisson process, meaning that there is only statistical insight into request times, including the probability that two requests may be pooled together. Taking advantage of this feature, we devise a method to capture ride-pooling from a stochastic mesoscopic perspective. This way, we are able to transform the original set of requests into an equivalent set including pooled ones which can be integrated within standard network flow problems, which in turn can be efficiently solved with off-the-shelf LP solvers for a given ride-pooling request assignment. Thereby, to compute such an assignment, we devise a polynomial-time algorithm that is optimal w.r.t. an approximated version of the problem. Finally, we perform a case study of Sioux Falls, USA, where we quantify the effects that waiting time and experienced delay have on the vehicle-hours traveled. Our results suggest that the higher the demands per unit time, the lower the waiting time and delay experienced by users. In addition, for a sufficiently large number of demands per unit time, with a maximum waiting time and experienced delay of 5 minutes, more than 90% of the requests can be pooled.
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13:50-14:10, Paper ThB04.2 | |
>Credit-Based Congestion Pricing: Equilibrium Properties and Optimal Scheme Design (I) |
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Jalota, Devansh | Stanford University |
Lazarus, Jessica | University of California, Berkeley |
Bayen, Alexandre | University of California, Berkeley |
Pavone, Marco | Stanford University |
Keywords: Transportation networks, Game theory, Optimization
Abstract: Credit-based congestion pricing (CBCP) has emerged as a mechanism to alleviate the social inequity concerns of road congestion pricing - a promising strategy for traffic congestion mitigation - by providing low-income users with travel credits to offset some of their toll payments. While CBCP offers immense potential for addressing inequity issues that hamper the practical viability of congestion pricing, the deployment of CBCP in practice is nascent, and the potential efficacy and optimal design of CBCP schemes have yet to be formalized. In this work, we study the design of CBCP schemes to achieve particular societal objectives and investigate their influence on traffic patterns when routing heterogeneous users with different values of time (VoTs) on a multi-lane highway with an express lane (EL). To this end, we introduce a new non-atomic congestion game model of a mixed-economy, wherein eligible users receive travel credits while the remaining ineligible users pay out-of-pocket to use the EL. In this setting, we investigate the effect of CBCP schemes on traffic patterns by characterizing the properties (i.e., existence, comparative statics) of the corresponding Nash equilibria and, in the setting when eligible users have time-invariant VoTs, develop a convex program to compute these equilibria. We further present a bi-level optimization framework to design optimal CBCP schemes to achieve a central planner’s societal objectives. Finally, we conduct numerical experiments based on a case study of the San Mateo 101 Express Lanes Project, one of the first CBCP pilots. Our results demonstrate the potential of CBCP to enable low-income users to avail of the travel time savings provided by congestion pricing on ELs while having comparatively low impacts on the travel costs of other road users.
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14:10-14:30, Paper ThB04.3 | |
>Decentralized Control of Intercity Electric Automated Buses Via Time-Varying Objective Prioritization (I) |
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Pasquale, Cecilia | University of Genova |
Sacone, Simona | University of Genova |
Siri, Silvia | University of Genova |
Ferrara, Antonella | University of Pavia |
Keywords: Autonomous vehicles, Emerging control applications, Optimal control
Abstract: This paper considers electric automated buses traveling in inter-urban roads and following a given route including stops, that must be reached according to a given timetable. Some of these stops are provided with a charging infrastructure allowing to charge the bus batteries. The paper proposes a decentralized control scheme for determining the optimal speed profiles, the dwell and charging times of the buses, by taking into account the traffic conditions along the road through a suitable traffic flow prediction model. Two objectives are considered contemporarily: the minimization of the deviations from the timetable and the minimization of the energy lack at the end of the bus route. To attain both these conflicting objectives, a lexicographic approach is adopted to design the controller which considers that, depending on the system state, the priority of the two objectives can change. Accordingly, the proposed control scheme changes the objective prioritization in real time and switches between two different lexicographic-based optimal control solutions. Some tests are discussed in the paper to show the effectiveness of the proposed control scheme.
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14:30-14:50, Paper ThB04.4 | |
>Mean-Field Learning for Day-To-Day Departure Time Choice with Mode Switching (I) |
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Wang, Ben | University of Michigan |
Luo, Qi | Clemson University |
Yin, Yafeng | University of Michigan |
Keywords: Transportation networks, Mean field games, Iterative learning control
Abstract: Understanding travelers' day-to-day departure time choice (DDTC) is vital for managing traffic congestion, especially in multi-modal transportation systems. While providing real-time traffic information and alternative trip plans brings convenience to travelers, their collective travel patterns may conversely lead to unstable traffic equilibrium states. We investigate a DDTC problem with mode switching in this paper. A group of heterogeneous agents can adaptively choose their modes and departure times to minimize total travel costs in a dynamic game. Using a customized hierarchical soft actor-critic (HSAC) algorithm with a continuum approximation of other agents, the traffic dynamics will converge to an approximate Markovian Perfect Equilibrium (MPE). Our findings also shed light on changes in long-term travel behavior due to the widespread deployment of emerging mobility and travel information technology. This approach serves as a foundation for promoting intelligent travel plans through adaptive traffic control policies.
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14:50-15:10, Paper ThB04.5 | |
>Urgency-Aware Routing in Single Origin-Destination Itineraries through Artificial Currencies (I) |
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Pedroso, Leonardo | Eindhoven University of Technology |
Heemels, W.P.M.H. | Eindhoven University of Technology |
Salazar, Mauro | Eindhoven University of Technology |
Keywords: Game theory, Traffic control
Abstract: Within mobility systems, the presence of self-interested users can lead to aggregate routing patterns that are far from the societal optimum which could be achieved by centrally controlling the users' choices. In this paper, we design a fair incentive mechanism to steer the selfish behavior of the users to align with the societally optimal aggregate routing. The proposed mechanism is based on an artificial currency that cannot be traded or bought, but only spent or received when traveling. Specifically, we consider a parallel-arc network with a single origin and destination node within a repeated game setting whereby each user chooses from one of the available arcs to reach their destination on a daily basis. In this framework, taking faster routes comes at a cost, whereas taking slower routes is incentivized by a reward. The users are thus playing against their future selves when choosing their present actions. To capture this complex behavior, we assume the users to be rational and to minimize an urgency-weighted combination of their immediate and future discomfort. To design the optimal pricing, we first derive a closed-form expression for the best individual response strategy. Second, we formulate the pricing design problem for each arc to achieve the societally optimal aggregate flows, and reformulate it so that it can be solved with gradient-free optimization methods. Our numerical simulations show that it is possible to achieve a near-optimal routing whilst significantly reducing the users' perceived discomfort when compared to a centralized optimal but urgency-unaware policy.
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15:10-15:30, Paper ThB04.6 | |
>Coordination for Connected Automated Vehicles at Merging Roadways in Mixed Traffic Environment (I) |
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Le, Viet-Anh | University of Delaware |
Wang, Hao | University of Michigan |
Orosz, Gabor | University of Michigan |
Malikopoulos, Andreas A. | Cornell University |
Keywords: Traffic control, Autonomous vehicles, Optimal control
Abstract: In this paper, we present an optimal control framework to address motion coordination of connected automated vehicles (CAVs) in the presence of human-driven vehicles (HDVs) in merging scenarios. Our framework combines an unconstrained trajectory solution of a low-level energy-optimal control problem with an upper-level optimization problem that yields the minimum travel time for CAVs. We predict the future trajectories of the HDVs using Newell's car-following model. To handle potential deviations of HDVs' actual behavior from the predicted one, we design a safety filter for CAVs based on control barrier functions. The effectiveness of the proposed control framework is demonstrated via simulations with heterogeneous human driving behaviors.
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ThB05 |
Simpor Junior 4912 |
Recent Advances in Distributed Optimization and Its Applications |
Invited Session |
Chair: Xu, Jinming | Zhejiang University |
Co-Chair: Pu, Shi | The Chinese University of Hong Kong, Shenzhen |
Organizer: Xu, Jinming | Zhejiang University |
Organizer: Pu, Shi | Shenzhen Research Institute of Big Data, the Chinese University of Hong Kong, Shenzhen |
Organizer: Sun, Ying | The Pennsylvania State University |
Organizer: Wai, Hoi-To | The Chinese University of Hong Kong |
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13:30-13:50, Paper ThB05.1 | |
>A Linearly Convergent Robust Compressed Push-Pull Method for Decentralized Optimization (I) |
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Liao, Yiwei | The Chinese University of Hong Kong, Shenzhen |
Li, Zhuorui | Shenzhen Research Institute of Big Data |
Pu, Shi | Shenzhen Research Institute of Big Data, the Chinese University |
Keywords: Communication networks, Optimization algorithms, Quantized systems
Abstract: In the modern paradigm of multi-agent networks, communication has become one of the main bottlenecks for decentralized optimization, where a large number of agents are involved in minimizing the average of the local cost functions. In this paper, we propose a robust compressed push-pull algorithm (RCPP) that combines gradient tracking with communication compression. In particular, RCPP is compatible with a much more general class of compression operators that allow both relative and absolute compression errors. We show that RCPP achieves linear convergence rate for smooth objective functions satisfying the Polyak-Łojasiewicz condition over general directed networks. Numerical examples verify the theoretical findings and demonstrate the efficiency, flexibility, and robustness of the proposed algorithm.
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13:50-14:10, Paper ThB05.2 | |
>Differentially-Private Distributed Optimization with Guaranteed Optimality (I) |
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Wang, Yongqiang | Clemson University |
Nedich, Angelia | Arizona State University |
Keywords: Optimization algorithms, Control Systems Privacy, Cooperative control
Abstract: Privacy protection is gaining increased attention in distributed optimization and learning. As differential privacy is becoming a de facto standard for privacy preservation, recently results have emerged integrating differential privacy with distributed optimization. However, to ensure differential privacy (with a finite cumulative privacy budget), all existing approaches have to sacrifice provable convergence to the optimal solution. In this paper, we propose a differentially-private distributed optimization algorithm that can ensure, for the first time, both epsilon-differential privacy and optimality, even on the infinite time horizon. Numerical simulation results confirm the effectiveness of the proposed approach.
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14:10-14:30, Paper ThB05.3 | |
>A Distributed Stochastic First-Order Method for Strongly Concave-Convex Saddle Point Problems (I) |
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Qureshi, Muhammad I. | Tufts University |
Khan, Usman A. | Tufts University |
Keywords: Optimization algorithms, Distributed control, Machine learning
Abstract: In this paper, we propose a distributed stochastic first-order method for saddle point problems over strongly connected graphs. Existing methods generally suffer from a steady-state error that arises due to the heterogeneous nature of data distribution (captured by the local versus global cost gaps) and the variance of the stochastic gradients. We propose~SGDA, a distributed stochastic gradient descent ascent method that uses network-level textit{gradient tracking} to eliminate the steady-state error component due to the local versus global cost gap. We show that~SGDA converges linearly to an error ball around the unique saddle point for sufficiently small constant step-sizes when the global cost is strongly concave-convex (a necessary condition for the existence of a unique saddle point). Moreover, we show that the size of this error ball depends on the variance of the stochastic gradients. We provide numerical experiments to illustrate the convergence properties of~SGDA for different applications and highlight the significance of gradient tracking. We also show the performance of~SGDA for training modern applications like distributed generative adversarial networks (GANs).
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14:30-14:50, Paper ThB05.4 | |
>On First-Order Meta-Reinforcement Learning with Moreau Envelopes (I) |
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Toghani, Mohammad Taha | Rice University |
Perez-Salazar, Sebastian | Rice University |
Uribe, Cesar A. | Rice University |
Keywords: Machine learning, Optimization, Markov processes
Abstract: Meta-Reinforcement Learning (MRL) is a promising framework for training agents that can quickly adapt to new environments and tasks. In this work, we study the MRL problem under the policy gradient formulation, where we propose a novel algorithm that uses Moreau envelope surrogate regularizers to jointly learn a meta policy that is adjustable to the environment of each individual task. Our algorithm, called Moreau Envelope Meta-Reinforcement Learning (MEMRL), learns a meta-policy that can adapt to a distribution of tasks by efficiently updating the policy parameters using a combination of gradient-based optimization and Moreau Envelope regularization. Moreau Envelopes provide a smooth approximation of the policy optimization problem, which enables us to apply standard optimization techniques and converge to an appropriate stationary point. We provide a detailed analysis of the MEMRL algorithm, where we show a sublinear convergence rate to a first-order stationary point for non-convex policy gradient optimization. We finally show the effectiveness of MEMRL on a multi-task 2D-navigation problem.
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14:50-15:10, Paper ThB05.5 | |
>Distributed Nash Equilibrium Seeking in N-Cluster Games with Fully Uncoordinated Constant Step-Sizes (I) |
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Pang, Yipeng | Nanyang Technological University |
Hu, Guoqiang | Nanyang Technological University, Singapore |
Keywords: Game theory, Optimization algorithms, Distributed control
Abstract: This paper studies a class of non-cooperative games, known as N-cluster game, which subsumes both cooperative and non-cooperative nature among multiple agents in the two problems. Moreover, we consider a partial-decision information game setup, i.e., the agents have no direct access to the decisions of other agents in all clusters, and hence need to communicate with each other. We propose a distributed NE seeking algorithm by a synthesis of consensus and gradient tracking. Unlike other existing discrete-time methods for N-cluster games where a common step-size is either publicly known by all agents or only known by agents from the same cluster, the proposed algorithm can work with fully uncoordinated constant step-sizes, which allows the agents (both within and across the clusters) to choose their own preferred step-sizes. We prove that all agents' decisions converge linearly to their corresponding NE so long as the largest step-size and the heterogeneity of the step-sizes are small. We verify the derived results through a numerical example in a Cournot competition game.
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15:10-15:30, Paper ThB05.6 | |
>A Loopless Distributed Algorithm for Personalized Bilevel Optimization (I) |
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Niu, Youcheng | Zhejiang University |
Sun, Ying | The Pennsylvania State University |
Huang, Yan | Zhejiang University |
Xu, Jinming | Zhejiang University |
Keywords: Optimization algorithms, Cooperative control, Agents-based systems
Abstract: This paper studies a class of personalized distributed bilevel optimization problems over networks, where nodes aim at jointly optimizing the sum of outer-level objectives that depend on the solution of inner-level optimization problems. The existing algorithms for distributed bilevel optimization problems usually require extra computation loops for estimating hypergradients. To facilitate computational efficiency, we develop a loopless distributed algorithm that employs certain steps to approximate the optimal solution of inner-level optimization problems, and track Hessian-inverse-vector products in a recursive manner. We prove that for stochastic nonconvex-strongly-convex problems, the proposed algorithm achieves the state of the art O(epsilon ^{-2}) communication cost, while improving the computational cost by O(log(frac{1}{epsilon})). Numerical experiments validate our theoretical findings.
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ThB06 |
Simpor Junior 4911 |
Estimation V |
Regular Session |
Chair: Solo, Victor | University of New South Wales |
Co-Chair: Dokoupil, Jakub | CEITEC, Brno University of Technology |
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13:30-13:50, Paper ThB06.1 | |
>Stator Flux Linkage Estimation of Synchronous Machines Based on Integration Error Estimation for Improved Transient Performance |
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Jang, Seunghoon | GIST |
Choi, Kyunghwan | GIST |
Keywords: Electrical machine control, Estimation, Identification for control
Abstract: The stator flux linkages of synchronous machines (SMs) are generally estimated by integrating their differential equations in the stationary frame. The technical challenge is removing the integration error arising from inaccurate integrator inputs and initial values. The conventional method uses a frequency domain approach to remove the integration error as a DC component by designing a high-pass filter. However, the frequency domain approach also affects irrelevant frequency components other than the DC component; thus, the magnitude or phase of the estimates could be distorted. Therefore, this study presents a novel stator flux linkage estimator for SMs, where the integration error is estimated in the time domain and subtracted from the integration result. This time domain approach does not affect other components than the integration error, guaranteeing accurate estimation. The key idea to estimating the integration error is using a linear state observer based on a circular motion of the stator flux linkages in the stationary frame. Simulation results obtained using a 35-kW SM drive demonstrate that the proposed estimator has significantly improved transient performance compared to existing methods.
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13:50-14:10, Paper ThB06.2 | |
>State Space Subspace Noise Modeling with Guaranteed Stability |
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Solo, Victor | University of New South Wales |
Rong, Xinhui | University of New South Wales |
Keywords: Subspace methods, Identification, Estimation
Abstract: A fundamental problem for state space system identification is guaranteeing stability of the fitted model. Here we consider state space subspace methods for noise models. The few existing algorithms that guarantee stability have various limitations. Most do not scale well to large state space dimension; have statistical biases and some have arbitrary tuning parameters that can cause bias. Here we present a new simple, computationally cheap method that guarantees stability and needs no tuning parameters. We illustrate its strong performance in comparative simulations.
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14:10-14:30, Paper ThB06.3 | |
>Recursive Variational Inference for Total Least-Squares |
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Friml, Dominik | Brno University of Technology |
Vaclavek, Pavel | Brno University of Technology |
Keywords: Variational methods, Estimation, Identification
Abstract: This article analyzes methods for deriving credible intervals to facilitate errors-in-variables identification by expanding on Bayesian total least squares. The credible intervals are approximated employing Laplace and variational approximations of the intractable posterior density function. Three recursive identification algorithms providing an approximation of the credible intervals for inference with the Bingham and the Gaussian priors are proposed. The introduced algorithms are evaluated on numerical experiments, and a practical example of application on battery cell total capacity estimation compared to the state-of-the-art algorithms is presented.
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14:30-14:50, Paper ThB06.4 | |
>Recursive Identification of the ARARX Model Based on the Variational Bayes Method |
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Dokoupil, Jakub | CEITEC, Brno University of Technology |
Vaclavek, Pavel | Brno University of Technology |
Keywords: Variational methods, Identification, Estimation
Abstract: Bayesian parameter estimation of autoregressive (AR) with exogenous input (X) systems in the presence of colored model noise is addressed. The stochastic system under consideration is driven by colored noise that arises from passing an initially white noise through an AR filter. Owing to the additional AR filter, the ARARX schema provides more flexibility than the ARX one. The gained flexibility is countered by the fact that the ARARX system is no longer linear-in-parameters unless the white noise components or the AR noise filter are available. This paper analyzes the problem of estimating the unknown coefficients of the ARARX system and the model noise precision under conditions where the AR noise filter is both available and unavailable. While the former condition reduces the estimation problem to standard linear least squares, the latter one gives rise to an analytically intractable estimation problem. The intractability is resolved by the distributional approximation technique based on the variational Bayes (VB) method.
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14:50-15:10, Paper ThB06.5 | |
>A Plane-Based LiDAR Odometry Method for Man-Made Scene |
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Yan, Zihao | Harbin Institute of Technology, Shenzhen |
Li, Peng | Harbin Institute of Technology, Shenzhen |
Wang, Rui | Harbin Institute of Technology, Shenzhen |
Chen, Boli | University College London |
Keywords: Autonomous robots, Estimation, Learning
Abstract: In this paper, a plane-based LiDAR odometry method is proposed. SLAM is an essential part of the autonomous robotic design that provides the estimated pose of a robot. Instead of using the point cloud map as in most existing works, the proposed method constructs a map consisting of a series of planes for estimating the pose in an efficient and accurate way. The plane map method reduces the number of objects processed in the map compared to point cloud map methods. Every time a LiDAR scan is received, the scan is voxelized and the planes included are extracted. The planes are matched with their counterparts in the plane map. Subsequently, the pose is optimized iteratively to get an accurate pose estimate. With the optimized pose, the plane map is updated. The effectiveness of the proposed method is verified by both public datasets and real-world experiments. The results show that the plane map based method can achieve accurate SLAM with a processing rate of more than 20 Hz in both indoor and outdoor scenarios in comparison with some recent LiDAR SLAM algorithms.
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15:10-15:30, Paper ThB06.6 | |
>Responsible and Effective Federated Learning in Financial Services: A Comprehensive Survey |
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Shi, Yueyue | South China University of Technology |
Song, Hengjie | South China University of Technology |
Xu, Jun | Standard Chartered Bank |
Keywords: Finance, Machine learning, Control Systems Privacy
Abstract: The financial sector is increasingly leveraging Artificial Intelligence (AI) to deliver intelligent, automated, and personalized services. However, it encounters significant data privacy challenges due to the dispersion of financial data across various entities. Federated Learning (FL) offers a potential solution by facilitating AI model training at the source of data, albeit with certain challenges. Irresponsible utilization of FL can compromise stakeholder interests, and the prevalent heterogeneity in data spaces in numerous financial FL scenarios can impede FL's performance. These complications necessitate the development of a Responsible and Effective Federated Learning (RE-FL) system in finance. In this paper, we explore the interdisciplinary field of RE-FL in finance and guide readers to understand this area thoroughly. We present a taxonomy of RE-FL approaches that address the concerns of stakeholders in FL-based financial services and identify six major dimensions: accountability, controllability, fairness, privacy, security, and effectiveness. We also propose potential directions for future research. To our understanding, this is the first literature review conducted on RE-FL in the financial sector.
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ThB07 |
Simpor Junior 4813 |
Game Theory IV |
Regular Session |
Chair: Zhu, Quanyan | New York University |
Co-Chair: Reddy, Puduru Viswanadha | Indian Institute of Technology Madras |
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13:30-13:50, Paper ThB07.1 | |
>Optimal Intervention in Non-Binary Super-Modular Games |
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Messina, Sebastiano | Polytechnic of Turin |
Como, Giacomo | Politecnico Di Torino |
Durand, Stephane | Politecnico Di Torino |
Fagnani, Fabio | Politecnico Di Torino |
Keywords: Game theory, Network analysis and control
Abstract: We study intervention design problems for general finite non-binary super-modular games. The considered interventions consist in constraining or incentivizing the players to play actions above designed lower bounds, with a cost for the system planner that is a separable increasing function of such bounds. We study the intervention of minimum cost for which a best response learning algorithm leads the system to its greatest Nash equilibrium. We show that, if the utility functions are unimodal, then the optimal intervention problem can be reformulated in terms of improvement paths, leading to a low complexity distributed iterative algorithm for its solution.
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13:50-14:10, Paper ThB07.2 | |
>A Semi-Decentralized Tikhonov-Based Algorithm for Optimal Generalized Nash Equilibrium Selection |
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Benenati, Emilio | Technische Universiteit Delft |
Ananduta, Wicak | Flemish Institute for Technological Research (VITO) |
Grammatico, Sergio | Delft University of Technology |
Keywords: Game theory, Optimization algorithms, Variational methods
Abstract: To optimally select a generalized Nash equilibrium, in this paper, we consider a semi-decentralized algorithm based on a double-layer Tikhonov regularization algorithm. Technically, we extend the Tikhonov method for equilibrium selection to generalized games. Next, we couple such an algorithm with the preconditioned forward-backward splitting, which guarantees linear convergence to a solution of the inner layer problem and allows for a semi-decentralized implementation. We then establish a conceptual connection and draw a comparison between the considered algorithm and the hybrid steepest descent method, the other known distributed approach for solving the equilibrium selection problem.
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14:10-14:30, Paper ThB07.3 | |
>Equilibration of Coordinating Imitation and Best-Response Dynamics |
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Hasheminejad, Nazanin | Brock University |
Ramazi, Pouria | Brock University |
Keywords: Game theory, Network analysis and control
Abstract: Decision-making individuals are often considered to be either emph{imitators} who copy the action of their most successful neighbors or emph{best-responders} who maximize their benefit based on the frequency of their neighbors. In the context of emph{coordination games}, where individuals earn more if they take the same action as those of their neighbors, by means of potential functions, it was shown that populations of all imitators and populations of all best-responders equilibrate in finite time when they become active to update their decisions sequentially. However, for mixed populations of the two, the equilibration was shown only for specific finite activation sequences. It is therefore, unknown, whether a potential function also exists for mixed populations or if there actually exists a counter example where an activation sequence prevents the population from reaching an equilibrium. We show that the number of consecutive individuals who have taken the same action in a emph{path} network serves as a potential function, leading to equilibration, and that this result can be extended to emph{sparse trees}. The existence of a potential function for other types of networks remains an open problem.
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14:30-14:50, Paper ThB07.4 | |
>Linear-Quadratic Mean-Field-Type Difference Games with Coupled Affine Inequality Constraints |
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Mohapatra, Partha Sarathi | Indian Institute of Technology, Madras |
Reddy, Puduru Viswanadha | Indian Institute of Technology Madras |
Keywords: Game theory, Optimal control, Mean field games
Abstract: In this paper, we study a class of linear-quadratic mean-field-type difference games with coupled affine inequality constraints. We show that the mean-filed-type equilibrium can be characterized by the existence of a multiplier process which satisfies some implicit complementarity conditions. Further, we show that the equilibrium strategies can be computed by reformulating these conditions as a single large-scale linear complementarity problem. We illustrate our results with an energy storage problem arising in the management of microgrids.
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14:50-15:10, Paper ThB07.5 | |
>Learning Rationality in Potential Games |
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Clarke, Stefan | Princeton University |
Dragotto, Gabriele | Princeton University |
Fernández Fisac, Jaime | Princeton University |
Stellato, Bartolomeo | Princeton University |
Keywords: Game theory, Optimization, Optimization algorithms
Abstract: We propose a stochastic first-order algorithm to learn the rationality parameters of simultaneous and non- cooperative potential games, i.e., the parameters of the agents’ optimization problems. Our technique combines (i.) an active- set step that enforces that the agents play at a Nash equilibrium and (i.) an implicit-differentiation step to update the estimates of the rationality parameters. We detail the convergence prop- erties of our algorithm and perform numerical experiments on Cournot and congestion games, showing that our algorithm effectively finds high-quality solutions (in terms of out-of- sample loss) and scales to large datasets.
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15:10-15:30, Paper ThB07.6 | |
>On the Price of Transparency: A Comparison between Overt Persuasion and Covert Signaling |
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Li, Tao | New York University |
Zhu, Quanyan | New York University |
Keywords: Game theory, Optimization
Abstract: Transparency of information disclosure has always been considered an instrumental component of effective governance, accountability, and ethical behavior in any organization or system. However, a natural question follows: emph{what is the cost or benefit of being transparent}, as one may suspect that transparency imposes additional constraints on the information structure, decreasing the maneuverability of the information provider. This work proposes and quantitatively investigates the emph{price of transparency} (PoT) in strategic information disclosure by comparing the perfect Bayesian equilibrium payoffs under two representative information structures: overt persuasion and covert signaling models. PoT is defined as the ratio between the payoff outcomes in covert and overt interactions. As the main contribution, this work develops a two-stage-bilinear (TSB) programming approach to solve for non-degenerate perfect Bayesian equilibria of dynamic incomplete information games with finite states and actions. Using TSB, we show that it is always in the information provider's interest to choose the transparent information structure, as 0leq textrm{PoT}leq 1. The upper bound is attainable for any strictly Bayesian-posterior competitive games, of which zero-sum games are a particular case. For continuous games, the PoT, still upper-bounded by 1, can be arbitrarily close to 0, indicating the tightness of the lower bound. This tight lower bound suggests that the lack of transparency can result in significant loss for the provider.
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ThB08 |
Simpor Junior 4812 |
Optimal Control V |
Regular Session |
Chair: Nikitina, Viktoriya | University of the Bundeswehr Munich |
Co-Chair: Kerrigan, Eric C. | Imperial College London |
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13:30-13:50, Paper ThB08.1 | |
>Accelerating Soft-Constrained MPC for Linear Systems through Online Constraint Removal |
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Nouwens, S.A.N. | Eindhoven University of Technology |
Paulides, Maarten | Erasmus MC Cancer Institute |
Heemels, W.P.M.H. | Eindhoven University of Technology |
Keywords: Optimal control, Predictive control for linear systems, Constrained control
Abstract: Optimization-based controllers, such as Model Predictive Control (MPC), have attracted significant research interest due to their intuitive concept, constraint handling capabilities, and natural application to multi-input multi-output systems. However, the computational complexity of solving a receding horizon problem at each time step remains a challenge for the deployment of MPC. This is particularly the case for systems constrained by many inequalities. In this paper, we present an extension to the recently introduced concept of constraint-adaptive MPC (ca-MPC), where at each time step a subset of the constraints is removed from the optimization problem, thereby accelerating the optimization procedure, while resulting in identical closed-loop behavior. The present paper extends this framework to soft-constrained MPC by detecting and removing constraints based on sub-optimal predicted input sequences. These input sequences, in turn, provide an ellipsoidal bound on the true minimizer, which can be used to remove constrains from the optimization problem, as we will show. Generating sub-optimal input sequences for soft-constrained MPC is easy due to the receding horizon principle and the inclusion of slack variables. We will translate these new ideas explicitly into an offset-free output tracking problem. We then demonstrate its effectiveness on a two-dimensional thermal output tracking problem. Here, we will show a three order of magnitude improvement in computational time and a large reduction in constraints required for the optimization problem.
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13:50-14:10, Paper ThB08.2 | |
>Complexity-Bounded Relaxed Dynamic Programming |
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Beumer, Ruben | Eindhoven University of Technology (TU/e) |
Molengraft, René van de | Eindhoven University of Technology |
Antunes, Duarte | Eindhoven University of Technology, the Netherlands |
Keywords: Optimal control, Optimization algorithms, LMIs
Abstract: The idea behind relaxed dynamic programming for optimal control problems is to settle with a suboptimal but simpler control policy that guarantees a cost within a fixed constant factor from the optimal cost. Such a policy results from parameterized approximate value functions and the complexity of these functions determines the complexity of the policy. Typically, the more stringent the constant factor from the optimal cost is, the larger the complexity. However, relaxed dynamic programming does not give any guarantees on the complexity, which might still be unpractical. To tackle this issue, we propose to rather find the best factor away from optimality for a given complexity bound. We consider a large class of problems where the value functions can be represented as the minimum of quadratic functions. For this class, we propose a modified relaxed dynamic programming algorithm that ensures bounded complexity while still providing tight cost guarantees. A crucial step in the algorithm is the search for the best cost factor for a given policy with desired complexity, shown to be an optimization problem subject to Linear Matrix Inequalities (LMIs). We provide a new subclass of problems within this class and illustrate the effectiveness of our policy in a numerical instance of this subclass.
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14:10-14:30, Paper ThB08.3 | |
>Numerical Comparison of Collocation vs Quadrature Penalty Methods |
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Neuenhofen, Martin P. | Imperial College London |
Kerrigan, Eric C. | Imperial College London |
Nie, Yuanbo | University of Sheffield |
Keywords: Optimal control, Optimization algorithms, Predictive control for nonlinear systems
Abstract: Direct transcription with collocation-type methods (CTM) is a popular approach for solving dynamic optimization problems. It is known that these types of methods can fail to converge for problems that feature singular-arc solutions, high-index differential-algebraic equations and overdetermined constraints. Recently, we proposed the use of quadrature penalty methods (QPM) as an alternative numerical approach to collocation-type methods. In contrast to the concept of collocation, which requires constraint-residuals to equal zero at individual points (e.g. at collocation points), the main idea of QPM is to simply oversample this number of points and use their respective quadrature weights in a quadratic penalty term, coining the name of quadrature penalty. In this paper, we provide numerical case studies and a broad numerical comparison on a wide range of problems, highlighting the benefits of QPM over CTM not only in difficult problems, but also in solving problems competitively to CTM. These results show that QPM can be considered an attractive first go-to method when solving general dynamic optimization problems.
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14:30-14:50, Paper ThB08.4 | |
>Discrete-Time Finite-Horizon Optimization of Singularly Perturbed Nonlinear Control Systems with State-Action Constraints |
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Pi, Jianzong | The Ohio State University |
Gupta, Abhishek | The Ohio State University |
Keywords: Optimal control, Optimization algorithms, Constrained control
Abstract: In this paper, an algorithm is introduced for the computation of an approximate optimal control policy for discrete-time finite-horizon nonlinear singularly perturbed systems. This is achieved through timescale separation and by utilizing ideas from parametric optimization and dynamic programming. We demonstrate that our proposed method produces a control policy that is both theoretically robust and nearly optimal.
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14:50-15:10, Paper ThB08.5 | |
>Multi-Agent Dynamic Scheduling with a Posteriori Path Tracking and Collision Avoidance Using Model Predictive Control |
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Bertoncini, Jeremy | Universität Der Bundeswehr |
Nikitina, Viktoriya | University of the Bundeswehr Munich |
Gerdts, Matthias | University of Munchen |
Keywords: Optimal control, Predictive control for linear systems, Constrained control
Abstract: This research work investigates a coordinated multi-agent path planning and tracking method. The solution of a pre-processed dynamic scheduling problem performs target assignment and provides optimal starting times and paths for each agent. Afterwards, a linear model predictive controller ensures robust and fast path tracking while preventing agents from collisions. This task is formulated as a discretized quadratic programming (QP) problem and is solved using an in-house developed semi-smooth Newton method. Numerical experiments have demonstrated the efficiency of the approach.
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15:10-15:30, Paper ThB08.6 | |
>Model Predictive Control for the Scheduling of Seedings in an Adaptive Vertical Farm |
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Bagnerini, Patrizia | University of Genoa |
Gaggero, Mauro | National Research Council of Italy |
Ghio, Marco | Space V Srl |
Keywords: Optimal control, Predictive control for linear systems, Optimization
Abstract: A model predictive control approach is presented for the scheduling of sowings in an adaptive vertical farm, i.e., an innovative vertical greenhouse in which the spacing between shelves is automatically adapted to crop growth. First, a dynamic model describing the evolution of occupancy and shelf height is developed. The model is affected by disturbances to account for possible deviations of crop growth from the nominal pattern. Then, an optimal control problem over a given timeframe is defined to determine the best time instants to perform seedings in the various shelves with the goal of maximizing production yield. The repeated solution of the optimal control problem over a shorter, moving window over time, according to the receding horizon paradigm, allows to devise robust control strategies with respect to disturbances, even in the absence of predictions about their future realizations. Preliminary simulation results are reported for different control horizons and type of disturbances to showcase the effectiveness of the proposed approach in maximizing production yield while exploiting almost all the available vertical space.
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ThB09 |
Simpor Junior 4811 |
Optimization Algorithms V |
Regular Session |
Chair: Wai, Hoi-To | The Chinese University of Hong Kong |
Co-Chair: Parisio, Alessandra | The University of Manchester |
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13:30-13:50, Paper ThB09.1 | |
>On the Performance of Gradient Tracking with Local Updates (I) |
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Nguyen, Edward Duc Hien | Rice University |
Alghunaim, Sulaiman A. | Kuwait University |
Yuan, Kun | Peking University |
Uribe, Cesar A. | Rice University |
Keywords: Optimization algorithms, Large-scale systems, Optimization
Abstract: We study the decentralized optimization problem where a network of n agents seeks to minimize the average of a set of heterogeneous non-convex cost functions distributedly. State-of-the-art decentralized algorithms like Exact Diffusion and Gradient Tracking (GT) involve communicating every iteration. However, communication is expensive, resource intensive, and slow. This work analyzes a locally updated GT method (LU-GT), where agents perform local recursions before interacting with their neighbors. While local updates have been shown to reduce communication overhead in practice, their theoretical influence has not been fully characterized. We show LU-GT has the same communication complexity as the Federated Learning setting but allows decentralized (symmetric) network topologies. In addition, we prove that the number of local updates does not degrade the quality of the solution achieved by LU-GT. Numerical results reveal that local updates may lead to lower communication costs in specific regimes (e.g., well-connected graphs).
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13:50-14:10, Paper ThB09.2 | |
>Linear Speedup of Incremental Aggregated Gradient Methods on Streaming Data (I) |
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Wang, Xiaolu | The Chinese University of Hong Kong |
Jin, Cheng | Tsinghua University |
Wai, Hoi-To | The Chinese University of Hong Kong |
Gu, Yuantao | Tsinghua University |
Keywords: Optimization algorithms
Abstract: This paper considers an incremental aggregated gradient (IAG) method for large-scale distributed optimization. The IAG method is well suited for the parameter server architecture as the latter can easily aggregate potentially staled gradients contributed by workers. Although the convergence of IAG in the case of deterministic gradient is well known, there are only a few results for the case of its stochastic variant based on streaming data. Considering strongly convex optimization, this paper shows that the streaming IAG method achieves linear speedup when the workers are updating frequently enough, even if the data sample distribution across workers are heterogeneous. We show that the expected squared distance to optimal solution decays at O((1+T)/(nt)), where n is the number of workers, t is the iteration number, and T/n is the update frequency of workers. Our analysis involves careful treatments of the conditional expectations with staled gradients and a recursive system with both delayed and noise terms, which are new to the analysis of IAG-type algorithms. Numerical results are presented to verify our findings.
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14:10-14:30, Paper ThB09.3 | |
>Distributionally Robust Optimization for Nonconvex QCQPs with Stochastic Constraints |
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Brock, Eli | University of California Berkeley |
Zhang, Haixiang | University of California, Berkeley |
Mulvaney-Kemp, Julie | University of California, Berkeley |
Lavaei, Javad | UC Berkeley |
Sojoudi, Somayeh | UC Berkeley |
Keywords: Optimization algorithms, Power systems, Optimization
Abstract: The quadratically constrained quadratic program (QCQP) with stochastic constraints appears in a wide range of real-world problems, including but not limited to the control of power systems. The randomness in the constraints prohibits the application of classic stochastic optimization algorithms. In this work, we utilize the techniques from the distributionally robust optimization (DRO) and propose a novel optimization formulation to solve the QCQP problems under strong duality. The proposed formulation does not contain stochastic constraints. The solutions to the optimization formulation attain the optimal objective value among all solutions that satisfy the stochastic constraints with high probability under the data-generating distribution, even when only a few samples from the distribution are available. We design corresponding algorithms to solve the optimization problems under the new formulation. Numerical experiments are conducted to verify the theory and illustrate the empirical performance of the proposed algorithm. This work provides the first results on the application of DRO techniques to non-convex optimization problems with stochastic constraints and the approach can be extended to a broad class of optimization problems.
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14:30-14:50, Paper ThB09.4 | |
>Fractional Budget Allocation for Influence Maximization |
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Umrawal, Abhishek Kumar | Purdue University; University of Illinois Urbana-Champaign |
Aggarwal, Vaneet | Purdue University |
Quinn, Christopher J. | Iowa State University |
Keywords: Optimization algorithms, Stochastic systems, Control of networks
Abstract: We consider a generalization of the widely studied discrete influence maximization problem. We consider that instead of marketers using a budget to send free products to a few influencers, they can provide discounts to partly incentivize a larger set of influencers with the same budget. We show that this problem is an instance of maximizing the multilinear extension of a monotone submodular set function subject to an L_1 constraint. We propose and analyze an efficient (1-1/e)-approximation algorithm. We run experiments on a real-world social network to show the performance of our method in contrast to methods proposed for other generalizations of influence maximization.
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14:50-15:10, Paper ThB09.5 | |
>Distributed Feedforward Optimization for Control of Multi-Energy Network with Temporal Variations (I) |
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Xu, Yiqiao | University of Manchester |
Zhang, Zhengfa | Aalborg University |
Ding, Zhengtao | The University of Manchester |
Jiang, Shuoying | University of Manchester |
Parisio, Alessandra | The University of Manchester |
Keywords: Optimization algorithms, Distributed control, Energy systems
Abstract: Multi-Energy Network (MEN) is a promising approach to improve the overall efficiency of energy utilization. Yet, balancing its electrical and thermal power in real-time is challenging due to variable demands. In this paper, we formulate a distributed Time Varying Optimization Problem (TVOP) and solve it in continuous-time to track the unknown time-varying optimal trajectories. First, we apply the principles of output regulation theory to reverse engineer the feedforward laws in the presence of projection. These laws are responsible for proactively canceling the effects of temporal demand variations. Then, a projection-based distributed optimization algorithm, alongside a distributed auxiliary protocol based on weighted-sum consensus, result in a novel scheme we term distributed feedforward optimization. One of the key features of our scheme is its data-driven nature, where temporal variations are captured from Ultra-Short-Term Forecasting (USTF) profiles using an exosystem. Under mild assumptions, the proposed scheme provides a guarantee for asymptotic convergence. Simulation results demonstrate the effectiveness of our scheme under an non-ideal case.
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15:10-15:30, Paper ThB09.6 | |
>Variance Reduction for Faster Decentralized General Convex Optimization (I) |
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Xin, Ran | ByteDance |
Das, Subhro | IBM Research |
Kar, Soummya | Carnegie Mellon University |
Khan, Usman A. | Tufts University |
Keywords: Optimization algorithms, Machine learning, Cooperative control
Abstract: This paper studies decentralized stochastic empirical risk minimization over a network of nodes, where each node has access to a finite collection of risk functions. While this formulation has been well-studied when each local function is strongly convex or nonconvex, it is still not clear if acceleration (in the stochastic settings) can be achieved for general convex functions. In this paper, we show that GT-SAGA, an algorithm that combines gradient tracking and incremental variance reduction, converges to a global minimizer at a provably faster rate than the existing decentralized methods for this general convex formulation. In particular, GT-SAGA achieves a topology-independent iteration and gradient complexity when the local sample size is sufficiently large. Our proof techniques hinge on a simple linear coupling of convex descent inequality and variance bounds developed for nonconvex optimization, which can be of independent interest. To the best of our knowledge, these are the first such results in decentralized general convex empirical risk minimization.
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ThB10 |
Roselle Junior 4713 |
Machine Learning V |
Regular Session |
Chair: Gomes, Diogo | King Abdullah University of Science and Technology |
Co-Chair: Bai, Ting | KTH Royal Institute of Technology |
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13:30-13:50, Paper ThB10.1 | |
>Machine Learning Architectures for Price Formation Models with Common Noise |
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Gutierrez, Julian | King Abdullah University of Science and Technology |
Gomes, Diogo | King Abdullah University of Science and Technology |
Lauriere, Mathieu | NYU Shanghai |
Keywords: Mean field games, Machine learning, Stochastic optimal control
Abstract: We propose a machine-learning method to solve a mean-field game price formation model with common noise. This involves determining the price of a commodity traded among rational agents subject to a market clearing condition imposed by random supply, which presents additional challenges compared to the deterministic counterpart. Our approach uses a dual recurrent neural network encoding noise dependence and a particle approximation of the mean-field model with a single loss function optimized by adversarial training. We provide a posteriori estimates for convergence and illustrate our method through numerical experiments.
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13:50-14:10, Paper ThB10.2 | |
>Reinforcement Learning Based Demand Charge Minimization Using Energy Storage |
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Weber, Lucas | Inria |
Busic, Ana | Inria |
Zhu, Jiamin | IFPEN |
Keywords: Machine learning, Smart grid, Optimization algorithms
Abstract: Utilities have introduced demand charges to encourage customers to reduce their demand peaks, since a high peak may cause very high costs for both the utility and the consumer. We herein study the bill minimization problem for customers equipped with an energy storage device and a self-owned renewable energy production. A model-free reinforcement learning algorithm is carefully designed to reduce both the energy charge and the demand charge of the consumer. The proposed algorithm does not need forecasting models for the energy demand and the renewable energy production. The resulting controller can be used online, and progressively improved with newly gathered data. The algorithm is validated on real data from an office building of IFPEN Solaize site. Numerical results show that our algorithm can reduce electricity bills with both daily and monthly demand charges.
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14:10-14:30, Paper ThB10.3 | |
>Reinforcement Learning for Image-Based Visual Servo Control |
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Dani, Ashwin | University of Connecticut |
Bhasin, Shubhendu | Indian Institute of Technology Delhi |
Keywords: Learning, Vision-based control, Adaptive control
Abstract: In this paper, a continuous-time reinforcement learning (RL)-based controller is developed for image-based visual servoing (IBVS). The IBVS control dynamics is of the form where the drift term is absent and there is an uncertainty in the Jacobian matrix that is multiplied with the input. This poses a challenge for developing a continuous-time RL controller. The paper presents an actor-critic or synchronous policy iteration (PI)-based RL controller along with a parameter update law for the unknown parameter in the image Jacobian and proves closed-loop stability with the proposed controller. An infinite-horizon value function minimization objective is achieved by regulating the current image features to the desired with near-optimal control efforts. The proposed controller is tested using a simulation use case and the results validate the proposed theory.
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14:30-14:50, Paper ThB10.4 | |
>Observability-Based Energy Efficient Path Planning with Background Flow Via Deep Reinforcement Learning |
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Mei, Jiazhong | University of Washington |
Kutz, J. Nathan | University of Washington |
Brunton, Steven L. | University of Washington |
Keywords: Optimal control, Machine learning, Nonlinear systems
Abstract: In many sensor estimation and monitoring tasks, the mobile sensor travels through the state-space under the influence of a complex background flow environment. System observability is commonly used to assess the performance of the sensor-based estimation, although for a mobile sensor there are other important metrics. We consider the path planning problem under the environmental background flow and focus on a cyclic trajectory that (i) maximizes the log determinant of the observability matrix, (ii) minimizes total energy consumption, and (iii) returns close to the initial location at the end of the period. We formulate a reinforcement learning (RL) scheme and define a reward function that justifies multiple objectives. We investigate the performance of a policy-based proximal policy optimization (PPO) algorithm and address the issue of partially observed states with an additional recurrent module. We present our results on two complex unsteady fluid dynamical systems.
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14:50-15:10, Paper ThB10.5 | |
>Safe Reinforcement Learning with Probabilistic Guarantees Satisfying Temporal Logic Specifications in Continuous Action Spaces |
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Krasowski, Hanna | Technical University of Munich |
Akella, Prithvi | California Institute of Technology |
Ames, Aaron D. | California Institute of Technology |
Althoff, Matthias | Technische Universität München |
Keywords: Autonomous robots, Machine learning, Formal Verification/Synthesis
Abstract: Vanilla Reinforcement Learning (RL) can efficiently solve complex tasks but does not provide any guarantees on system behavior. To bridge this gap, we propose a three-step safe RL procedure for continuous action spaces that provides probabilistic guarantees with respect to temporal logic specifications. First, our approach probabilistically verifies a candidate controller with respect to a temporal logic specification while randomizing the control inputs to the system within a bounded set. Second, we improve the performance of this probabilistically verified controller by adding an RL agent that optimizes the verified controller for performance in the same bounded set around the control input. Third, we verify probabilistic safety guarantees with respect to temporal logic specifications for the learned agent. Our approach is efficiently implementable for continuous action and state spaces. The separation of safety verification and performance improvement into two distinct steps realizes both explicit probabilistic safety guarantees and a straightforward RL setup that focuses on performance. We evaluate our approach on an evasion task where a robot has to reach a goal while evading a dynamic obstacle with a specific maneuver. Our results show that our safe RL approach leads to efficient learning while maintaining its probabilistic safety specification.
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15:10-15:30, Paper ThB10.6 | |
>Federated Learning in Wireless Networks Via Over-The-Air Computations |
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Oksuz, Halil Yigit | TU Berlin |
Molinari, Fabio | TU Berlin |
Sprekeler, Henning | TU Berlin |
Raisch, Joerg | Technical University Berlin |
Keywords: Optimization, Communication networks, Machine learning
Abstract: In a multi-agent system, agents can cooperatively learn a model from data by exchanging their estimated model parameters, without the need to exchange the locally available data used by the agents. This strategy, often called federated learning, is mainly employed for two reasons: (i) improving resource-efficiency by avoiding to share potentially large data sets and (ii) guaranteeing privacy of local agents' data. Efficiency can be further increased by adopting a beyond-5G communication strategy that goes under the name of Over-the-Air Computation. This strategy exploits the interference property of the wireless channel. Standard communication schemes prevent interference by enabling transmissions of signals from different agents at distinct time or frequency slots, which is not required with Over-the-Air Computation, thus saving resources. In this case, the received signal is a weighted sum of transmitted signals, with unknown weights (fading channel coefficients). State of the art papers in the field aim at reconstructing those unknown coefficients. In contrast, the approach presented here does not require reconstructing channel coefficients by complex encoding-decoding schemes. This improves both efficiency and privacy.
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ThB11 |
Roselle Junior 4712 |
Autonomous Systems I |
Regular Session |
Chair: Langbort, Cedric | University of Illinois at Urbana Champaign |
Co-Chair: Zhu, Shanying | Shanghai Jiao Tong University |
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13:30-13:50, Paper ThB11.1 | |
>Pointwise-In-Time Explanation for Linear Temporal Logic Rules |
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Brindise, Noel | University of Illinois at Urbana-Champaign |
Langbort, Cedric | University of Illinois at Urbana Champaign |
Keywords: Autonomous systems, Automata, Human-in-the-loop control
Abstract: The new field of Explainable Planning (XAIP) has produced a variety of approaches to explain and describe the behavior of autonomous agents to human observers. Many summarize agent behavior in terms of the constraints, or ''rules,'' which the agent adheres to during its trajectories. In this work, we narrow the focus from summary to specific moments in individual trajectories, offering a ''pointwise-in-time'' view. Our novel framework, which we define on Linear Temporal Logic (LTL) rules, assigns an intuitive status to any rule in order to describe the trajectory progress at individual time steps; here, a rule is classified as active, satisfied, inactive, or violated. Given a trajectory, a user may query for status of specific LTL rules at individual trajectory time steps. In this paper, we present this novel framework, named Rule Status Assessment (RSA), and provide examples of its implementation. We find that pointwise-in-time status assessment is useful as a post-hoc diagnostic, enabling a user to systematically track the agent's behavior with respect to a set of rules.
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13:50-14:10, Paper ThB11.2 | |
>Safe Control Design through Risk-Tunable Control Barrier Functions |
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Sharma, Vipul Kumar | Purdue University |
Sivaranjani, S | Purdue University |
Keywords: Autonomous systems, Constrained control, Robust control
Abstract: We consider the problem of designing controllers to guarantee safety for a class of nonlinear systems under uncertainties in the system dynamics and/or the environment. We define a class of uncertain control barrier functions (CBFs), and formulate the safe control design problem as a chance-constrained optimization problem with uncertain CBF constraints. We leverage the scenario approach for chance-constrained optimization to develop a risk-tunable control design that provably guarantees the satisfaction of uncertain CBF safety constraints up to a user-defined probabilistic risk bound, and provides a trade-off between the sample complexity and risk tolerance. We demonstrate the performance of this approach through simulations on a quadcopter navigation problem with obstacle avoidance constraints.
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14:10-14:30, Paper ThB11.3 | |
>Cooperative Receding Horizon 3D Coverage Control with a Team of Networked Aerial Agents |
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Papaioannou, Savvas | KIOS CoE |
Kolios, Panayiotis | University of Cyprus |
Theocharides, Theocharis | University of Cyprus |
Panayiotou, Christos | University of Cyprus |
Polycarpou, Marios M. | University of Cyprus |
Keywords: Autonomous systems, Cooperative control, Optimization
Abstract: This work proposes a receding horizon coverage control approach which allows multiple autonomous aerial agents to work cooperatively in order cover the total surface area of a 3D object of interest. The cooperative coverage problem which is posed in this work as an optimal control problem, jointly optimizes the agents' kinematic and camera control inputs, while considering coupling constraints amongst the team of agents which aim at minimizing the duplication of work. To generate look-ahead coverage trajectories over a finite planning horizon, the proposed approach integrates visibility constraints into the proposed coverage controller in order to determine the visible part of the object with respect to the agents' future states. In particular, we show how non-linear and non-convex visibility determination constraints can be transformed into logical constraints which can easily be embedded into a mixed integer optimization program.
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14:30-14:50, Paper ThB11.4 | |
>Distributed Optimal Formation Control of Second-Order Multiagent Systems with Obstacle Avoidance |
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Huang, Fengping | Shanghai Jiao Tong University |
Duan, Mengmeng | Shanghai Jiao Tong University |
Su, Haifan | Shanghai Jiao Tong University |
Zhu, Shanying | Shanghai Jiao Tong University |
Keywords: Autonomous systems, Cooperative control, Optimization algorithms
Abstract: This paper formulates a class of generic optimal formation control problems for second-order multiagent systems, where agents are steered to achieve the optimal formation determined by a convex optimization problem with generic formation constraints and admissible range constraints. These constraints determine the geometric pattern and limit the range of the optimal formation, respectively. A generic optimal algorithm based on the primal-dual dynamics is proposed for various formation requirements. Based on Lyapunov stability and optimization theories, the states of the second-order multiagent system are shown to converge to the optimal solutions. Moreover, an obstacle avoidance mechanism based on the control barrier function is introduced to make our algorithm more practical. Finally, numerical simulations illustrate the effectiveness of the proposed algorithm.
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14:50-15:10, Paper ThB11.5 | |
>On a Probabilistic Approach for Inverse Data-Driven Optimal Control |
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Garrabé, Émiland | University of Salerno |
Jesawada, Hozefa Zuzer | University of Sannio |
Del Vecchio, Carmen | Università Del Sannio |
Russo, Giovanni | University of Salerno |
Keywords: Autonomous systems, Data driven control, Optimal control
Abstract: We consider the problem of estimating the possibly non-convex cost of an agent by observing its interactions with a nonlinear, non-stationary and stochastic environment. For this inverse problem, we give a result that allows to estimate the cost by solving a convex optimization problem. To obtain this result we also tackle a forward problem. This leads to the formulation of a finite-horizon optimal control problem for which we show convexity and find the optimal solution. Our approach leverages certain probabilistic descriptions that can be obtained both from data and/or from first-principles. The effectiveness of our results, which are turned in an algorithm, is illustrated via simulations on the problem of estimating the cost of an agent that is stabilizing the unstable equilibrium of a pendulum.
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15:10-15:30, Paper ThB11.6 | |
>Distributed Algorithms for Edge-Agreements: More Than Consensus |
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Rai, Ayush | Purdue University |
Mou, Shaoshuai | Purdue University |
Keywords: Autonomous systems, Distributed control
Abstract: In this paper, we propose distributed algorithms for multi-agent systems to achieve edge-agreements. Different from consensus, where all agents’ states converge to be the same value, the edge agreement is characterized by linear constraints defined for edges, i.e. one linear constraint involving two neighboring agents’ states for each edge. Such agreement allows more general coordination among agents, with consensus on a special case. Given the underlying graph of the multiagent system is undirected (not necessarily to be connected), we propose two discrete-time distributed algorithms that enable all agents’ states to converge to constants satisfying edge agreements. Besides theoretical proofs, effectiveness of the proposed algorithms is also shown by simulations on a four-agent multi-agent system.
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ThB12 |
Roselle Junior 4711 |
Cooperative Control V |
Regular Session |
Chair: Liu, Shuai | Shandong University |
Co-Chair: Li, Dongyu | National University of Singapore |
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13:30-13:50, Paper ThB12.1 | |
>Consensus Control Based on Privacy-Preserving Two-Party Relationship Test Protocol |
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Wang, Hanzhou | Beihang University |
Li, Dongyu | BEIHANG UNIVERSITY |
Guan, Zhenyu | Beihang University |
Liu, Yizhong | Beihang University |
Liu, Jianwei | Beihang University |
Keywords: Agents-based systems, Constrained control, Cooperative control
Abstract: Preservation of privacy is a challenging and significant constraint in multi-agent systems. This paper aims to introduce a framework that enables the states of a multi-agent system to reach a consensus while preserving the confidentiality of each agent's initial states from others. First, a protocol for a privacy-preserving two-party relationship test is proposed. Subsequently, the protocol is employed to devise the average consensus controller for the first-order system, and the rendezvous controller for the second-order system. In contrast to prior research that relies on stochastic coupling weights, our approach circumvents the random chattering problem of the control input, resulting in improved convergence performance. Finally, numerical verification is conducted to demonstrate the effectiveness of the proposed controllers in both first- and second-order systems.
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13:50-14:10, Paper ThB12.2 | |
>Bearing-Based Formation Control Simultaneously Involving Several Heterogeneous Multi-Agent Systems with Nonlinear Uncertainties |
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Wang, Yujie | Shandong University |
Liu, Shuai | Shandong University |
Keywords: Agents-based systems, Cooperative control, Adaptive control
Abstract: For a large-scale multi-agent system consisting of agents that have different types of dynamics, employing bearing rigidity theory to handle formation problems is unrealistic since the bearing-based rigid graph is extremely complicated and heterogeneous agents are hard to analyze as a whole. Therefore, we inventively propose to separate the large-scale system into smaller subsystems, and each subsystem is generated by agents which share the same dynamics. In such sense, formation control turns to focus on several systems with milder conditions rather than a system with complex analysis. The control objectives are to drive all systems to acquire the desired formation shapes, and make all systems simultaneously maneuver along with the desired velocities and maintain the formation shapes. To reduce communication cost, the leader-follower strategy is applied. To make formation control suitable for general environments, nonlinear uncertainties are considered, and the desired maneuvering velocities are time-varying. Adaptive nonsmooth distributed controllers are appropriately designed for all agents in bearing-based formation control.
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14:10-14:30, Paper ThB12.3 | |
>Distributed Prescribed-Time and Adaptive Synchronization of Complex Dynamical Networks under Directed Topologies |
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Feng, Zhi | Beihang University |
Dong, Xiwang | Beihang University |
Lu, Jinhu | Beihang University |
Keywords: Agents-based systems, Cooperative control, Adaptive control
Abstract: This paper addresses an adaptively distributed prescribed-time synchronization problem of complex dynamical networks (CDNs) via distributed pinning control strategies using neighboring information over a directed graph. The novel distributed prescribed-time synchronization pinning control algorithms with static and dynamic coupling laws are developed to achieve global synchronization in a specified time, where each node can adjust its strategy on its procurable synchronization error. Based on the time transformation method and Lyapunov analysis theory, it is proved that global synchronization can be guaranteed in a pre-defined time and moreover, this synchronization can be preserved after the time, and further the control inputs are kept uniformly bounded. Lastly, the numerical simulation results are further presented to illustrate the effectiveness of the developed synchronization control methods.
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14:30-14:50, Paper ThB12.4 | |
>Bipartite Containment Control of Nonuniform Delayed Fractional-Order Multi-Agent Systems Over Signed Networks |
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Li, Weihao | School of Aeronautics and Astronautics |
Qin, Kaiyu | University of Electronic Science and Technology of China |
Shao, Jinliang | University of Electronic Science and Technology of China, Chengd |
Shi, Lei | Henan University |
Shi, Mengji | University of Electronic Science and Technology of China |
Zheng, Wei Xing | Western Sydney University |
Keywords: Agents-based systems, Cooperative control, Network analysis and control
Abstract: In this study, the bipartite containment control problem of fractional-order multi-agent systems with nonuniform time delays is addressed. An in-depth analysis of the system stability and bipartite containment control performance from a delay margin perspective is provided. Theoretically, the corresponding delay margin (maximum allowable time delay) over undirected and directed signed networks is obtained in the presence of nonuniform time delays, respectively. In addition, numerical relationships between the delay margin and the control coefficients, fractional order, and topology parameters are established, thus enabling easy and direct calculation of the maximum allowable time delay and facilitating distributed controller design and controller parameter tuning. Finally, some simulation examples are given to verify the effectiveness of the proposed bipartite containment controller and the obtained delay margin.
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14:50-15:10, Paper ThB12.5 | |
>Impact of Relational Networks in Multi-Agent Learning: A Value-Based Factorization View |
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Findik, Yasin | University of Massachusetts Lowell |
Robinette, Paul | UMass Lowell |
Jerath, Kshitij | University of Massachusetts Lowell |
Ahmadzadeh, S. Reza | University of Massachusetts Lowell |
Keywords: Agents-based systems, Cooperative control
Abstract: Effective coordination and cooperation among agents are crucial for accomplishing individual or shared objectives in multi-agent systems. In many real-world multi-agent systems, agents possess varying abilities and constraints, making it necessary to prioritize agents based on their specific properties to ensure successful coordination and cooperation within the team. However, most existing cooperative multi-agent algorithms do not take into account these individual differences, and lack an effective mechanism to guide coordination strategies. We propose a novel multi-agent learning approach that incorporates relationship awareness into value-based factorization methods. Given a relational network, our approach utilizes inter-agents relationships to discover new team behaviors by prioritizing certain agents over other, accounting for differences between them in cooperative tasks. We evaluated the effectiveness of our proposed approach by conducting fifteen experiments in two different environments. The results demonstrate that our proposed algorithm can influence and shape team behavior, guide cooperation strategies, and expedite agent learning. Therefore, our approach shows promise for use in multi-agent systems, especially when agents have diverse properties.
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15:10-15:30, Paper ThB12.6 | |
>Designing Cluster Consensus on Higher-Order Interaction Networks |
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Wei, Haoyu | Shanghai Jiao Tong University |
Pan, Lulu | University of Washington |
Shao, Haibin | Shanghai Jiao Tong University |
Li, Dewei | Shanghai Jiao Tong University |
Yu, Wenbin | Shanghai Jiao Tong University |
Xue, Shibei | Shanghai Jiao Tong University |
Keywords: Agents-based systems, Cooperative control
Abstract: This paper examines the cluster consensus design problem on higher-order interaction networks. Specifically, the higher-order interaction mechanism is captured by matrix-weighted networks that allow the interdependency across the dimensions of the agents’ states, and the matrix-valued weight matrices Aij ∈ Rd×d associated with specific edges are further assumed to share the same nullspace for design purposes. Under mild assumptions on network connectivity, we first examine the case that the nullspace of positive semi-definite edges is spanned by a nonzero vector ξ ∈ Rd and show that the predictable cluster consensus can be achieved, which is eventually located in the 1−dimensional linear space determined by span{ξ} and the average of agents’ initial states. Moreover, the transient state of agents in each cluster can also be explicitly characterized. Namely, the derivative of the average state of agents in each cluster is perpendicular to span{ξ}. To generalize the above results, we proceed to examine the case that the nullspace of positive semi-definite edges is spanned by more than one linearly independent d−dimensional vector, in which case, analogous results can be obtained, and the explicit geometric interpretation is also provided.
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ThB13 |
Roselle Junior 4613 |
Networked Control Systems II |
Regular Session |
Chair: Kishida, Masako | National Institute of Informatics |
Co-Chair: Batista, Pedro | Instituto Superior Técnico / University of Lisbon |
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13:30-13:50, Paper ThB13.1 | |
>Consensus on Lie Groups for the Riemannian Center of Mass |
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Kraisler, Spencer | University of Washington |
Talebi, Shahriar | University of Washington |
Mesbahi, Mehran | University of Washington |
Keywords: Networked control systems, Cooperative control, Optimization algorithms
Abstract: In this paper, we develop a consensus algorithm for distributed computation of the Riemannian Center of Mass (RCM) on Lie Groups. The algorithm is built upon a distributed optimization reformulation that allows developing an intrinsic, distributed (without relying on a consensus subroutine), and a computationally efficient protocol for the RCM computation. The novel idea for developing this fast distributed algorithm is to utilize a Riemannian version of distributed gradient flow combined with a gradient tracking technique. We first guarantee that, under certain conditions, the limit point of our algorithm is the RCM point of interest. We then provide a proof of global convergence in the Euclidean setting, that can be viewed as a "geometric" dynamic consensus that converges to the average from arbitrary initial points. Finally, we proceed to showcase the superior convergence properties of the proposed approach as compared with other classes of consensus optimization-based algorithms for the RCM computation.
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13:50-14:10, Paper ThB13.2 | |
>Greedy Synthesis of Event and Self-Triggered Controls with Control Lyapunov-Barrier Function |
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Kishida, Masako | National Institute of Informatics |
Keywords: Networked control systems, Cyber-Physical Security, Stability of nonlinear systems
Abstract: This paper addresses the co-design problem of control inputs and execution decisions for event- and self-triggered controls subject to constraints given by the control Lyapunov function and control barrier function. The proposed approach computes the control input in a way that allows for longer inter-execution intervals, which distinguishes it from many existing event- and self-triggered controllers or control Lyapunov-barrier function controllers. The proposed approach guarantees lower bounds on the minimum inter-execution times. The effectiveness of the proposed approach is demonstrated and compared with existing approaches using a numerical example.
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14:10-14:30, Paper ThB13.3 | |
>First and Second-Order Consensus with Constant Uniform Delays |
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Trindade, Pedro | Institute for Systems and Robotics, Instituto Superior Técnico, |
Cunha, Rita | Instituto Superior Técnico, Universidade De Lisboa |
Batista, Pedro | Instituto Superior Técnico / University of Lisbon |
Keywords: Networked control systems, Decentralized control, Stability of linear systems
Abstract: This paper analyzes first- and second-order consensus protocols subject to a constant uniform delay, when these are applied to single and double integrator agents interacting over a directed network. First, the consensus protocols are analyzed using frequency domain tools and necessary and sufficient bounds on the delay such that the agents achieve consensus are derived. Then, assuming that the delay is known, bounds on the coupling gains such that the agents achieve consensus for a given delay are sought. For first-order consensus, it turns out that it suffices to invert the bound obtained for the delay, but for second-order consensus, that is no longer possible. Instead, the Padé approximation of the delay is used to derive sufficient bounds on the coupling gains for second-order consensus.
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14:30-14:50, Paper ThB13.4 | |
>Distributed Finite-Time Supremum/Infimum Dynamic Consensus under Directed Network Topology |
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Furchì, Antonio | Roma Tre University |
Lippi, Martina | Roma Tre University |
Marino, Alessandro | Università Degli Studi Di Cassino E Del Lazio Meridionale |
Gasparri, Andrea | Roma Tre University |
Keywords: Networked control systems, Distributed control, Decentralized control
Abstract: In this paper, we address the distributed supremum/infimum dynamic consensus problem in networked multi-agent systems. More in detail, by considering that each agent has access to a local exogenous time-varying signal, the objective is to have all the agents distributively track the global maximum supremum (or minimum infimum) of these exogenous signals. We propose a distributed protocol guaranteeing finite-time convergence under directed network topology. The sole requirements are the strong connectivity of the communication graph and the boundedness of the derivatives of the exogenous signals, with known bounds. The effectiveness of the proposed protocol is corroborated through numerical simulations in a precision farming case study.
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14:50-15:10, Paper ThB13.5 | |
>Natural Policy Gradient Preserves Spatial Decay Properties for Control of Networked Dynamical Systems |
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Xu, Eric | Carnegie Mellon University |
Qu, Guannan | Carnegie Mellon University |
Keywords: Networked control systems, Distributed control, Learning
Abstract: We consider the distributed control of networked linear time-invariant systems. Previous work has established the spatial decay property of the centralized controller, which allows truncating the centralized controller to obtain a κhop distributed controller with small performance loss. This paper makes a step further by showing a policy optimization approach, Natural Policy Gradient (NPG), preserves the spatial decay property of controllers. This enables “truncating” Natural Policy Gradient to directly learn a κ-hop distributed controller.
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15:10-15:30, Paper ThB13.6 | |
>Connectivity-Preserving Formation Tracking for Multiple Double Integrators by a Self-Tuning Adaptive Distributed Observer |
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Pan, Zini | The Chinese University of Hong Kong |
Chen, Ben M. | Chinese University of Hong Kong |
Keywords: Networked control systems, Distributed control
Abstract: In this letter, we study the distributed formation tracking problem for multiple double-integrator systems with connectivity preservation over a state-dependent communication network. In particular, we employ an adaptive distributed observer for the leader system that can estimate both the state and the system matrix of the leader. As a result, unlike the existing results, we do not require all vehicles to know the system matrix of the leader. Furthermore, the adaptive distributed observer incorporates a self-tuning dynamic observer gain, which eliminates the need of computing the observer gain in advance. The effectiveness of our approach is illustrated by an example.
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ThB14 |
Roselle Junior 4612 |
Identification IV |
Regular Session |
Chair: Sznaier, Mario | Northeastern University |
Co-Chair: Chang, Chin-Yao | National Renewable Energy Laboratory |
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13:30-13:50, Paper ThB14.1 | |
>A Privacy Preserving Distributed Model Identification Algorithm for Power Distribution Systems |
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Chang, Chin-Yao | National Renewable Energy Laboratory |
Keywords: Identification, Distributed control, Data driven control
Abstract: Distributed control/optimization is a promising approach for network systems due to its advantages over centralized schemes, such as robustness, cost-effectiveness, and improved privacy. However, distributed methods can have drawbacks, such as slower convergence rates due to limited knowledge of the overall network model. Additionally, ensuring privacy in the communication of sensitive information can pose implementation challenges. To address this issue, we propose a distributed model identification algorithm that enables each agent to identify the sub-model that characterizes the relationship between its local control and the overall system outputs. The proposed algorithm maintains the privacy of local agents by only communicating through dummy variables. We demonstrate the efficacy of our algorithm in the context of power distribution systems by applying it to the voltage regulation of a modified IEEE distribution system. The proposed algorithm is well-suited to the needs of power distribution controls and offers an effective solution to the challenges of distributed model identification in network systems.
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13:50-14:10, Paper ThB14.2 | |
>A Dual System-Level Parameterization for Identification from Closed-Loop Data |
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Srivastava, Amber | Indian Institute of Technology Delhi |
Yin, Mingzhou | ETH Zurich |
Iannelli, Andrea | University of Stuttgart |
Smith, Roy S. | ETH Zurich |
Keywords: Closed-loop identification, Identification, Estimation
Abstract: This work presents a dual system-level parameterization (D-SLP) method for closed-loop identification of linear time-invariant systems. The recent system-level synthesis framework parameterizes all stabilizing controllers via linear constraints on closed-loop response functions, known as system-level parameters. It was demonstrated that several structural, locality, and communication constraints on the controller can be posed as convex constraints on these system-level parameters. In the current work, the identification problem is treated as a dual of the system-level synthesis problem. The plant model is identified from the dual system-level parameters associated to the plant. In comparison to existing closed-loop identification approaches (such as the dual-Youla parameterization), the D-SLP framework neither requires the knowledge of a nominal plant that is stabilized by the known controller, nor depends upon the choice of factorization of the nominal plant and the stabilizing controller. Numerical simulations demonstrate the efficacy of the proposed D-SLP method in terms of identification errors, compared to existing closed-loop identification techniques.
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14:10-14:30, Paper ThB14.3 | |
>Efficient MIMO Iterative Feedback Tuning Via Randomization |
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Aarnoudse, Leontine | TU Eindhoven |
Oomen, Tom | Eindhoven University of Technology |
Keywords: Identification for control, Closed-loop identification, Identification
Abstract: Iterative feedback tuning (IFT) enables the tuning of feedback controllers based on measured data without the need for a parametric model. The aim of this paper is to develop an efficient method for MIMO IFT that reduces the required number of experiments. Using a randomization technique, an unbiased gradient estimate is obtained from a single dedicated experiment, regardless of the size of the MIMO system. This gradient estimate is employed in a stochastic gradient descent algorithm. Simulation examples illustrate that the approach reduces the number of experiments required to converge.
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14:30-14:50, Paper ThB14.4 | |
>Certified Control Oriented Learning: A Robust Predictor Based Approach |
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Singh, Rajiv | The MathWorks |
Sznaier, Mario | Northeastern University |
Keywords: Identification for control, Identification, Robust control
Abstract: We present an efficient and scalable solution to the problem of learning the behavior of dynamical systems for the purpose of robust control design. The approach is centered around the derivation of stable predictors of potentially unstable systems and using them to identify plant models that can be ranked by their complexity (order) vs. empirical nu-gap value.
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14:50-15:10, Paper ThB14.5 | |
>An Efficient Method for the Joint Estimation of System Parameters and Noise Covariances for Linear Time-Variant Systems |
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Simpson, Léo | Tool-Temp AG |
Diehl, Moritz | University of Freiburg |
Asprion, Jonas | Tool-Temp AG |
Ghezzi, Andrea | University of Freiburg |
Keywords: Identification for control, Linear systems, Optimization
Abstract: We present an optimization-based method for the joint estimation of system parameters and noise covariances of linear time-variant systems. Given measured data, this method maximizes the likelihood of the parameters. We solve the optimization problem of interest via a novel structure-exploiting solver. We present the advantages of the proposed approach over commonly used methods in the framework of Moving Horizon Estimation. Finally, we show the performance of the method through numerical simulations on a realistic example of a thermal system. In this example, the method can successfully estimate the model parameters in a short computational time.
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15:10-15:30, Paper ThB14.6 | |
>Data-Driven Feedforward Control Design for Nonlinear Systems: A Control-Oriented System Identification Approach |
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Bolderman, Max | Eindhoven University of Technology |
Lazar, Mircea | Eindhoven University of Technology |
Butler, Hans | ASML |
Keywords: Identification for control, Neural networks, Iterative learning control
Abstract: Feedforward controllers typically rely on accurately identified inverse models of the system dynamics to achieve high reference tracking performance. However, the impact of the (inverse) model identification error on the resulting tracking error is only analyzed a posteriori in experiments. Therefore, in this work, we develop an approach to feedforward control design that aims at minimizing the tracking error a priori. To achieve this, we present a model of the system in a lifted space of trajectories, based on which we derive an upperbound on the reference tracking performance. Minimization of this bound yields a feedforward control-oriented system identification cost function, and a finite-horizon optimization to compute the feedforward control signal. The nonlinear feedforward control design method is validated using physics-guided neural networks on a nonlinear, nonminimum phase mechatronic example, where it outperforms linear ILC.
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ThB15 |
Roselle Junior 4611 |
Robust Control I |
Regular Session |
Chair: Tan, Ying | The University of Melbourne |
Co-Chair: Turner, Matthew C. | University of Southampton |
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13:30-13:50, Paper ThB15.1 | |
>Data-Driven Robust Backward Reachable Sets for Set-Theoretic Model Predictive Control |
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Attar, Mehran | Concordia University |
Lucia, Walter | Concordia University |
Keywords: Robust control, Constrained control, Predictive control for linear systems
Abstract: In this paper, we propose a novel approach for computing robust backward reachable sets from noisy data for unknown constrained linear systems subject to bounded disturbances. In particular, we develop an algorithm for obtaining zonotopic inner approximations that can be used for control purposes. It is shown that such sets, if built on an extended space including states and inputs, can be used to embed the system's one-step evolution in the computed extended regions. Such a result is then exploited to build a set-theoretic model predictive controller that, offline, builds a recursive family of robust data-driven reachable sets and, online, computes recursively admissible control actions without explicitly resorting to either a model of the system or the available data. The validity of the proposed data-driven solution is verified by means of a numerical simulation and its performance is contrasted with the model-based counterpart.
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13:50-14:10, Paper ThB15.2 | |
>Robust Admittance Control with Complementary Passivity |
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Xu, Jiapeng | University of Windsor |
Chen, Xiang | University of Windsor |
Tan, Ying | The University of Melbourne |
Zou, Wulin | Hong Kong University of Science and Technology |
Keywords: Robust control, Control system architecture, Control applications
Abstract: This paper studies a robust admittance control problem with a passivity requirement for stable and unstable linear time-invariant systems, motivated by control issues originated from physical human-robot interaction. A complementary admittance control structure is proposed and analyzed, revealing that the nominal performance (admittance tracking and passivity) is decoupled from robustness. Simulations on the admittance control for human arm strength augmentation with a passivity requirement validate the proposed controller design.
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14:10-14:30, Paper ThB15.3 | |
>On the Benefit of Nonlinear Control for Robust Logarithmic Growth: Coin Flipping Games As a Demonstration Case |
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Proskurnikov, Anton V. | Politecnico Di Torino |
Barmish, B. Ross | Boston University |
Keywords: Robust control, Finance, Markov processes
Abstract: The takeoff point for this paper is the voluminous body of literature addressing recursive betting games with expected logarithmic growth of wealth being the performance criterion. Whereas almost all existing papers involve use of linear feedback, the use of nonlinear control is conspicuously absent. This is epitomized by the large subset of this literature dealing with Kelly Betting. With this as the high-level motivation, we study the potential for use of nonlinear control in this framework. To this end, we consider a "demonstration case" which is one of the simplest scenarios encountered in this line of research: repeated flips of a biased coin with probability of heads p and even-money payoff on each flip. First, we formulate a new robust nonlinear control problem which we believe is both simple to understand and apropos for dealing with concerns about distributional robustness; i.e., instead of assuming that p is perfectly known as in the case of the classical Kelly formulation, we begin with a bounding set P for this probability. Then, we provide a theorem, our main result, which gives a closed-form description of the optimal robust nonlinear controller and a corollary which establishes that it robustly outperforms linear controllers such as those found in the literature. A second contribution of this paper bears upon the computability of our solution. For an n-flip game, whereas an admissible controller has 2^n-1 parameters, at the optimum only O(n^2) of them turn out to be distinct. Finally, we provide some illustrations comparing robust performance with what is possible when working with the so-called perfect-information Kelly optimum.
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14:30-14:50, Paper ThB15.4 | |
>Mixed Gain/Phase Robustness Criterion for Structured Perturbations with an Application to Power System Stability |
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Woolcock, Luke | University of Melbourne |
Schmid, Robert | The University of Melbourne |
Keywords: Robust control, Linear systems, Power systems
Abstract: A novel conception of phase for linear time-invariant multivariable systems was recently introduced. It enables robustness of such systems to be determined in terms of a phase-bounded set of perturbations via a so-called small phase theorem, in analogy to the well-known small gain theorem. However, it requires the system's frequency response to satisfy the relatively strong condition known as "sectoriality," which not all practical systems have. This paper aims to show that if the perturbation is assumed to have a block diagonal structure, a matrix-valued multiplier function can be calculated that can enable phase-based robustness margins to be defined in some cases when the original system is not sectorial. A real-world power systems example is presented to show how the small phase criterion using a multiplier can significantly reduce the conservatism of the small gain theorem, providing computationally straightforward methods to inform further nonlinear stability analysis of power systems.
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14:50-15:10, Paper ThB15.5 | |
>Strengthened Circle and Popov Criteria for the Stability Analysis of Feedback Systems with ReLU Neural Networks |
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Richardson, Carl Robert | University of Southampton |
Turner, Matthew C. | University of Southampton |
Gunn, Steve | University of Southampton |
Keywords: Robust control, Neural networks, Stability of nonlinear systems
Abstract: This paper considers the stability analysis of a Lurie system with a static repeated ReLU (rectified linear unit) nonlinearity. Properties of the ReLU function are leveraged to derive new tailored quadratic constraints (QCs) which are satisfied by the repeated ReLU. These QCs are used to strengthen the Circle and Popov Criteria for this specialised Lurie system. It is shown that the criteria can be cast as a set of linear matrix inequalities (LMIs) with less restrictive conditions on the matrix variables. Many systems involving a neural network (NN) with ReLU activations are important instances of this specialised Lurie system; for example, a continuous time recurrent neural network (RNN) or the interconnection of a linear system with a feedforward NN. Numerical examples show the strengthened criteria strike an appealing balance between reduced conservatism and complexity, compared to existing criteria.
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15:10-15:30, Paper ThB15.6 | |
>Verification of Low-Dimensional Neural Network Control |
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Gronqvist, Johan | Lund University |
Rantzer, Anders | Lund University |
Keywords: Robust control, Nonlinear systems, Neural networks
Abstract: We verify safety of a nonlinear continuous-time system controlled by a neural network controller. The system is decomposed into low-dimensional subsystems connected in a feedback loop. Our application is a rocket landing, and open-loop properties of the two-dimensional altitude subsystem are verified using worst-case simulations. Closed-loop safety properties (crash-avoidance) of the full system are obtained from composition of contracts for open-loop safety properties of subsystems in a fashion analogous to the small-gain theorem.
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ThB16 |
Peony Junior 4512 |
Power Systems II |
Regular Session |
Chair: Jiang, Yuning | EPFL |
Co-Chair: Glista, Elizabeth | University of California, Berkeley |
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13:30-13:50, Paper ThB16.1 | |
>Hypergraph-Based Fast Distributed AC Power Flow Optimization |
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Dai, Xinliang | Karlsruhe Institute of Technology |
Lian, Yingzhao | EPFL |
Jiang, Yuning | EPFL |
Jones, Colin N. | EPFL |
Hagenmeyer, Veit | Karlsruhe Institute of Technology (KIT) |
Keywords: Power systems, Optimization algorithms, Nonlinear systems
Abstract: This paper presents a novel distributed approach for solving AC power flow (PF) problems. The optimization problem is reformulated into a distributed form using a communication structure corresponds to a hypergraph, by which complex relationships between subgrids can be expressed as hyperedges. Then, a hypergraph-based distributed sequential quadratic programming (HDSQP) approach is proposed to handle the reformulated problems, and the hypergraph based distributed quadratic optimization algorithm (HDQ) is used as the inner algorithm to solve the corresponding QP subproblems, which are respectively condensed using Schur complements with respect to coupling variables defined by hyperedges. Furthermore, we rigorously establish the convergence guarantee of the proposed algorithm with a locally quadratic rate and the one-step convergence of the inner algorithm when using the Levenberg-Marquardt regularization. Our analysis also demonstrates that the computational complexity of the proposed algorithm is much lower than the state-of-art distributed algorithm. We implement the proposed algorithm in an open-source toolbox, rapidPF, and conduct numerical tests that validate the proof and demonstrate the great potential of the proposed distributed algorithm in terms of communication effort and computational speed.
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13:50-14:10, Paper ThB16.2 | |
>A Control Leonov Function Guaranteeing Global ISS of Two Coupled Synchronverters |
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Mercado Uribe, José Angel | Brandenburgische Technische Universität Cottbus-Senftenberg |
Mendoza-Avila, Jesus | INRIA Lille-Nord Europe |
Efimov, Denis | Inria |
Schiffer, Johannes | Brandenburg University of Technology |
Keywords: Power systems, Nonlinear systems, Control applications
Abstract: Abstract—The synchronverter control algorithm is a highly promising option for operating AC power inverters in future low-inertia power systems. Yet, as with conventional synchronous generators, the standard synchronverter algorithm only provides limited robustness guarantees. Therefore, we propose an additional control that confers the closed-loop system with global robustness in the Input-to-State Stability (ISS) sense. In this paper, such a control law is derived for the case of two identical synchronverters interconnected over dynamic power lines by using the Control Leonov Function (CLeF) framework. The control is illustrated by simulations.
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14:10-14:30, Paper ThB16.3 | |
>An Optimization-Based Method for Transient Stability Assessment |
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Gao, Jianli | Imperial College London |
Chaudhuri, Balarko | Imperial College London |
Astolfi, Alessandro | Imperial College & Univ. of Rome |
Keywords: Power systems, Lyapunov methods, Electrical machine control
Abstract: The paper proposes an optimization-based method for the transient stability assessment of lossy multi-machine power systems. To achieve this objective, a global control Lyapunov function candidate including an auxiliary state is introduced. On this basis, a new excitation control law is proposed. This control law is well-defined provided that an ‘index’ matrix remains non-singular along the closed-loop trajectories. Such a matrix plays a key role in the formulation of an optimization problem, which allows calculating the so-called critical value associated to the introduced Lyapunov function. This permits a direct assessment of transient stability property of the considered post-fault power system. To illustrate the effectiveness of such an optimization-based method, a case study on the model of a three-machine system is presented.
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14:30-14:50, Paper ThB16.4 | |
>Differentially Private Algorithms for Synthetic Power System Datasets |
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Dvorkin, Vladimir | Massachusetts Institute of Technology |
Botterud, Audun | MIT |
Keywords: Power systems, Optimization, Randomized algorithms
Abstract: While power systems research relies on the availability of real-world network datasets, data owners (e.g., system operators) are hesitant to share data due to privacy risks. To control these risks, we develop privacy-preserving algorithms for synthetic generation of optimization and machine learning datasets. Taking a real-world dataset as input, the algorithms output its noisy, synthetic version, which preserves the accuracy of the real data on a specific downstream model or even a large population of those. We control the privacy loss using Laplace and Exponential mechanisms of differential privacy and preserve data accuracy using a post-processing convex (or mixed-integer) optimization. We apply the algorithms to generate synthetic network parameters and wind power data.
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14:50-15:10, Paper ThB16.5 | |
>Optimization-Based Bound Tightening Using a Strengthened QC-Relaxation of the Optimal Power Flow Problem |
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Sundar, Kaarthik | Los Alamos National Laboratory |
Nagarajan, Harsha | Los Alamos National Laboratory |
Misra, Sidhant | Los Alamos National Laboratory |
Lu, Mowen | Walmart Global Tech |
Coffrin, Carleton | Los Alamos National Laboratory |
Bent, Russell | Los Alamos National Laboratory |
Keywords: Power systems, Optimization, Optimization algorithms
Abstract: This paper develops a novel strengthened convex quadratic convex (QC) relaxation of the AC Optimal Power Flow (AC-OPF) problem and presents an optimization-based bound-tightening (OBBT) algorithm to compute tight, feasible bounds on the voltage magnitude variables for each bus and the phase angle difference variables for each branch in the network. Theoretical properties of the strengthened QC relaxation, that show its dominance over the other variants of the QC relaxation studied in the literature, are also derived. The effectiveness of the strengthened QC relaxation is corroborated via extensive numerical results on benchmark AC-OPF test networks. In particular, the results demonstrate that the proposed relaxation consistently provides the tightest variable bounds and optimality gaps with negligible impacts on runtime performance.
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15:10-15:30, Paper ThB16.6 | |
>Leveraging the Physics of AC Power Flow in Support Vector Regression to Identify Power System Topology |
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Glista, Elizabeth | University of California, Berkeley |
Sojoudi, Somayeh | UC Berkeley |
Keywords: Power systems, Smart grid, Machine learning
Abstract: Understanding an electric power system's topology, including both its nodal connectivity and physical parameters, is critically important to the reliable operation and control of the power grid. In cases where this power system topology may be unavailable, due to data collection deficiencies, real-time line switching, or intentional cyberattacks, it is important to be able to estimate the real power system topology with high accuracy. In this paper, we propose a new data-driven constrained support vector regression (SVR) method that aims to map voltage data collected from phasor measurement units (PMUs) to data collected by Supervisory Data Acquisition and Control (SCADA) systems. We show that the dual of the constrained SVR model can be formulated as a quadratic program (QP) and solved efficiently with off-the-shelf solvers. Testing our method on standard IEEE test cases, we demonstrate that our proposed method significantly outperforms existing state-of-the-art SVR methods in learning the true network topology, even in the presence of measurement noise, outliers, and missing data.
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ThB17 |
Peony Junior 4511 |
Iterative Learning Control I |
Regular Session |
Chair: Rogers, Eric | University of Southampton |
Co-Chair: Poot, Maurice | Eindhoven University of Technology |
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13:30-13:50, Paper ThB17.1 | |
>Trackability-Based Distributed Learning Control for Multi-Agent Systems under Switching Topologies |
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Wu, Yuxin | Beihang University (BUAA) |
Meng, Deyuan | Beihang University (BUAA) |
Wang, Jing | North China University of Technology |
Keywords: Iterative learning control, Agents-based systems, Cooperative control
Abstract: This paper aims to address the distributed learning control problem for irregular multi-agent systems subject to switching topologies. The cooperative trackability property for the desired reference is discussed, which ensures the existence of the desired inputs for realizing the cooperative perfect tracking objective. Then, a trackability-based distributed learning control algorithm is presented with the integration of the complete experience information from the previous iteration. It is shown that for the cooperatively trackable desired reference, all agents learn to achieve the cooperative perfect tracking objective in the presence of the developed distributed learning control algorithm despite their irregular dynamics, provided that their associated directed graphs jointly have a spanning tree. The simulation is implemented to illustrate the validity of the trackability-based distributed learning control algorithm.
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13:50-14:10, Paper ThB17.2 | |
>Online Stochastic Allocation of Reusable Resources |
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Zhang, Xilin | National University of Singapore |
Cheung, Wang Chi | National University of Singapore |
Keywords: Iterative learning control, Data driven control, Stochastic optimal control
Abstract: We study a multi-objective model on the allocation of reusable resources under model uncertainty. Heterogeneous customers arrive sequentially according to a latent stochastic process, request for certain amounts of resources, and occupy them for random durations of time and return them. The decision maker's goal is to simultaneously maximize multiple types of rewards generated by the customers, while satisfying the resource capacity constraints in each time step. We develop models and algorithms for deciding on the allocation actions. We show that when the usage duration is relatively small compared with the length of the planning horizon, our policy achieves 1-O(epsilon) fraction of the optimal expected rewards, where epsilon decays to zero at a near optimal rate as the resource capacities grow. We further conduct numerical experiments to justify the performance of our algorithm.
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14:10-14:30, Paper ThB17.3 | |
>Data-Driven Iterative Learning Control for Continuous-Time Systems |
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Chu, Bing | University of Southampton |
Rapisarda, Paolo | Univ. of Southampton |
Keywords: Iterative learning control, Data driven control
Abstract: We develop a data-driven iterative learning control design framework for continuous-time systems that does not require explicit or implicit identification of a system model. Using Chebyshev polynomial orthogonal bases, we show that all system trajectories can be characterised from sufficiently rich input/output data. Using this crucial result we develop a data-driven version of the model-based norm-optimal iterative learning control algorithm, and provide a computationally efficient implementation thereof. We rigorously analyse the convergence properties of the resulting design and also present a numerical example to illustrate its effectiveness.
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14:30-14:50, Paper ThB17.4 | |
>Boundary Iterative Learning Control for Repetitive Spatio-Temporal Processes |
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Patan, Maciej | University of Zielona Gora |
Klimkowicz, Kamil | University of Zielona Gora |
Patan, Krzysztof | University of Zielona Gora |
Rogers, Eric | University of Southampton |
Keywords: Iterative learning control, Distributed parameter systems, Data driven control
Abstract: Iterative learning control for lumped processes is well established. Therefore, there is strong interest in developing designs that would produce similar flexibility for classes of distributed parameter systems. This paper develops a design for application to examples described by partial differential equations of convection-diffusion type in the multidimensional spatial domain, which have many applications, such as heat transfer problems. The system response is measured, and then the control is applied via specific boundary conditions using a sensor/actuator network, i.e., boundary control, as opposed to designs that require sensing and actuating application over the domain the dynamics are defined over. The convergence properties of the design are established together with rules for tuning its parameters for performance enhancement. Finally, the new design is applied to a laser heating problem in wafer staging, which requires boundary control.
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14:50-15:10, Paper ThB17.5 | |
>Risk-Constrained Control of Mean-Field Linear Quadratic Systems |
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Roudneshin, Masoud | Concordia University |
Sanami, Saba | Concordia University |
Aghdam, Amir G. | Concordia University |
Keywords: Iterative learning control, Linear systems, Control of networks
Abstract: The risk-neutral LQR controller is optimal for stochastic linear dynamical systems. However, the classical optimal controller performs inefficiently in the presence of low probability yet statistically significant (risky) events. The present research focuses on infinite-horizon risk-constrained linear quadratic regulators in a mean-field setting. We address the risk constraint by bounding the cumulative one-stage variance of the state penalty of all players. It is shown that the optimal controller is affine in the state of each player with an additive term that controls the risk constraint. In addition, we propose a solution independent of the number of players. Finally, simulations are presented to verify the theoretical findings.
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15:10-15:30, Paper ThB17.6 | |
>Rational Basis Functions in Iterative Learning Control for Multivariable Systems |
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Poot, Maurice | Eindhoven University of Technology |
Portegies, Jim | Eindhoven University of Technology |
Kostic, Dragan | ASM Pacific Technology |
Oomen, Tom | Eindhoven University of Technology |
Keywords: Iterative learning control, Mechatronics, Data driven control
Abstract: Feedforward control with task flexibility for MIMO systems is essential to meet ever-increasing demands on throughput and accuracy. The aim of this paper is to develop a framework for data-driven tuning of rational feedforward controllers in iterative learning control (ILC) for noncommutative MIMO systems. A convex optimization problem in ILC is achieved by rewriting the nonlinear terms in the control scheme as a function of the previous feedforward parameters. A simulation study on an multivariable industrial printer shows that the developed framework converges and achieves significant better performance than direct application of the RBF algorithm using SK-iterations for SISO systems.
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ThB18 |
Peony Junior 4412 |
Stability of Nonlinear Systems I |
Regular Session |
Chair: Heath, William Paul | University of Manchester |
Co-Chair: Zaccarian, Luca | LAAS-CNRS and University of Trento |
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13:30-13:50, Paper ThB18.1 | |
>A Compositional Approach to Certifying Almost Global Asymptotic Stability of Cascade Systems |
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Welde, Jake | University of Pennsylvania |
Kvalheim, Matthew | University of Maryland, Baltimore County |
Kumar, Vijay | University of Pennsylvania |
Keywords: Stability of nonlinear systems, Algebraic/geometric methods
Abstract: In this work, we give sufficient conditions for the almost global asymptotic stability of a cascade in which the subsystems are only almost globally asymptotically stable. The result is extended to upper triangular systems of arbitrary size. In particular, if the unforced subsystems are almost globally asymptotically stable and their only chain recurrent points are hyperbolic equilibria, then the boundedness of forward trajectories is sufficient for the almost global asymptotic stability of the full upper triangular system. We show that unboundedness of such cascades is prohibited by growth rate conditions on the interconnection term and a Lyapunov function for the unforced outer subsystem, and the required structure for the chain recurrent set is enjoyed by classes of systems common in geometric control e.g. dissipative mechanical systems. Our results stand in contrast to prior works that require either time scale separation, strong disturbance robustness properties, or global asymptotic stability in the subsystems.
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13:50-14:10, Paper ThB18.2 | |
>Phase Limitations of Multipliers at Harmonics Via Frequency Intervals |
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Heath, William Paul | University of Manchester |
Carrasco, Joaquin | University of Manchester |
Keywords: Stability of nonlinear systems, Constrained control
Abstract: The absolute stability of a Lurye system with a monotone nonlinearity is guaranteed by the existence of a suitable O'Shea-Zames-Falb (OZF) multiplier. A numerically tractable phase condition has recently been proposed under which there can be no suitable OZF multiplier for the transfer function of a given continuous-time plant. The condition has been derived via the so-called duality approach. Here we show that the condition may also be derived from an established frequency interval approach providing an important link between the two hitherto distinct approaches. We show that it leads to significantly improved results compared with the frequency interval approach on a benchmark example.
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14:10-14:30, Paper ThB18.3 | |
>Some Relations between Different Stability Notions for Discrete-Time Systems with Inputs |
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Dashkovskiy, Sergey | University of Wuerzburg |
Schroll, Andreas | University of Würzburg |
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14:30-14:50, Paper ThB18.4 | |
>Local Static Anti-Windup Design with Sign-Indefinite Quadratic Forms |
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Pantano-Calderón, Santiago | LAAS-CNRS |
Tarbouriech, Sophie | LAAS-CNRS |
Zaccarian, Luca | LAAS-CNRS |
Keywords: Stability of nonlinear systems, LMIs, Lyapunov methods
Abstract: This note proposes static anti-windup gains design for closed-loop linear systems with saturating inputs providing maximized non-ellipsoidal estimates of the basin of attraction. The proposed design uses sign-indefinite quadratic forms leading to locally positive definite nonquadratic Lyapunov functions. An iterative algorithm that solves the bilinear matrix conditions inherent to this problem is proposed, based on a convex-concave decomposition. A numerical application is presented to illustrate the effectiveness of the proposed method.
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14:50-15:10, Paper ThB18.5 | |
>Control of Bilinear Systems Using Gain-Scheduling: Stability and Performance Guarantees |
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Strässer, Robin | University of Stuttgart |
Berberich, Julian | University of Stuttgart |
Allgöwer, Frank | University of Stuttgart |
Keywords: Stability of nonlinear systems, LMIs
Abstract: In this paper, we present a state-feedback controller design method for bilinear systems. To this end, we write the bilinear system as a linear fractional representation by interpreting the state in the bilinearity as a structured uncertainty. Based on that, we derive convex conditions in terms of linear matrix inequalities for the controller design, which are efficiently solvable by semidefinite programming. Further, we prove asymptotic stability and quadratic performance of the resulting closed-loop system locally in a predefined region. The proposed design uses gain-scheduling techniques and results in a state feedback with rational dependence on the state, which can substantially reduce conservatism and improve performance in comparison to a simpler, linear state feedback. Moreover, the design method is easily adaptable to various scenarios due to its modular formulation in the robust control framework. Finally, we apply the developed approaches to numerical examples and illustrate the benefits of the approach.
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15:10-15:30, Paper ThB18.6 | |
>Estimation of Regions of Attraction with Formal Certificates in a Purely Data-Driven Setting |
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Mauroy, Alexandre | University of Namur |
Sootla, Aivar | University of Oxford |
Keywords: Stability of nonlinear systems, Lyapunov methods, Computational methods
Abstract: We provide a Koopman operator based method to estimate the region of attraction of equilibria in a purely data-driven setting. The proposed method yields formal stability certificates, while not requiring prior knowledge of the system dynamics or online addition of data points along the way. It consists in three steps. First, a candidate Lyapunov is constructed through an approximated linear lifted dynamics. Next, the validity domain of the Lyapunov function is assessed from the data set. This validation step is performed with the sole knowledge of a (possibly loose) second-order bound on the flow, and without the usual a priori knowledge of a Lipschitz constant. Finally, an inner approximation of the region of attraction is obtained on an adaptive grid via a branch-and-bound algorithm.
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ThB19 |
Peony Junior 4411 |
Stability of Linear Systems |
Regular Session |
Chair: Lindquist, Anders | Shanghai Jiao Tong University |
Co-Chair: Park, PooGyeon | Pohang Univ. of Sci. & Tech |
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13:30-13:50, Paper ThB19.1 | |
>A Novel Free-Matrix-Based Summation Inequality for Stability Analysis of Discrete-Time Delayed System |
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Park, Yongbeom | POSTECH |
Park, PooGyeon | POSTECH (Pohang Univ. of Sci. & Tech.) |
Keywords: Stability of linear systems, Delay systems, Lyapunov methods
Abstract: This paper introduces an improved stability criterion for discrete-time systems with time-varying delay. A novel summation inequality based on the free-matrix is suggested which considers the augmented vector of the state and its forward difference. Additionally, the proposed summation inequality is employed to derive an improved stability criterion for the discrete-time system with time-varying delay. A new Lyapunov-Krasovskii functional is established for applying the summation lemma to reduce the conservatism of the stability analysis. To verify the effectiveness of the proposed approach, the maximum admissible upper bounds of the proposed method is presented in comparison to existing methods with two numerical examples.
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13:50-14:10, Paper ThB19.2 | |
>Linear Stability of Plane Poiseuille Flow in the Sense of Lyapunov |
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Peet, Yulia | Arizona State University |
Edwards, Collin | Arizona State University |
Keywords: Stability of linear systems, Fluid flow systems, LMIs
Abstract: In this paper, we present a linear stability analysis formulation for a plane Poiseuille flow developed in a continuous time domain. Contrary to a conventional approach based on an eigenvalue analysis, which can only proof stability with respect to certain solutions that are assumed to be time harmonics modulated by an exponentially growing or decaying amplitude, the presented methodology does not make any assumptions on a solution form. By analyzing all time-varying solutions and not only the ones restricted to a specific functional form, the developed stability test provides a stronger condition with regard to the system stability. Stability analysis is performed by first casting the corresponding linearized partial differential equation into a partial integral equation (PIE) form, and subsequently employing a linear partial inequality (LPI) stability test, which searches for a corresponding Lyapunov function parameterized through polynomial expansions to prove or disprove stability. Stability results of the continuous-time formulation for the plane Poiseuille flow are compared with a traditional eigenvalue-based analysis, demonstrating that the developed methodology represents a stricter condition on stability.
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14:10-14:30, Paper ThB19.3 | |
>Coercive Quadratic ISS Lyapunov Functions for Analytic Systems |
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Mironchenko, Andrii | University of Passau |
Schwenninger, Felix | University of Twente |
Keywords: Stability of linear systems, Lyapunov methods, Distributed parameter systems
Abstract: We investigate the relationship between input-to-state stability (ISS) of linear infinite-dimensional systems and existence of coercive ISS Lyapunov functions. We show that input-to-state stability of a linear system does not imply existence of a coercive quadratic ISS Lyapunov function, even if the underlying semigroup is analytic, and the input operator is bounded. However, if in addition the semigroup is similar to a contraction semigroup on a Hilbert space, then a quadratic ISS Lyapunov function always exists. Next we consider analytic and similar to contraction semigroups in Hilbert spaces with unbounded input operator B. If B is slightly stronger than 2-admissible, we construct explicitly a coercive L^2-ISS Lyapunov function. If the generator of a semigroup is additionally self-adjoint, this Lyapunov function is precisely a square norm in the state space.
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14:30-14:50, Paper ThB19.4 | |
>A Generalized Stopping Criterion for Real-Time MPC with Guaranteed Stability |
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Fedorová, Kristína | Slovak University of Technology in Bratislava |
Jiang, Yuning | EPFL |
Oravec, Juraj | Slovak University of Technology in Bratislava |
Jones, Colin N. | EPFL |
Kvasnica, Michal | Slovak University of Technology in Bratislava |
Keywords: Stability of linear systems, Predictive control for linear systems, Optimization algorithms
Abstract: Most of the real-time implementations of the stabilizing optimal control actions suffer from the necessity to provide high computational effort. This paper presents a cutting-edge approach for real-time evaluation of linear-quadratic model predictive control (MPC) that employs a novel generalized stopping criterion achieving asymptotic stability in the presence of input constraints. The proposed method evaluates a fixed number of iterations independent of the initial condition, eliminating the necessity for computationally expensive methods. We demonstrate the effectiveness of the introduced technique by its implementation of two widely-used first-order optimization methods: the projected gradient descent method (PGDM) and the alternating directions method of multipliers (ADMM). The numerical simulation confirmed a significantly reduced number of iterations resulting in suboptimality rates of less than 2, while the reductions exceeded 80. These results nominate the proposed criterion as an efficient real-time implementation method of MPC controllers.
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14:50-15:10, Paper ThB19.5 | |
>A Parameterized Solution to the Simultaneous Stabilization Problem |
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Cui, Yufang | Shanghai Jiao Tong University |
Lindquist, Anders | Shanghai Jiao Tong University |
Keywords: Stability of linear systems, Modeling, Computational methods
Abstract: In a series of fundamental papers BK Ghosh reduced the simultaneous stabilization problem to a Nevanlinna-Pick interpolation problem. In this paper we generalize some of these results allowing for derivative constraints. Moreover, we apply a method based on a Riccati-type matrix equation, called the Covariance Extension Equation, which provides a parameterization of all solutions in terms of a monic Schur polynomial. The procedure is illustrated by examples.
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15:10-15:30, Paper ThB19.6 | |
>On Solving Infinite-Dimensional Toeplitz Block LMIs |
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Vernerey, Flora | Université De Lorraine, CNRS |
Riedinger, Pierre | Université De Lorraine - CNRS |
Daafouz, Jamal | Université De Lorraine, CRAN, CNRS |
Keywords: LMIs, Stability of linear systems, Time-varying systems
Abstract: This paper focuses on the resolution of infinite-dimensional Toeplitz Block LMIs, which are frequently encountered in the context of stability analysis and control design problems formulated in the harmonic framework. We propose {a consistent truncation method that makes this infinite dimensional problem tractable} and demonstrate that a solution to the truncated problem can always be found at any order, provided that the original infinite-dimensional Toeplitz Block LMI problem is feasible. Using this approach, we illustrate how the infinite dimensional solution of a Toeplitz Block LMI based convex optimization problem can be recovered up to {an arbitrarily} small error, by solving a finite dimensional truncated problem. The obtained results are applied to stability analysis and harmonic LQR for linear time periodic (LTP) systems.
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ThB20 |
Orchid Junior 4312 |
Robotics |
Regular Session |
Chair: Campolo, Domenico | Nanyang Technological University, Singapore |
Co-Chair: Schoellig, Angela P | University of Toronto |
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13:30-13:50, Paper ThB20.1 | |
>Multi-Step Model Predictive Safety Filters: Reducing Chattering by Increasing the Prediction Horizon |
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Pizarro Bejarano, Federico | University of Toronto |
Brunke, Lukas | University of Toronto |
Schoellig, Angela P | University of Toronto |
Keywords: Robotics
Abstract: Learning-based controllers have demonstrated superior performance compared to classical controllers in various tasks. However, providing safety guarantees is not trivial. Safety, the satisfaction of state and input constraints, can be guaranteed by augmenting the learned control policy with a safety filter. Model predictive safety filters (MPSFs) are a common safety filtering approach based on model predictive control (MPC). MPSFs seek to guarantee safety while minimizing the difference between the proposed and applied inputs in the immediate next time step. This limited foresight can lead to jerky motions and undesired oscillations close to constraint boundaries, known as chattering. In this paper, we reduce chattering by considering input corrections over a longer horizon. Under the assumption of bounded model uncertainties, we prove recursive feasibility using techniques from robust MPC. We verified the proposed approach in both extensive simulation and quadrotor experiments. In experiments with a Crazyflie 2.0 drone, we show that, in addition to preserving the desired safety guarantees, the proposed MPSF reduces chattering by more than a factor of 4 compared to previous MPSF formulations.
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13:50-14:10, Paper ThB20.2 | |
>An SDP Optimization Formulation for the Inverse Kinematics Problem |
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Wu, Liangting | Boston University |
Tron, Roberto | Boston University |
Keywords: Robotics
Abstract: Inverse kinematics (IK) is an important problem in robot control and motion planning; however, the nonlinearity of the map from joint angles to robot configurations makes the problem nonconvex. In this paper, we propose an inverse kinematics solver that works in the space of rotation matrices of the link reference frames rather than joint angles. To overcome the nonlinearity of the manifold of rotation matrices SO(3), we propose a semidefinite programming (SDP) relaxation of the kinematic constraints followed by a fixed-trace rank minimization via maximization of a convex function. Along the way, we show that the feasible set of an IK problem is exactly the intersection of a convex set and fixed-trace rank-1 matrices. Thanks to the use of matrices with fixed trace, our algorithm to obtain rank-1 solutions has guaranteed local convergence. Unlike some traditional solvers, our method does not require an initial guess, and can be applied to robots with closed kinematic chains without ad-hoc modifications such as splitting the kinematic chain. Compared to other work that performs SDP relaxation for IK problems, our formulation is simpler, and uses variables with smaller sizes. We validate our approach via simulations on a closed kinematic chain constituted by two robotic arms holding a box, comparing against a standard IK method.
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14:10-14:30, Paper ThB20.3 | |
>Acceleration-Free Recursive Composite Learning Control of High-DoF Robot Manipulators |
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Zhu, Yuejiang | Sun Yat-Sen University |
Shi, Tian | Sun Yat-Sen University |
Li, Weibing | Sun Yat-Sen University |
Pan, Yongping | Sun Yat-Sen University |
Keywords: Robotics, Adaptive control, Closed-loop identification
Abstract: Composite learning robot control (CLRC) is an adaptive control approach that achieves exponential parameter convergence without using a stringent condition termed persistent excitation (PE). For robots with low degrees of freedom (DoFs), a filtered regressor of the robot dynamics needed in CLRC can be calculated analytically without joint accelerations, but this is difficult for high-DoF robots. Under the linear parameterization by the recursive Newton-Euler algorithm, this paper proposes an acceleration-free recursive CLRC (RCLRC) method for high-DoF robots to achieve exponential parameter convergence under a weakened condition termed interval excitation (IE). The proposed method has a low computational cost and avoids undesirable acceleration estimation that seriously affects performance. Simulations and experiments on a 7-DoF robot manipulator have verified the superiority of the proposed RCLRC, where it outperforms its analytical version in both estimation and tracking.
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14:30-14:50, Paper ThB20.4 | |
>The Inherent Representation of Tactile Manipulation Using Unified Force-Impedance Control |
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Karacan, Kübra | TUM, MIRMI |
Kirschner, Robin | TU Munich - MIRMI |
Sadeghian, Hamid | Technical University of Munich |
Wu, Fan | Technical University of Munich |
Haddadin, Sami | Technische Universität München |
Keywords: Robotics, Autonomous robots
Abstract: Different robotic manipulation tasks require different execution and planning strategies. Nevertheless, the versatility of tasks in assembly and disassembly demands flexible control strategies. Fundamental to achieving such adaptive control methods is understanding and generalizing the interactions between tools, the object that is manipulated, and the environment required to perform a manipulation. In this paper, we address the problem of generating adaptive manipulation by introducing the force-velocity task phase plot that represents the inherent nature of tactile manipulation skills. This representation enables us to identify the basic phases of the interaction in the force-velocity domain. Using unified force-impedance control, we establish a tactile manipulation plan to robustly conduct versatile manipulation tasks even in case of disturbances or imprecise task information. The proposed control scheme features a dynamic process for impedance shaping based on the external force applied to the robot and the skill motion error for collision response, as well as a force-shaping function that enables both a smooth transition from free motion to contact and force regulation. We implement and compare the control strategy to previously proposed strategies using peg-in-hole reference experiments that include force disturbance and positioning inaccuracies and show the respective task phase plots. As a result, we observe high controller robustness and conclude that using the task phase plot as the inherent representation of tactile manipulation via unified force-impedance control enables successful adaptive controller design and creates a quantifiable basis for robotic skill solution comparison.
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14:50-15:10, Paper ThB20.5 | |
>Quasi-Static Mechanical Manipulation As an Optimal Process |
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Campolo, Domenico | Nanyang Technological University, Singapore |
Cardin, Franco | Univ. Di Padova |
Keywords: Robotics, Differential-algebraic systems, Optimization algorithms
Abstract: This work focuses on quasi-static manipulation of elastically-interconnected rigid bodies by an agent, e.g. a robot assembling mechanical parts. The whole system is seen as an underactuated control problem, where only certain degrees of freedom (e.g. robot end-effector) are directly controllable. Mechanical contact is regularized via nonlinear yet smooth elastic interaction giving rise to a smooth total potential energy. The squared-Hessian of such a potential is used as optimality measure and quasi-static mechanical manipulation is rephrased as optimal path planning on the manifold of mechanical equilibria. A simple example of an elastically-driven inverted pendulum is presented as a toy model. Numerical implementation as a minimum path on graphs is also described.
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15:10-15:30, Paper ThB20.6 | |
>MrDMD-Based Sensor Placement in Distributed Flow Estimation for the Design of the Artificial Lateral Line of an Underwater Robot |
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Wang, Jun | Peking University |
Shen, Tongsheng | National Innovation Institute of Defense Technology |
Zhao, Dexin | National Innovation Institute of Defense Technology |
Zhang, Feitian | Peking University |
Keywords: Robotics, Estimation, Optimization
Abstract: An artificial lateral line (ALL) is a sensing system that imitates the distributed perception organs of fish and plays a major role in enhancing the flow estimation capability of underwater robots. Whereas various ALLs have been designed and developed, it is still an open question how to better place ALL sensors on underwater robots, especially for those with complex shapes and working in dynamic flow and robot operating conditions. Aiming to answer this question, this paper presents a novel data-driven sensor placement method for ALLs of underwater robots. This method adopts distributed pressure sensors to measure the flow field along the profile or the outermost boundary of an underwater robot, and quantifies the dynamic information embedded within these measurements using multi-resolution dynamic mode decomposition (mrDMD). The sensors are then positioned by optimizing the dynamic flow information to enhance the perception. Compared with existing sensor placement methods, such as observability maximization and exhaustive experimental search, the proposed method focuses on the modes of dynamics variability at various spatio-temporal scales, thus leading to improved sensing ability especially in complex and dynamic flows. In addition, comprehensively considering the sensor placement under different flow and robot operating conditions, the proposed method is expected to provide an optimal solution for the overall sensing performance of the ALL system. To demonstrate the effectiveness of the proposed method, a case study of background flow speed estimation of oscillating underwater robots of different shapes in a uniform flow is presented.
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ThB21 |
Orchid Junior 4311 |
Predictive Control for Nonlinear Systems II |
Regular Session |
Chair: Zeilinger, Melanie N. | ETH Zurich |
Co-Chair: Krishnamoorthy, Dinesh | TU Eindhoven |
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13:30-13:50, Paper ThB21.1 | |
>Imitation Learning from Nonlinear MPC Via the Exact Q-Loss and Its Gauss-Newton Approximation |
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Ghezzi, Andrea | University of Freiburg |
Hoffmann, Jasper | University of Freiburg |
Frey, Jonathan | University of Freiburg |
Boedecker, Joschka | University of Freiburg |
Diehl, Moritz | University of Freiburg |
Keywords: Predictive control for nonlinear systems, Machine learning, Optimal control
Abstract: This work presents a novel loss function for learning nonlinear Model Predictive Control policies via Imitation Learning. Standard approaches to Imitation Learning neglect information about the expert and generally adopt a loss function based on the distance between expert and learned controls. In this work, we present a loss based on the Q-function directly embedding the performance objectives and constraint satisfaction of the associated Optimal Control Problem (OCP). However, training a Neural Network with the Q-loss requires solving the associated OCP for each new sample. To alleviate the computational burden, we derive a second Q-loss based on the Gauss-Newton approximation of the OCP resulting in a faster training time. We validate our losses against Behavioral Cloning, the standard approach to Imitation Learning, on the control of a nonlinear system with constraints. The final results show that the Q-function-based losses significantly reduce the amount of constraint violations while achieving comparable or better closed-loop costs.
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13:50-14:10, Paper ThB21.2 | |
>An Improved Data Augmentation Scheme for Model Predictive Control Policy Approximation |
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Krishnamoorthy, Dinesh | TU Eindhoven |
Keywords: Predictive control for nonlinear systems, Machine learning, Optimization
Abstract: This paper considers the problem of data generation for MPC policy approximation. Learning an approximate MPC policy from expert demonstrations requires a large data set consisting of optimal state-action pairs, sampled across the feasible state space. Yet, the key challenge of efficiently generating the training samples has not been studied widely. Recently, a sensitivity-based data augmentation framework for MPC policy approximation was proposed, where the parametric sensitivities are exploited to cheaply generate several additional samples from a single offline MPC computation. The error due to augmenting the training data set with inexact samples was shown to increase with the size of the neighborhood around each sample used for data augmentation. Building upon this work, this letter paper presents an improved data augmentation scheme based on predictor-corrector steps that enforces a user-defined level of accuracy, and shows that the error bound of the augmented samples are independent of the size of the neighborhood used for data augmentation.
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14:10-14:30, Paper ThB21.3 | |
>Data-Enabled Neighboring Extremal Optimal Control: A Computationally Efficient DeePC |
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Vahidimoghaddam, Amin | Miichigan State University |
Zhang, Kaixiang | Michigan State University |
Li, Zhaojian | Michigan State University |
Wang, Yan | Self Employed |
Keywords: Predictive control for nonlinear systems, Optimal control, Constrained control
Abstract: Model-based optimal control strategies typically rely on accurate parametric representations of the underlying systems, which can be challenging to obtain, especially for nonlinear and complex systems. Therefore, data-driven optimal controllers have become increasingly attractive to both academics and industry practitioners. As a data-driven optimal control approach that can explicitly handle constraints, data-enabled predictive control (DeePC) makes a transition from model-based optimal control strategies (e.g. model predictive control (MPC)) to a data-driven one such that it seeks an optimal control policy from raw input/output (I/O) data without requiring system identification prior to control deployment, achieving remarkable successes in various applications. However, this approach involves high computational cost due to the dimension of the decision variable, which is generally significantly higher than its MPC counterpart. Several approaches have been proposed to reduce the computational cost of the DeePC for linear time-invariant (LTI) systems. However, finding a computationally efficient method to implement the DeePC for the nonlinear systems is still an open challenge. In this paper, we propose a data-enabled neighboring extremal (DeeNE) to approximate the DeePC policy and reduce its computational cost for the constrained nonlinear systems. The DeeNE adapts a pre-computed nominal DeePC solution to the perturbations of the initial I/O trajectory and the reference trajectory from the nominal ones. We also develop a scheme to handle nominal non-optimal solutions so that we can use the DeeNE solution as the nominal solution during the control process. Promising simulation results on the cart inverted pendulum problem demonstrate the efficacy of the DeeNE framework.
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14:30-14:50, Paper ThB21.4 | |
>Robust Optimal Control for Nonlinear Systems with Parametric Uncertainties Via System Level Synthesis |
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Leeman, Antoine | ETH Zurich |
Sieber, Jerome | ETH Zurich |
Bennani, Samir | European Space Agency |
Zeilinger, Melanie N. | ETH Zurich |
Keywords: Predictive control for nonlinear systems, Optimal control, Uncertain systems
Abstract: This paper addresses the problem of optimally controlling nonlinear systems with norm-bounded disturbances and parametric uncertainties while robustly satisfying constraints. The proposed approach jointly optimizes a nominal nonlinear trajectory and an error feedback, requiring minimal offline design effort and offering low conservatism. This is achieved by decomposing the affine-in-the-parameter uncertain nonlinear system into a nominal nonlinear system and an uncertain linear time-varying system. Using this decomposition, we can apply established tools from system level synthesis to convexly over-bound all uncertainties in the nonlinear optimization problem. Moreover, it enables tight joint optimization of the linearization error bounds, parametric uncertainties bounds, nonlinear trajectory, and error feedback. With this novel controller parameterization, we can formulate a convex constraint to ensure robust performance guarantees for the nonlinear system. The presented method is relevant for numerous applications related to trajectory optimization, e.g., in robotics and aerospace engineering. We demonstrate the performance of the approach and its low conservatism through the simulation example of a post-capture satellite stabilization.
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14:50-15:10, Paper ThB21.5 | |
>Tracking MPC Tuning in Continuous Time: A First-Order Approximation of Economic MPC |
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Facchino, Matteo | IMT School for Advanced Studies Lucca |
Bemporad, Alberto | IMT School for Advanced Studies Lucca |
Zanon, Mario | IMT Institute for Advanced Studies Lucca |
Keywords: Predictive control for nonlinear systems, Predictive control for linear systems, Optimal control
Abstract: Economic MPC (EMPC) optimizes closed-loop performance by directly minimizing a given objective function, as opposed to Tracking MPC (TMPC) which instead penalizes deviations from a precalculated optimal reference. The main difference between the two approaches can be observed during transients, as the former always acts optimally, while the latter is only optimal when the reference is accurately tracked. Unfortunately, stability for EMPC is in general difficult to prove, as opposed to TMPC which builds on a rich theory. Additionally, many efficient algorithms are available for TMPC, while solving the EMPC problem can be much harder. A family of discrete-time TMPC schemes that provide approximate economic optimality has been developed in order to partially overcome these issues. In this paper, we aim at extending such a family of TMPC schemes by deriving them also in continuous time. Similarly to the discrete-time version, also our TMPC scheme provides a first-order approximation of the EMPC control law. We demonstrate the theory with a numerical example that confirms the first-order approximation and show that our continuous-time formulation can be made equivalent to the discrete-time one.
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15:10-15:30, Paper ThB21.6 | |
>Robust Nonlinear Reduced-Order Model Predictive Control |
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Alora, John Irvin | Stanford University |
Pabon, Luis A. | Stanford University |
Köhler, Johannes | ETH Zurich |
Cenedese, Mattia | ETH Zurich |
Schmerling, Edward | Stanford University |
Zeilinger, Melanie N. | ETH Zurich |
Haller, George | ETH Zurich |
Pavone, Marco | Stanford University |
Keywords: Predictive control for nonlinear systems, Reduced order modeling, Robotics
Abstract: Real-world systems are often characterized by high-dimensional nonlinear dynamics, making them challenging to control in real time. While reduced-order models (ROMs) are frequently employed in model-based control schemes, dimensionality reduction introduces model uncertainty which can potentially compromise the stability and safety of the original high-dimensional system. In this work, we propose a novel reduced-order model predictive control (ROMPC) scheme to solve constrained optimal control problems for nonlinear, high-dimensional systems. To address the challenges of using ROMs in predictive control schemes, we derive an error bounding system that dynamically accounts for model reduction error. Using these bounds, we design a robust MPC scheme that ensures robust constraint satisfaction, recursive feasibility, and asymptotic stability. We demonstrate the effectiveness of our proposed method in simulations on a high-dimensional soft robot with nearly 10,000 states.
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ThB22 |
Orchid Junior 4212 |
Stochastic Systems II |
Regular Session |
Chair: Li, Tao | East China Normal University |
Co-Chair: Nishimura, Yuki | Kagoshima University |
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13:30-13:50, Paper ThB22.1 | |
>A Large-Scale Stochastic Gradient Descent Algorithm Over a Graphon |
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Chen, Yan | East China Normal University |
Li, Tao | East China Normal University / New York University Shanghai |
Keywords: Stochastic systems, Large-scale systems, Mean field games
Abstract: We study the large-scale stochastic gradient descent algorithm over a graphon with a continuum of nodes, which is regarded as the limit of the distributed networked optimization as the number of nodes goes to infinity. Each node has a private local cost function. The global cost function, which all nodes cooperatively minimize, is the integral of the local cost functions on the node set. We propose a stochastic gradient descent algorithm evolving as a graphon particle system, where each node heterogeneously interacts with others through a coupled mean field term. It is proved that if the graphon is connected, then by properly choosing the algorithm gains, all nodes’states achieve consensus uniformly in mean square. Furthermore, if the local cost functions are strongly convex, then all nodes’states converge uniformly to the minimizer of the global cost function in mean square.
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13:50-14:10, Paper ThB22.2 | |
>Prescribed-Time Nonlinear Control with Multiplicative Noise |
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Li, Wuquan | Ludong University |
Krstic, Miroslav | University of California, San Diego |
Keywords: Stochastic systems, Lyapunov methods
Abstract: We study the prescribed-time design problem for strict-feedback nonlinear systems with multiplicative measurement noise. With the assumption that the noise is small and linearly vanishing, we propose a new postulated feedback to solve the prescribed-time mean-square stabilization problem. In contrast to the existing stochastic prescribed-time designs, the merit of our design is that it can effectively deal with multiplicative measurement noise. The existence of measurement noise makes the design rather challenging since the resulting process noise intensity, in closed loop, depends on the feedback gains and even goes to infinity. Finally, a simulation example is given to illustrate the design.
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14:10-14:30, Paper ThB22.3 | |
>Safety-Probability Analysis and Control for Stochastic Systems Based on Lyapunov Candidate Functions |
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Nishimura, Yuki | Kagoshima University |
Hoshino, Kenta | Kyoto University |
Keywords: Stochastic systems, Lyapunov methods
Abstract: In recent control theory, safety analysis and safety-critical control based on a (control) barrier function have been actively pursued. The barrier function is closely related to a Lyapunov function, which is an important property that guarantees asymptotic stability of the system, i.e., the settling to the target state, which is a fundamental control performance. Therefore, control strategies that simultaneously guarantee safety and stability are important in the recent control scene. In this paper, we propose a method for quantitative evaluation of safety probability for stochastic systems based on barrier functions generated from Lyapunov functions, and then develop control design methods to increase the safety probability. In particular, safety analysis and safety-critical control of linear stochastic systems having additive noises are performed based on linear algebra. We also discuss design methods for safety and safety-critical control for input-affine stochastic systems. The effectiveness of the proposed method is demonstrated based on a simple example.
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14:30-14:50, Paper ThB22.4 | |
>The Impact of Recommendation Systems on Opinion Dynamics: Microscopic versus Macroscopic Effects |
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Lanzetti, Nicolas | ETH Zürich |
Dörfler, Florian | Swiss Federal Institute of Technology (ETH) Zurich |
Pagan, Nicolò | University of Zürich |
Keywords: Stochastic systems, Network analysis and control, Agents-based systems
Abstract: Recommendation systems are widely used in web services, such as social networks and e-commerce platforms, to serve personalized content to the users and, thus, enhance their experience. While personalization assists users in navigating through the available options, there have been growing concerns regarding its repercussions on the users and their opinions. Examples of negative impacts include the emergence of filter bubbles and the amplification of users' confirmation bias, which can cause opinion polarization and radicalization. In this paper, we study the impact of recommendation systems on users, both from a microscopic (i.e., at the level of individual users) and a macroscopic (i.e., at the level of a homogenous population) perspective. Specifically, we build on recent work on the interactions between opinion dynamics and recommendation systems to propose a model for this closed loop, which we then study both analytically and numerically. Among others, our analysis reveals that shifts in the opinions of individual users do not always align with shifts in the opinion distribution of the population. In particular, even in settings where the opinion distribution appears unaltered (e.g., measured via surveys across the population), the opinion of individual users might be significantly distorted by the recommendation system.
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14:50-15:10, Paper ThB22.5 | |
>Adaptive Sampling for Online Learning Spectral Properties of Networks |
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Abdullah, Mohammed | Telecom-Sud Paris |
Hayel, Yezekael | University of Avignon |
Reiffers, Alexandre | IMT Atlantique |
Chonavel, Thierry | IMT Atlantique |
Keywords: Stochastic systems, Network analysis and control, Learning
Abstract: Recently, the area of decision and control has been interested in studying the connectivity of large-scale networks. As networks under study are large, to have a complete knowledge of the network is impossible, whereas little but representative information is available with an efficient exploration scheme. Machine learning approaches were presented and used to tackle this difficulty to hold it up. In this regard, we present and prove the convergence of an efficient algorithm that converges to the Fielder vector when the topology is initially unknown and the only accessible information is gathered by a random walk process throughout the entire network. The Rayleigh quotient optimization problem and the notion of stochastic approximation are the foundations of our technique. We consider multiple sampling strategies that are categorized under random walks, as well as adapting another sampling approach that are considered random walk, the Gibbs sampling, and it showed better results. Finally, we demonstrate its performance on different network topologies.
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15:10-15:30, Paper ThB22.6 | |
>Peak Value-At-Risk Estimation for Stochastic Differential Equations Using Occupation Measures |
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Miller, Jared | ETH Zurich |
Tacchi, Matteo | Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-Lab |
Sznaier, Mario | Northeastern University |
Jasour, Ashkan | NASA JPL |
Keywords: Stochastic systems, Nonlinear systems, LMIs
Abstract: This paper proposes an algorithm to upper-bound maximal quantile statistics of a state function over the course of a Stochastic Differential Equation (SDE) system execution. This chance-peak problem is posed as a nonconvex program aiming to maximize the Value-at-Risk (VaR) of a state function along SDE state distributions. The VaR problem is upper-bounded by an infinite-dimensional Second-Order Cone Program in occupation measures through the use of one-sided Cantelli or Vysochanskii-Petunin inequalities. These upper bounds on the true quantile statistics may be approximated from above by a sequence of Semidefinite Programs in increasing size using the moment-Sum-of-Squares hierarchy when all data is polynomial. Effectiveness of this approach is demonstrated on example stochastic polynomial dynamical systems.
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ThB23 |
Orchid Junior 4211 |
Fault Detection |
Regular Session |
Chair: Previdi, Fabio | Università Degli Studi Di Bergamo |
Co-Chair: Qiu, Gen | University of Electronic Science and Technology of China |
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13:30-13:50, Paper ThB23.1 | |
>Quickest Change Point Detection with Measurements Over a Lossy Link |
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Chaythanya KV, Krishna | Indian Institute of Science |
Chattopadhyay, Arpan | Indian Institute of Technology, Delhi |
Kumar, Anurag | Indian Institute of Science |
Sundaresan, Rajesh | Indian Institute of Science |
Keywords: Fault detection, Estimation, Sensor networks
Abstract: Motivated by Industry 4.0 applications, we consider quickest change point detection (QCD) when process measurements are transmitted by a sensor over a lossy wireless link to a decision maker (DM). The sensor node samples measurements using a Bernoulli sampling process, and places the measurement samples in a transmit queue of the transmitter. The transmitter uses a retransmit-until-success transmission strategy to deliver packets to the DM over the lossy link, which is modeled as an independent Bernoulli process and has different loss probabilities before and after the change. We pose the QCD problem in the non-Bayesian setting under Lorden's framework, and derive a CUSUM algorithm. By defining a suitable Markov process, involving the DM measurements and the queue length process, we show that the problem reduces to QCD of a Markov process. Characterizing the information measure per measurement sample at the DM, our analysis proves the asymptotic optimality of our algorithm when the false alarm rate tends to zero. We discuss extensions of the analysis to periodic sampling and no-retransmission cases. Through numerical analysis, we demonstrate trade-offs that can be used to optimize system design parameters such as the sampling rate of the measurement process in the non-asymptotic regime.
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13:50-14:10, Paper ThB23.2 | |
>Model Uncertainty-Aware Residual Generators for SISO LTI Systems Based on Kernel Identification and Randomized Approaches |
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Mazzoleni, Mirko | University of Bergamo |
Valceschini, Nicholas | University of Bergamo |
Previdi, Fabio | Università Degli Studi Di Bergamo |
Keywords: Fault detection, Identification
Abstract: Robustness of residual signals to model uncertainties and noise in the measurements is of paramount importance in model-based fault diagnosis. Model uncertainty has been mainly represented in a structured way by considering known bounds on the model parameters, thus relying on prior knowledge about the plant structure and values of its physical parameters. When the plant is completely unknown, system identification techniques must be used for model-based diagnosis. In this work, we present a data-driven approach to represent the uncertainty in the identified model. This uncertainty is described in the frequency domain using kernel based identification and robust control tools. The estimated model uncertainty region overlaps with the true uncertainty region with a probability specified by the user. The user choices are thus reduced to the selection of only some interpretable hyperparameters. Then, a residual generator robust to the estimated model uncertainty and measurements noise is designed by a standard H∞ approach. Simulation results on SISO LTI systems show the effectiveness of the approach in producing a residual signal viable for the detection of additive faults.
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14:10-14:30, Paper ThB23.3 | |
>Fault Detection Via Occupation Kernel Principal Component Analysis |
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Morrison, Zachary | Oklahoma State University |
Russo, Benjamin | Oak Ridge National Laboratory |
Lian, Yingzhao | EPFL |
Kamalapurkar, Rushikesh | Oklahoma State University |
Keywords: Fault detection, Statistical learning, Machine learning
Abstract: The reliable operation of automatic systems is heavily dependent on the ability to detect faults in the underlying dynamical system. While traditional model-based methods have been widely used for fault detection, data-driven approaches have garnered increasing attention due to their ease of deployment and minimal need for expert knowledge. In this paper, we present a novel principal component analysis (PCA) method that uses occupation kernels. Occupation kernels result in feature maps that are tailored to the measured data, have inherent noise-robustness due to the use of integration, and can utilize irregularly sampled system trajectories of variable lengths for PCA. The occupation kernel PCA method is used to develop a reconstruction error approach to fault detection and its efficacy is validated using numerical simulations.
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14:30-14:50, Paper ThB23.4 | |
>Statistical Times Series Based Damage Detection in the Fiber Rope Mooring Lines of the Semi-Submersible OO-STAR Wind Floater |
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Sakaris, Christos | Norwegian Research Center NORCE AS |
Schlanbusch, Rune | Norwegian Research Centre |
Nygaard, Tor | Institute for Energy Technology |
Sakellariou, John | University of Patras |
Tutkun, Murat | Institute for Energy Technology |
Keywords: Fault detection, Modeling, Machine learning
Abstract: The Floating Offshore Wind Turbines (FOWTs) based on semi-submersible floaters constitute a popular choice in most markets due to their installation being flexible and in need of low infrastructural requirements. A simple and robust three-legged semi-submersible floater for FOWTs, the OO-STAR wind floater, has been introduced and it can be anchored to the seabed with steel chain mooring lines or hybrid mooring lines - a combination of chains and synthetic fiber ropes. The fiber rope mooring lines present a number of advantages thus leading to a lighter and less costly mooring system. These lines are important for the FOWT's integrity as their loss can lead to the change of the floater's position, a damaged power cable, a possible collision with other infrastructure and high maintenance costs. This why an early detection of damages in the mooring system is crucial. In this study, damage detection in the main part of fiber rope mooring lines of semi-submersible based FOWTs is investigated for the first time. In particular, the OO-STAR floater based FOWT is considered. Two Statistical Time Series based detection methods, the Multiple Model-AutoRegressive (MM-AR) method and the Functional Model Based Method (FMBM) are used and compared. The MM-AR is based on multiple AR models whereas the FMBM on a single Functional Model, for the description of the healthy FOWT's dynamics under varying environmental conditions. The results based on seven healthy and eight damage cases under varying wind speed and wave height show that the two methods are able to achieve damage detection in fiber rope mooring lines without any false alarm or missed damage despite of damages having small effects on the FOWT's dynamics and the fiber ropes presenting a non-linear behaviour.
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14:50-15:10, Paper ThB23.5 | |
>Incipient Fault Detection with Feature Ensemble Based on One-Class Machine Learning Methods |
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Wang, Min | University of Electronic Science and Technology of China |
Cheng, Feiyang | University of Electronic Science and Technology of China |
Chen, Kai | University of Electronic Science and Technology of China |
Mi, Jinhua | University of Electronic Science and Technology of China |
Xu, Zhiwei | Shandong University |
Qiu, Gen | University of Electronic Science and Technology of China |
Keywords: Fault detection, Machine learning, Neural networks
Abstract: Considering production quality and process safety, incipient fault detection has drawn more and more attention. With the rapid development of machine learning, numerous researches for fault detection based on machine learning have been published. However, almost all machine learning methods used for fault detection need abnormal data to construct models. Unfortunately, it is difficult to obtain sufficient fault samples in practical industrial processes. In addition, the existing fault detection methods are based on single feature extraction strategy. Process monitoring methods with different working principles often extract and utilize different process information. Reasonable integration of features extracted by multiple methods can usually effectively improve the performance of incipient fault detection. Therefore, this paper proposes an one-class machine learning feature ensemble model (OCMLFEM) for incipient fault detection. In OCMLFEM, various one-class machine learning models are constructed as basic detectors. In order to effectively mine the features obtained by basic detectors, a feature ensemble strategy with the technologies of sliding window singular value and principal component analysis is adopted. Then, Tennessee Eastman process is utilized to verify the validity of the proposed detection model, which proves that OCMLFEM has significant superiority.
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15:10-15:30, Paper ThB23.6 | |
>Anomaly Search Over Many Sequences with Switching Costs |
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Ubl, Matthew | University of Florida |
Robinson, Benjamin | AFRL |
Hale, Matthew | University of Florida |
Keywords: Fault detection, Statistical learning
Abstract: This paper considers the quickest search problem to identify anomalies among large numbers of data streams. These streams can model, for example, disjoint regions monitored by a mobile robot. A particular challenge is a version of the problem in which the experimenter must suffer a cost each time the data stream being sampled changes, such as the time the robot must spend moving between regions. In this paper, we propose an algorithm which accounts for switching costs by varying a confidence threshold that governs when the algorithm switches to a new data stream. Our main contributions are easily computable approximations for both the optimal value of this threshold and the optimal value of the parameter that determines when a stream is flagged as an anomaly, using the Brownian motion approximations. Further, we empirically show (i) a uniform improvement for switching costs of interest and (ii) roughly equivalent performance for small switching costs when comparing to the closest available algorithm.
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ThB24 |
Orchid Main 4201AB |
Switched Systems I |
Regular Session |
Chair: Incremona, Gian Paolo | Politecnico Di Milano |
Co-Chair: Zhang, Wentao | Nanyang Technological University |
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13:30-13:50, Paper ThB24.1 | |
>Design of a Distributed Switching Model Predictive Control for Quadrotor UAVs Aggregation |
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Yuca Huanca, Chrystian Pool Edmundo | Politecnico Di Milano |
Incremona, Gian Paolo | Politecnico Di Milano |
Colaneri, Patrizio | Politecnico Di Milano |
Keywords: Switched systems, Distributed control, Optimization algorithms
Abstract: This letter proposes a novel distributed model predictive control (MPC) strategy to address the swarm aggregation of a team of quadrotor unmanned aerial vehicles (UAVs). First, a switched formulation of the quadrotor model is derived by mapping the UAVs dynamics into a set of finite motion modes. Then, relying on a suitably selected control Lyapunov function (CLF), the inter-agent collisions and the aggregation task are taken into account to design a switching MPC (SMPC) strategy. A clustering method is also introduced to define the communication network among the agents, which is essential to sequentially solve the optimal control problem. Finally, the efficacy of the proposal, also in comparison with other methodologies, is satisfactorily shown in simulation.
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13:50-14:10, Paper ThB24.2 | |
>Identification of Piecewise Affine Systems with Online Deterministic Annealing |
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Mavridis, Christos | University of Maryland, College Park |
Baras, John S. | University of Maryland |
Keywords: Switched systems, Identification, Intelligent systems
Abstract: We propose a new online identification scheme for discrete-time piece-wise affine models based on a system of adaptive algorithms. A stochastic approximation algorithm based on online deterministic annealing runs at a slow timescale, estimating the partition of the space that defines the modes of the system. At the same time, a recursive identification algorithm, running at a higher timescale, updates the parameters of local identification models based on the estimate of the modes. Convergence results under mild assumptions are given based on the theory of two timescale stochastic approximation. In contrast to standard identification algorithms for piece-wise affine systems, the proposed approach is appropriate for online system identification using sequential data acquisition, and is computationally more efficient compared to standard algebraic, mixed-integer programming, and clustering-based methods. The progressive nature of the algorithm provides real-time control over the performance-complexity trade-off, desired in practical applications. Experimental results validate the efficacy of the proposed methodology.
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14:10-14:30, Paper ThB24.3 | |
>Sufficient Stability Conditions for a Class of Switched Systems with Multiple Steady States |
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Piccini, Jacopo | Reykjavik University |
August, Elias | Reykjavik University |
Hafstein, Sigurdur | University of Iceland |
Andersen, Stefania | University of Iceland |
Keywords: Switched systems, Lyapunov methods
Abstract: In this paper, we present a novel approach to determine the stability of switched linear and nonlinear systems using Sum of Squares optimisation. Particularly, we use Sum of Squares optimisation to search for a Lyapunov function that defines an absorbing set that confines solution trajectories. For linear systems, we show that this also implies global asymptotic stability. Using this approach, we can study stability for a broader range of switched systems, particularly, we can search for a global attractor for switched nonlinear systems, whose dynamics are given by polynomial vector fields and which have multiple equilibria or limit cycles.
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14:30-14:50, Paper ThB24.4 | |
>False Data Injection Attack for Switched Systems |
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Zhao, Rui | Tianjin University |
Zuo, Zhiqiang | Tianjin University |
Wang, Yijing | Tianjin University |
Zhang, Wentao | Nanyang Technological University |
Keywords: Switched systems, Networked control systems, Estimation
Abstract: This paper studies the secure state estimation problem for switched systems. The single/joint false data injection attacks are designed with the aim at altering the sensor signal and/or switching signal. Firstly, it is shown that the attack will steer system state to infinity but could be detectable by kappa^2 detector when only the switching signal is attacked. In addition, the attack acting on sensor signal is designed, which can be recognized by the summation (SUM) detector but fails by kappa^2 detector. Then a joint attack strategy is devised and a sufficient condition is given to guarantee that the joint attack is strictly stealthy. The joint attack performs well since it can launch a strictly stealthy attack compared with the sensor signal attack. Finally, a numerical example is given to verify the theoretical results.
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14:50-15:10, Paper ThB24.5 | |
>Approximate Model Predictive Control of Switched Affine Systems Using Multitask Learning with Safety and Stability Guarantees |
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Ghawash, Faiq | Norwegian University of Science and Technology (NTNU) |
Hovd, Morten | Norwegian Univ of Sci & Tech |
Schofield, Brad | CERN |
Keywords: Switched systems, Neural networks, Optimal control
Abstract: We study the problem of designing an approximate model predictive control (MPC) for discrete time switched affine systems. The MPC design for the switched affine system requires an online solution of a mixed integer program. However, the combinatorial nature of the mixed integer problems might require a large computational time limiting its applicability in real time scenarios. To this end, we propose a framework based on the multitask learning paradigm to approximate the solution of mixed integer MPC for switched affine systems. We also provide a computational method to overapproximate the reachable sets of the closed-loop system that helps to analyze the safety and stability of the system under the influence of the learned controller. Once trained offline, the resulting controller results in a solver free approach especially suited for implementation on resource constrained embedded hardware. We demonstrate the efficacy of the approach on a real world example of an induced draft cooling tower.
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15:10-15:30, Paper ThB24.6 | |
>On Some Geometric Behavior of Value Iteration on the Orthant: Switching System Perspective |
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Lee, Donghwan | KAIST |
Keywords: Switched systems, Stability of linear systems, Optimal control
Abstract: In this paper, the primary goal is to offer additional insights into the value iteration through the lens of switching system models in the control community. These models establish a connection between value iteration and switching system theory and reveal additional geometric behaviors of value iteration in solving discounted Markov decision problems. Specifically, the main contributions of this paper are twofold: 1) We provide a switching system model of value iteration and, based on it, offer a different proof for the contraction property of the value iteration. 2) Furthermore, from the additional insights, new geometric behaviors of value iteration are proven when the initial iterate lies in a special region. We anticipate that the proposed perspectives might have the potential to be a useful tool, applicable in various settings. Therefore, further development of these methods could be a valuable avenue for future research.
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ThB25 |
Lotus Junior 4DE |
Information Theory and Control |
Regular Session |
Chair: Papadopoulos, Alessandro Vittorio | Mälardalen University |
Co-Chair: Petersen, Ian R. | Australian National University |
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13:30-13:50, Paper ThB25.1 | |
>Multi-Criteria Optimization of Application Offloading in the Edge-To-Cloud Continuum |
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Miloradovic, Branko | Malardalen University |
Papadopoulos, Alessandro Vittorio | Mälardalen University |
Keywords: Information technology systems, Optimization
Abstract: Applications are becoming increasingly data-intensive, requiring a significant amount of computational resources for meeting their demand. Cloud-based services are not sufficient to meet such demand, leading to a shift of the computation towards the devices closer to the edge of the network, leading to the emergence of an Edge-to-Cloud compute Continuum (E2C). Application can offload part of their computation towards the E2C. The allocation of applications to a set of available computing nodes is a challenging problem, as the allocation needs to take into account several factors, including the application requirements and demands as well as the optimization of the resource utilization in the E2C infrastructure and the minimization the CO2 footprint of the executed applications. Control and optimization techniques provide a vast array of tools for the optimized management of the Edge-to-Cloud continuum. In this paper, we provide a mathematical formulation for the application offloading with specific requirements in the cloud computing domain. The problem is modeled both as integer linear programming and constraint programming model, and implemented in commercially available software. Finally, we provide the results of performed comparison between the two models.
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13:50-14:10, Paper ThB25.2 | |
>Sensor-Based Planning and Control for Robotic Systems: Introducing Clarity and Perceivability |
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Agrawal, Devansh Ramgopal | University of Michigan |
Panagou, Dimitra | University of Michigan, Ann Arbor |
Keywords: Information theory and control, Lyapunov methods, Constrained control
Abstract: In this paper, we first introduce an information measure, termed clarity, motivated by information entropy, and show that it has intuitive properties relevant to dynamic coverage control and informative path planning. Clarity defines on a scale of [0, 1] the quality of the information that we have about a variable of interest in an environment. Clarity lower bounds the expected estimation error of any estimator, and is used as the information metric in the notion of perceivability, which is defined later on and is the primary contribution of the paper. Perceivability captures whether a given robotic (or more generally, sensing and control) system has sufficient sensing and actuation capabilities to gather desired information about an environment. We show that perceivability relates to the reachability of an augmented system, which encompasses the robot dynamics and the clarity about the environment, and we derive the corresponding Hamilton-Jacobi-Bellman equations. Thus, we provide an algorithm to measure an environment's perceivability, and obtain optimal controllers that maximize information gain. In simulations, we demonstrate how clarity is a useful concept for planning trajectories, how perceivability can be determined using reachability analysis, and how a Control Barrier Function controller can be used to design controllers to maintain a desired level of information.
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14:10-14:30, Paper ThB25.3 | |
>Steering a Linear System at the Minimum Information Rate: Quantifying Redundancy Via Covariance Assignment Theory |
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Wendel, Eric | Boston University, Draper |
Baillieul, John | Boston Univ |
Hollmann, Joseph | The Charles Stark Draper Laboratory, Inc |
Keywords: Information theory and control, Sampled-data control, Linear systems
Abstract: We compute fundamental performance limitations in the data rate constrained control of continuous-time linear stochastic control systems using information theoretic tools and principles. Specifically, we find the minimum achievable mean square error for steering a linear system to sequences of uncertain steering objectives under a rate constraint as the solution of a convex optimization problem. We propose the redundancy of a control system as a measure of the relative inefficiency of information transmission through a linear control system vs. an ideal communications channel.
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14:30-14:50, Paper ThB25.4 | |
>On Iterative Parameter Identification of FIR Systems with Batched Possibly Incorrect Binary-Valued Observations |
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Guo, Jian | Academy of Mathematics and Systems Science, Chinese Academy of S |
Xue, Wenchao | Academy of Mathematics and Systems Science, Chinese Academy of S |
Wang, Ting | Chinese Academy of Sciences |
Zhang, Ji-Feng | Chinese Academy of Sciences |
Zhang, Yanjun | Beijing Institute of Technology |
Keywords: Quantized systems, Identification, Linear systems
Abstract: This paper considers the problem of parameter identification for a binary output finite impulse response (FIR) system with measurement error, where the measurement error makes the binary measurement values take opposite values with a certain probability. First, the maximum likelihood estimation (MLE) of the parameters is given, and an iterative algorithm with projection based on the Expectation-Maximization algorithm is presented to calculate the MLE. Furthermore, the necessary and sufficient condition for the likelihood function to have a unique maximum point is obtained. It is proved that the iterative estimation error converges to zero at an exponential rate under persistently excitation input conditions. Finally, some numerical simulation results based on a typical system show the effectiveness of the proposed algorithm.
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14:50-15:10, Paper ThB25.5 | |
>Reachable Set-Based Dynamic Quantization for the Remote State Estimation of Linear Systems |
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Li, Yaodong | Eindhoven University of Technology |
Chong, Michelle | Eindhoven University of Technology |
Keywords: Quantized systems, Observers for Linear systems
Abstract: We employ reachability analysis in designing dynamic quantization schemes for the remote state estimation of linear systems over a finite date rate communication channel. The quantization region is dynamically updated at each transmission instant, with an approximated reachable set of the linear system. We propose a set-based method using zonotopes and compare it to a norm-based method in dynamically updating the quantization region. For both methods, we guarantee that the quantization error is bounded and consequently, the remote state reconstruction error is also bounded. To the best of our knowledge, the set-based method using zonotopes has no precedent in the literature and admits a larger class of linear systems and communication channels, where the set-based method allows for a longer inter-transmission time and lower bit rate. Finally, we corroborate our theoretical guarantees with a numerical example.
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15:10-15:30, Paper ThB25.6 | |
>A Coherent LQG Approach to Quantum Equalization |
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Thien, Rebbecca Tze Yean | Australian National University |
Vuglar, Shanon Leigh | Princeton University |
Petersen, Ian R. | Australian National University |
Keywords: Quantum information and control, Control applications
Abstract: We propose a method to design a suboptimal, coherent quantum LQG controller to solve a quantum equalization problem. Our method involves reformulating the problem as a control problem and then designing a classical LQG controller and implementing it as a quantum system. Illustrative examples are included which demonstrate the algorithm for both active and passive systems, i.e., systems where the dynamics are described in terms of both position and momentum operators and systems with dynamics in terms of annihilation operators only.
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ThB26 |
Orchid Main 4301AB |
Model Reduction |
Regular Session |
Chair: Moreschini, Alessio | Imperial College London |
Co-Chair: Kamalapurkar, Rushikesh | Oklahoma State University |
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13:30-13:50, Paper ThB26.1 | |
>Closed-Loop Model Reduction by Moment Matching for Linear Systems |
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Bhattacharjee, Debraj | Imperial College London |
Astolfi, Alessandro | Imperial College & Univ. of Rome |
Keywords: Reduced order modeling, Model/Controller reduction
Abstract: We study the model reduction by moment matching problem for linear systems in a closed-loop configuration. First we show that the moments of a linear system can be expressed in a form that is independent of the structure of the signal generator. Then we define a class of reduced-order models that can replicate the steady-state response of the original system from input-output data. Finally, we demonstrate the applicability of the results using two simple numerical examples.
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13:50-14:10, Paper ThB26.2 | |
>Learning Latent Representations in High-Dimensional State Spaces Using Polynomial Manifold Constructions |
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Geelen, Rudy | University of Texas at Austin |
Balzano, Laura | University of Michigan |
Willcox, Karen Elizabeth | Massachusetts Institute of Technology |
Keywords: Reduced order modeling, Large-scale systems, Optimization
Abstract: We present a novel framework for learning cost-efficient latent representations in problems with high-dimensional state spaces through nonlinear dimension reduction. By enriching linear state approximations with low-order polynomial terms we account for key nonlinear interactions existing in the data thereby reducing the problem's intrinsic dimensionality. Two methods are introduced for learning the representation of such low-dimensional, polynomial manifolds for embedding the data. The manifold parametrization coefficients can be obtained by regression via either a proper orthogonal decomposition or an alternating minimization based approach. Our numerical results focus on the one-dimensional Korteweg-de Vries equation where accounting for nonlinear correlations in the data was found to lower the representation error by up to two orders of magnitude compared to linear dimension reduction techniques.
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14:10-14:30, Paper ThB26.3 | |
>Model Reduction by Matching Zero-Order Moments for 2-D Discrete Systems |
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Mao, Junyu | Imperial College London |
Scarciotti, Giordano | Imperial College London |
Keywords: Reduced order modeling, Distributed parameter systems, Model/Controller reduction
Abstract: In this paper, the problem of model reduction for two-dimensional (2-D) systems in the Fornasini-Marchesini local state-space form is addressed by matching zero-order moments. Two characterizations of zero-order moments are proposed: the first based on the notion of interpolation of complex points and the second based on the concept of steady state. A parameterized family of reduced-order models that achieves moment matching while preserving the 2-D structure of the original system is presented. The developed theory is illustrated by means of a 2-D low-pass filter reduction problem.
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14:30-14:50, Paper ThB26.4 | |
>Convergent Dynamic Mode Decomposition |
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Rosenfeld, Joel A. | University of South Florida |
Kamalapurkar, Rushikesh | Oklahoma State University |
Keywords: Nonlinear systems identification, Reduced order modeling, Data driven control
Abstract: This manuscript addresses convergence of dynamic mode decomposition (DMD) algorithms and the existence of associated Koopman modes. Convergence relies on reformulation of dynamic mode decomposition in terms of newly defined compact operators defined with pairs of Hilbert spaces selected separately as the domain and range of the operator. With the Hilbert spaces selected so that the domain is embedded in the range, an eigenfunction approach to DMD is developed by leveraging a finite rank representation. The finite rank representation is proven to converge, in norm, to the original operator with increasing rank. The manuscript concludes with the description of a DMD algorithm that converges when a dense collection of occupation kernels, arising from the data, are leveraged in the analysis.
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14:50-15:10, Paper ThB26.5 | |
>Moment Matching for Nonlinear Systems of Second-Order Equations |
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Simard, Joel David | Imperial College London |
Moreschini, Alessio | Imperial College London |
Astolfi, Alessandro | Imperial College & Univ. of Rome |
Keywords: Reduced order modeling, Nonlinear systems, Differential-algebraic systems
Abstract: In this paper we consider the problem of constructing nonlinear systems of second-order equations that achieve moment matching. In particular, necessary and sufficient conditions are given for which a system of second-order equations achieves moment matching, and a family of systems of second-order equations achieving moment matching is directly constructed by extracting it, via particular choices of the free mappings, from a parameterization of all systems achieving moment matching. The results are specialized for the scenario in which the signal generator is a linear system. Finally, the results of the paper are demonstrated by constructing reduced order models of a two link robotic manipulator in the second-order equation form.
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15:10-15:30, Paper ThB26.6 | |
>Globally Optimal SISO H2-Norm Model Reduction Using Walsh's Theorem |
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Lagauw, Sibren | KU Leuven |
Agudelo, Oscar Mauricio | Katholieke Universiteit Leuven |
De Moor, Bart L.R. | Katholieke Universiteit Leuven |
Keywords: Model/Controller reduction, Linear systems, Optimization
Abstract: We present a novel methodology for single-input single-output (SISO) H2-norm model reduction that guarantees global optimality of the obtained solution(s). By exploiting Walsh's theorem, which is an elegant formulation of the first-order necessary conditions for optimality, we reformulate the model reduction problem as a multiparameter eigenvalue problem (MEVP), the real-valued eigentuples of which characterize the globally optimal solution(s) of the model reduction problem. While aiming for global optimality comes at the cost of a combinatorial growth of the problem complexity for increasing model orders, the novel methodology allows us to tackle larger problems compared to the few other globally optimal approaches in the literature. In particular, the degree of the obtained MEVP is independent of the order of the original higher order and obtained reduced-order model, a property that is favorable from a computational point of view. We perform three numerical experiments to illustrate the effectiveness of the methodology.
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ThC01 |
Orchid Main 4202-4306 |
Learning, Optimization, and Game Theory II |
Invited Session |
Chair: Sayin, Muhammed Omer | Bilkent University |
Co-Chair: Sundaram, Shreyas | Purdue University |
Organizer: Doan, Thinh T. | Virginia Tech |
Organizer: Sayin, Muhammed Omer | Bilkent University |
Organizer: Vamvoudakis, Kyriakos G. | Georgia Inst. of Tech |
Organizer: Zhang, Kaiqing | University of Maryland |
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16:00-16:20, Paper ThC01.1 | |
>Analysis of Contagion Dynamics with Active Cyber Defenders (I) |
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Paarporn, Keith | University of Colorado, Colorado Springs |
Brown, Philip N. | University of Colorado Colorado Springs |
Xu, Shouhuai | UTSA |
Keywords: Computer/Network Security, Cyber-Physical Security, Stability of nonlinear systems
Abstract: In this paper, we analyze the infection spreading dynamics of malware in a population of cyber nodes (i.e., computers or devices). Unlike most prior studies where nodes are reactive to infections, in our setting some nodes are active defenders meaning that they are able to clean up malware infections of their neighboring nodes, much like how spreading malware exploits the network connectivity properties in order to propagate. We formulate these dynamics as an Active Susceptible-Infected-Susceptible (A-SIS) compartmental model of contagion. We completely characterize the system's asymptotic behavior by establishing conditions for the global asymptotic stability of the infection-free equilibrium and for an endemic equilibrium state. We show that the presence of active defenders counter-acts infectious spreading, effectively increasing the epidemic threshold on parameters for which an endemic state prevails. Leveraging this characterization, we investigate a general class of problems for finding optimal investments in active cyber defense capabilities given limited resources. We show that this class of problems has unique solutions under mild assumptions. We then analyze an Active Susceptible-Infected-Recovered (A-SIR) compartmental model, where the peak infection level of any trajectory is explicitly derived.
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16:20-16:40, Paper ThC01.2 | |
>Online Learning for Equilibrium Pricing in Markets under Incomplete Information (I) |
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Jalota, Devansh | Stanford University |
Sun, Haoyuan | Massachusetts Institute of Technology |
Azizan, Navid | MIT |
Keywords: Learning, Game theory, Smart grid
Abstract: The study of market equilibria is central to economic theory, particularly in efficiently allocating scarce resources. However, the computation of equilibrium prices at which the supply of goods matches their demand typically relies on having access to complete information on private attributes of agents, e.g., suppliers' cost functions, which are often unavailable in practice. Motivated by this practical consideration, we consider the problem of setting equilibrium prices in the incomplete information setting wherein a market operator seeks to satisfy the customer demand for a commodity by purchasing the required amount from competing suppliers with privately known cost functions unknown to the market operator. In this incomplete information setting, we consider the online learning problem of learning equilibrium prices over time while jointly optimizing three performance metrics -- unmet demand, cost regret, and payment regret -- pertinent in the context of equilibrium pricing over a horizon of T periods. In the general setting when suppliers' cost functions are time-varying, we show that no online algorithm can achieve sublinear regret on all three metrics. Thus, we consider the setting when suppliers' cost functions are fixed and develop algorithms that achieve a regret of (i) O(log log T) when the customer demand is constant over time and (ii) O(sqrt{T} log log T) when the demand is variable over time.
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16:40-17:00, Paper ThC01.3 | |
>Robust Online Covariance and Sparse Precision Estimation under Arbitrary Data Corruption (I) |
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Yao, Tong | Purdue University |
Sundaram, Shreyas | Purdue University |
Keywords: Statistical learning, Machine learning
Abstract: Gaussian graphical models are widely used to represent correlations among entities, but they remain vulnerable to data corruption. In this work, we introduce a modified trimmed-inner-product algorithm to robustly estimate the covariance in an online scenario even in the presence of arbitrary and adversarial data attacks. At each time step, data points, drawn nominally independently and identically from a multivariate Gaussian distribution, arrive. However, a certain fraction of these points may have been arbitrarily corrupted. We propose an online algorithm to estimate the sparse inverse covariance (i.e., precision) matrix despite this corruption. We provide the error-bound and the convergence properties of the estimates to the true precision matrix under our algorithms.
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17:00-17:20, Paper ThC01.4 | |
>Asynchronous Decentralized Q-Learning in Stochastic Games (I) |
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Yongacoglu, Bora | Queen's University |
Arslan, Gurdal | University of Hawaii at Manoa |
Yuksel, Serdar | Queen's University |
Keywords: Game theory, Learning, Decentralized control
Abstract: Non-stationarity is a fundamental challenge in multi-agent reinforcement learning (MARL), where agents update their behaviour as they learn. In multi-agent settings, individual agents may have an incomplete view of the actions of others, which can complicate the learning process. Many theoretical advances in MARL avoid the challenge of non-stationarity by coordinating the policy updates of agents in various ways, including synchronizing times at which agents are allowed to revise their policies. In this paper, we study an asynchronous variant of the decentralized Q-learning algorithm, a recent MARL algorithm for stochastic games. We provide sufficient conditions under which the asynchronous algorithm drives play to equilibrium with high probability. In this generalization, players need not agree on the schedule of policy update times, and may change their policies at their own separately selected times. This work extends the applicability of the decentralized Q-learning algorithm to settings in which parameters are selected in an independent manner, and tames non-stationarity without imposing the coordination assumptions of prior work.
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17:20-17:40, Paper ThC01.5 | |
>PrimeTime: A Finite-Time Consensus Protocol for Open Networks (I) |
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Abrahamson, Henry Waichi | Northwestern University |
Wei, Ermin | Northwestern Univeristy |
Keywords: Agents-based systems, Autonomous vehicles, Sensor networks
Abstract: In distributed problems where consensus between agents is required but average consensus is not desired, it can be necessary for each agent to know not only the data of each other agent in the network, but also the origin of each piece of data before consensus can be reached. However, transmitting large tables of data with IDs can cause the size of an agent's message to increase dramatically, while truncating down to fewer pieces of data to keep the message size small can lead to problems with the speed of achieving consensus. Also, many existing consensus protocols are not robust against agents leaving and entering the network. We introduce PrimeTime, a novel communication protocol that exploits the properties of prime numbers to quickly and efficiently share small integer data across an open network. For sufficiently small networks or small integer data, we show that messages formed by PrimeTime require fewer bits than messages formed by simply tabularizing the data and IDs to be transmitted.
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17:40-18:00, Paper ThC01.6 | |
>Distributed Learning Dynamics for Coalitional Games (I) |
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Hamed, Aya | University of Illinois Urbana-Champaign |
Shamma, Jeff S. | University of Illinois at Urbana-Champaign |
Keywords: Game theory, Learning, Agents-based systems
Abstract: In the framework of transferable utility coalitional games, a scoring (characteristic) function determines the value of any subset/coalition of agents. Agents decide on both which coalitions to form and the allocations of the values of the formed coalitions among their members. An important concept in coalitional games is that of a core solution, which is a partitioning of agents into coalitions and an associated allocation to each agent under which no group of agents can get a higher allocation by forming an alternative coalition. We present distributed learning dynamics for coalitional games that converge to a core solution whenever one exists. In these dynamics, an agent maintains a state consisting of (i) an aspiration level for its allocation and (ii) the coalition, if any, to which it belongs. In each stage, a randomly activated agent proposes to form a new coalition and changes its aspiration based on the success or failure of its proposal. The coalition membership structure is changed, accordingly, whenever the proposal succeeds. Required communications are that: (i) agents in the proposed new coalition need to reveal their current aspirations to the proposing agent, and (ii) agents are informed if they are joining the proposed coalition or if their existing coalition is broken. The proposing agent computes the feasibility of forming the coalition. We show that the dynamics hit an absorbing state whenever a core solution is reached. We further illustrate the distributed learning dynamics on a multi-agent task allocation setting.
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ThC02 |
Melati Main 4001AB-4104 |
Online Learning for Optimization and Control |
Invited Session |
Chair: Balta, Efe C. | ETH Zurich |
Co-Chair: Didier, Alexandre | ETH Zurich |
Organizer: Balta, Efe C. | Inspire AG |
Organizer: Didier, Alexandre | ETH Zurich |
Organizer: Karapetyan, Aren | ETH Zürich |
Organizer: Iannelli, Andrea | University of Stuttgart |
Organizer: Martin, Andrea | École Polytechnique Fédérale De Lausanne |
Organizer: Tsiamis, Anastasios | ETH Zurich |
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16:00-16:20, Paper ThC02.1 | |
>Online Distributed Learning with Quantized Finite-Time Coordination (I) |
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Bastianello, Nicola | KTH Royal Institute of Technology |
Rikos, Apostolos I. | KTH Royal Institute of Technology |
Johansson, Karl H. | KTH Royal Institute of Technology |
Keywords: Optimization algorithms, Agents-based systems, Learning
Abstract: In this paper we consider online distributed learning problems. Online distributed learning refers to the process of training learning models on distributed data sources. In our setting a set of agents need to cooperatively train a learning model from streaming data. Differently from federated learning, the proposed approach does not rely on a central server but only on peer-to-peer communications among the agents. This approach is often used in scenarios where data cannot be moved to a centralized location due to privacy, security, or cost reasons. In order to overcome the absence of a central server, we propose a distributed algorithm that relies on a quantized, finite-time coordination protocol to aggregate the locally trained models. Furthermore, our algorithm allows for the use of stochastic gradients during local training. Stochastic gradients are computed using a randomly sampled subset of the local training data, which makes the proposed algorithm more efficient and scalable than traditional gradient descent. In our paper, we analyze the performance of the proposed algorithm in terms of the mean distance from the online solution. Finally, we present numerical results for a logistic regression task.
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16:20-16:40, Paper ThC02.2 | |
>Safe Non-Stochastic Control of Linear Dynamical Systems (I) |
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Zhou, Hongyu | University of Michigan |
Tzoumas, Vasileios | University of Michigan, Ann Arbor |
Keywords: Optimization, Time-varying systems
Abstract: We study the problem of safe control of linear dynamical systems corrupted with non-stochastic noise, and provide the first algorithm that guarantees (i) zero constraint violation of convex time-varying constraints, and (ii) bounded dynamic regret, i.e., bounded suboptimality against an optimal clairvoyant controller that knows the future noise a priori. The constraints bound the values of the state and of the control input such as to ensure collision avoidance and bounded control effort. We are motivated by the future of autonomy where robots will safely perform complex tasks despite real-world unpredictable disturbances such as wind and wake disturbances. To develop the algorithm, we capture our problem as a sequential game between a linear feedback controller and an adversary, assuming a known upper bound on the noise's magnitude. Particularly, at each step t=1,ldots, T, first the controller chooses a linear feedback control gain K_t in mathcal{K}_t, where mathcal{K}_t is constructed such that it guarantees that the safety constraints will be satisfied; then, the adversary reveals the current noise w_t and the controller suffers a loss f_t(K_t) ---eg f_t represents the system's tracking error at t upon the realization of the noise. The controller aims to minimize its cumulative loss, despite knowing w_t only after K_t has been chosen, and despite mathcal{K}_{t-1} being possibly disjoint from mathcal{K}_t. We validate our algorithm in simulated scenarios of safe control of linear dynamical systems in the presence of bounded noise.
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16:40-17:00, Paper ThC02.3 | |
>Change Point Detection Approach for Online Control of Unknown Time Varying Dynamical Systems (I) |
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Muthirayan, Deepan | University of California at Irvine |
Du, Ruijie | University of California Irvine |
Shen, Yanning | UCI |
Khargonekar, Pramod | Univ. of California, Irvine |
Keywords: Learning, Optimization, Adaptive control
Abstract: We propose a novel change point detection approach for online learning control with full information feedback (state, disturbance, and cost feedback) for unknown time-varying dynamical systems. We show that our algorithm can achieve a sub-linear regret with respect to the class of Disturbance Action Control (DAC) policies, which are a widely studied class of policies for online control of dynamical systems, for any sub-linear number of changes and very general class of systems: (i) matched disturbance system with general convex cost functions, (ii) general system with linear cost functions. Specifically, a (dynamic) regret of Sigma^{1/5}_TT^{4/5} can be achieved for these class of systems, where Sigma_T is the number of changes of the underlying system and T is the duration of the control episode. That is, the change point detection approach achieves a sub-linear regret for any sub-linear number of changes, which other previous algorithms such as in Minasyan et al. (2021) cannot. Numerically, we demonstrate that the change point detection approach is superior to Minasyan et al. (2021) and to standard online learning approaches for time-invariant dynamical systems. Our work presents the first regret guarantee for unknown time-varying dynamical systems in terms of a stronger notion of variability like the number of changes in the underlying system. The extension of the present work to state and output feedback controllers is a subject of future work.
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17:00-17:20, Paper ThC02.4 | |
>On-Policy Data-Driven Linear Quadratic Regulator Via Combined Policy Iteration and Recursive Least Squares (I) |
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Sforni, Lorenzo | Alma Mater Studiorum - Università Di Bologna |
Carnevale, Guido | University of Bologna |
Notarnicola, Ivano | University of Bologna |
Notarstefano, Giuseppe | University of Bologna |
Keywords: Data driven control, Optimal control, Optimization algorithms
Abstract: In this paper, we address infinite-horizon Linear Quadratic Regulator (LQR) problems for unknown discrete-time systems. As an additional challenge, we address an on-policy setup in which system matrices are identified while controlling the real system with a progressively optimized policy. Specifically, we consider a time-varying control policy that, while applied to the real unknown system, is iteratively refined (based on the most updated estimate of the system matrices) towards the optimal LQR solution. The overall learning procedure combines a recursive least squares method with a direct policy search based on the gradient method. By resorting to Lyapunov-based analysis tools in combination with averaging theory for nonlinear systems, exponential stability for the closed-loop scheme can be proven. Finally, a numerical example showing the effectiveness of the considered strategy corroborates the theoretical findings.
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17:20-17:40, Paper ThC02.5 | |
>On the Finite-Time Behavior of Suboptimal Linear Model Predictive Control (I) |
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Karapetyan, Aren | ETH Zürich |
Balta, Efe C. | ETH Zurich |
Iannelli, Andrea | University of Stuttgart |
Lygeros, John | ETH Zurich |
Keywords: Predictive control for linear systems, Optimal control, Optimization algorithms
Abstract: Inexact methods for model predictive control (MPC), such as real-time iterative schemes or time-distributed optimization, alleviate the computational burden of exact MPC by providing suboptimal solutions. While the asymptotic stability of such algorithms is well studied, their finite-time performance has not received much attention. In this work, we quantify the performance of suboptimal linear model predictive control in terms of the additional cost incurred due to performing only a finite number of optimization iterations. Leveraging this novel analysis framework, we propose a novel suboptimal MPC algorithm with a diminishing horizon length and guaranteed closed-loop stability and finite-time performance. This analysis allows the designer to plan a limited computational power budget distribution to achieve a desired performance level. We provide numerical examples to illustrate the algorithm's transient behavior and computational complexity.
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17:40-18:00, Paper ThC02.6 | |
>Safe and Stable Adaptive Control for a Class of Dynamic Systems (I) |
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Autenrieb, Johannes | German Aerospace Center (DLR) |
Annaswamy, Anuradha M. | Massachusetts Inst. of Tech |
Keywords: Adaptive control, Uncertain systems, Flight control
Abstract: Adaptive control has focused on online control of dynamic systems in the presence of parametric uncertainties, with solutions guaranteeing stability and control performance. Safety, a related property to stability, is becoming increasingly important as the footprint of autonomous systems grows in society. One of the popular ways for ensuring safety is through the notion of a control barrier function (CBF). In this paper, we combine adaptation and CBFs to develop a real-time controller that guarantees stability and remains safe in the presence of parametric uncertainties. The class of dynamic systems that we focus on is linear time-invariant systems whose states are accessible and where the inputs are subject to a magnitude limit. Conditions of stability, state convergence to a desired value, and parameter learning are all elucidated. One of the elements of the proposed adaptive controller that ensures stability and safety is the use of a CBF-based safety filter that suitably generates safe reference commands, employs error-based relaxation (EBR) of Nagumo’s theorem, and leads to guarantees of set invariance. To demonstrate the effectiveness of our approach, we present two numerical examples, an obstacle avoidance case and a missile flight control case.
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ThC03 |
Melati Junior 4010A-4111 |
Cyber-Physical Systems: Privacy |
Invited Session |
Chair: Sadabadi, Mahdieh S. | Queen Mary University of London |
Co-Chair: Murguia, Carlos | Eindhoven University of Technology |
Organizer: Sadabadi, Mahdieh S. | University of Manchester |
Organizer: Escudero, Cédric | INSA Lyon, Laboratoire Ampère |
Organizer: Selvi, Daniela | Università Di Pisa |
Organizer: Soudjani, Sadegh | Newcastle University |
Organizer: Murguia, Carlos | Eindhoven University of Technology |
Organizer: Chong, Michelle | Eindhoven University of Technology |
Organizer: Ferrari, Riccardo M.G. | Delft University of Technology |
Organizer: Sasahara, Hampei | Tokyo Institute of Technology |
Organizer: Zhu, Quanyan | New York University |
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16:00-16:20, Paper ThC03.1 | |
>Differential Privacy for Stochastic Matrices Using the Matrix Dirichlet Mechanism (I) |
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Fallin, Brandon | University of Florida |
Hawkins, Calvin | University of Florida |
Chen, Bo | University of Florida |
Gohari, Parham | The University of Texas at Austin |
Benvenuti, Alexander | University of Florida |
Topcu, Ufuk | The University of Texas at Austin |
Hale, Matthew | University of Florida |
Keywords: Control Systems Privacy, Markov processes
Abstract: Stochastic matrices are commonly used to analyze Markov chains, but revealing them can leak sensitive information. Therefore, in this paper we introduce a technique to privatize stochastic matrices in a way that (i) conceals the probabilities they contain, and (ii) still allows for accurate analyses of Markov chains. Specifically, we use differential privacy, which is a statistical framework for protecting sensitive data. To implement it, we introduce the Matrix Dirichlet Mechanism, which is a probabilistic mapping that perturbs a stochastic matrix to provide privacy. We prove that this mechanism provides differential privacy, and we quantify the error induced in private stochastic matrices as a function of the strength of privacy being provided. We then bound the distance between the stationary distribution of the underlying, sensitive stochastic matrix and the stationary distribution of its privatized form. Numerical results show that, under typical conditions, privacy introduces error as low as 5.05% in the stationary distribution of a stochastic matrix.
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16:20-16:40, Paper ThC03.2 | |
>Privacy Analysis for Quantized Networked Control Systems (I) |
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Liu, Le | University of Groningen |
Kawano, Yu | Hiroshima University |
Cao, Ming | University of Groningen |
Keywords: Control Systems Privacy, Quantized systems, Linear systems
Abstract: Quantized signals are widely used in engineering applications. Although quantization can potentially degrade system performances, previous research has demonstrated its usage to preserve privacy of the signals that are quantized. In this paper, we investigate the privacy-preserving properties of two types of quantizers: deterministic and stochastic ones. Specifically, for deterministic quantizers, we demonstrate that an eavesdropper cannot uniquely determine the initial state of a system if the system is Schur stable. Additionally, we propose a necessary condition on the system matrix A to ensure the initial state remains private. For stochastic quantizers, we investigate their differential privacy properties and show that appropriate quantization steps can guarantee differential privacy. However, the quantization step can lead to impreciseness of the quantized signal and we therefore also examine the trade-off between differential privacy and system performance. To optimize the quantization step, we formulate a convex optimization problem, which can be solved efficiently.
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16:40-17:00, Paper ThC03.3 | |
>A System-Theoretic Privacy-Informed Framework in Multi-Agent Systems (I) |
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Sadabadi, Mahdieh S. | University of Manchester |
Keywords: Agents-based systems, Control Systems Privacy, Distributed control
Abstract: The problem of privacy-preserving in multi-agent systems corresponds to prohibiting the disclosure of agents' initial states while ensuring desired performance such as distributed average consensus. In this paper, a system-theoretic dynamic privacy-informed framework is developed. The proposed privacy framework relies on an obfuscation phase where a dynamic mask is inserted on the agents' state trajectories and masked outputs are exchanged amongst agents, rendering the physical states of an agent indiscernible by the other agents or external curious attackers (eavesdropper adversaries). Application of the proposed dynamic privacy scheme to well-known problems in multi-agent systems including average consensus and social opinion dynamics are presented.
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17:00-17:20, Paper ThC03.4 | |
>A Data-Driven Approach to Approximate Opacity Verification (I) |
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Murali, Vishnu | University of Colorado, Boulder |
Tasdighi Kalat, Shadi | University of Colorado Boulder |
Zamani, Majid | University of Colorado Boulder |
Keywords: Formal Verification/Synthesis, Cyber-Physical Security
Abstract: Recent results in the verification of cyber-physical systems have focused not just in giving guarantees of properties such as safety, but also in ensuring that these systems are secure. One such notion of security is that of initial-state opacity, where one seeks to ensure that an outside intruder is not able to determine some sensitive information about the initial-state of the system by observing the output traces. An existing approach to verify the initial-state opacity of a system relies on finding a barrier certificate over an appropriately constructed augmented system. However this search for a barrier certificate relies on the dynamics of the system being known. Unfortunately, in many scenarios, it may be difficult or infeasible to determine the dynamics of a given system. We thus consider the problem of determining whether a system is opaque when its dynamics are unknown. To do so, we recast the conditions of opacity on the augmented system as a robust program with uncountably many constraints. By collecting data from the system's trajectories, we construct a corresponding scenario program. We show that if a feasible solution of the scenario program satisfies some conditions, then the original system with unknown dynamics is opaque under reasonable assumptions. We show the effectiveness of the proposed approach by demonstrating the opacity of a room-temperature model.
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17:20-17:40, Paper ThC03.5 | |
>Conversion of Controllers to Have Integer State Matrix for Encrypted Control: Non-Minimal Order Approach (I) |
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Lee, Joowon | Seoul National University |
Lee, Donggil | Seoul National University |
Lee, Seungbeom | Seoul National University |
Kim, Junsoo | Seoul National University of Science and Technology |
Shim, Hyungbo | Seoul National University |
Keywords: Control Systems Privacy, Linear systems, Cyber-Physical Security
Abstract: To implement an encrypted dynamic controller based on homomorphic encryption that operates for an infinite time horizon, it is essential for every component of the controller's state matrix to be an integer. In this paper, we tackle the challenge of converting a pre-designed controller into a new one with an integer state matrix while preserving its control performance in the closed-loop system. This enables encrypted dynamic systems to be realized without re-encryption and approximation of control parameters, compared to the previous results. To achieve this, we propose two approaches and provide sufficient conditions on the design parameter for each. The first approach is to design the new controller as an estimator of the original closed-loop system, and the conditions on the estimator gain are derived. Our second approach is to formulate a problem of finding certain polynomials, whose solution leads to the design of the new controller. In a special case when the numerator of the plant transfer function is a constant, we provide a constructive method to obtain such solution.
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17:40-18:00, Paper ThC03.6 | |
>Safety-Preserving Filters against Stealthy Sensor and Actuator Attacks (I) |
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Escudero, Cédric | INSA Lyon, Laboratoire Ampère |
Murguia, Carlos | Eindhoven University of Technology |
Massioni, Paolo | INSA Lyon |
Zamai, Eric | Institut National Polytechnique De Grenoble, Laboratoire |
Keywords: Cyber-Physical Security, Resilient Control Systems, Computer/Network Security
Abstract: This article proposes a novel strategy based on control input filtering for mitigating the effects of deception attacks on control and sensor measurement signals. We assume an adversary who can tamper data transmitted from a communication network in order to degrade the plant performance. The proposed strategy consists on adding multiple-input multiple-output (MIMO) filters to the control loop, between the received control actions and the plant actuators. The filter's goal is to dynamically steer the reachable set induced by the attack signals to a safe region of the state space. The article provides a filter synthesis method under the form of a semidefinite programming problem, yielding such filters in a way that attack-free control signals are distorted as little as possible, and plant trajectories are contained in the safe set. At the end of the paper, a set of simulations demonstrate the effectiveness of the approach.
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ThC04 |
Simpor Junior 4913 |
Autonomous Vehicles I |
Regular Session |
Chair: Murguia, Carlos | Eindhoven University of Technology |
Co-Chair: Cassandras, Christos G. | Boston University |
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16:00-16:20, Paper ThC04.1 | |
>Impact Sensitivity Analysis of Cooperative Adaptive Cruise Control against Resource-Limited Adversaries |
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Huisman, Mischa | Eindhoven University of Technology |
Murguia, Carlos | Eindhoven University of Technology |
Lefeber, Erjen | Eindhoven University of Technology |
Van De Wouw, Nathan | Eindhoven University of Technology |
Keywords: Autonomous vehicles, Automotive control, Cyber-Physical Security
Abstract: Cooperative Adaptive Cruise Control (CACC) is a technology that allows groups of vehicles to form in automated, tightly-coupled platoons. CACC schemes exploit Vehicle-to-Vehicle (V2V) wireless communications to exchange information between vehicles. However, the use of communication networks brings security concerns as it exposes network access points that the adversary can exploit to disrupt the vehicles' operation and even cause crashes. In this manuscript, we present a sensitivity analysis of CACC schemes against a class of resource-limited attacks. We present a modelling framework that allows us to systematically compute outer ellipsoidal approximations of reachable sets induced by attacks. We use the size of these sets as a security metric to quantify the potential damage of attacks affecting different signals in a CACC-controlled vehicle and study how two key system parameters change this metric. We carry out a sensitivity analysis for two different controller implementations (as given the available sensors there is an infinite number of realizations of the same controller) and show how different controller realizations can significantly affect the impact of attacks. We present extensive simulation experiments to illustrate the results.
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16:20-16:40, Paper ThC04.2 | |
>Learning Input Constrained Control Barrier Functions for Guaranteed Safety of Car-Like Robots |
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Brüggemann, Sven | University of California, San Diego |
Nightingale, Dominic | University of California San Diego |
Silberman, Jack | University of California San Diego |
de Oliveira, Mauricio | ASML |
Keywords: Autonomous vehicles, Control applications, Machine learning
Abstract: We propose a design method for a robust safety filter based on Input Constrained Control Barrier Functions (ICCBF) for car-like robots moving in complex environments. A robust ICCBF that can be efficiently implemented is obtained by learning a smooth function of the environment using Support Vector Machine regression. The method takes into account steering constraints and is validated in simulation and a real experiment.
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16:40-17:00, Paper ThC04.3 | |
>Attitude Consensus Control with Disturbance Rejection for Incompletely Cooperative Multi-Agent Systems on SO(3) |
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Meng, Qingkai | University of Cyprus |
Kasis, Andreas | University of Cyprus |
Polycarpou, Marios M. | University of Cyprus |
Keywords: Autonomous vehicles, Cooperative control, Distributed control
Abstract: The three-dimensional orthogonal matrix group SO(3) offers global, unique, and nonsingular attitude representation of the rotational motion. This paper addresses the attitude consensus problem with disturbance rejection for multi-agent systems consisting of incompletely cooperative agents evolving on SO(3). Firstly, we establish an individual cost functional that evaluates the agent consensus aim using the natural Riemannian metric on SO(3), and formulate the considered consensus problem as a differential game. Secondly, a baseline consensus protocol is designed following the inverse optimal control procedure. In addition, a finite-time disturbance observer on SO(3) is developed based on the non-singular terminal sliding mode technique, which is used for estimating and compensating for disturbances. The effectiveness of the proposed schemes is verified with simulations on a 4-vehicle formation setting.
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17:00-17:20, Paper ThC04.4 | |
>Cooperative Lane Changing in Mixed Traffic Can Be Robust to Human Driver Behavior |
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Li, Anni | Boston University |
Chavez Armijos, Andres | Boston University |
Cassandras, Christos G. | Boston University |
Keywords: Autonomous vehicles, Cooperative control, Transportation networks
Abstract: We derive time and energy-optimal control policies for a Connected Autonomous Vehicle (CAV) to complete lane change maneuvers in mixed traffic. The interaction between CAVs and Human-Driven Vehicles (HDVs) requires the best possible response from a CAV to actions by its neighboring HDVs. This interaction is formulated using a bilevel optimization setting with an appropriate behavioral model for an HDV. An iterated best response (IBR) method is then used to determine a Nash equilibrium. However, we also show that CAV cooperation can eliminate or greatly reduce the interaction between CAVs and HDVs. We derive a simple threshold-based criterion to select an optimal policy for the lane-changing CAV to merge ahead of a cooperating CAV in the target lane. In this case, the trajectory of the lane-changing CAV is independent of HDV behavior. Simulation results are included to demonstrate the effectiveness of our CAV controllers in terms of minimizing cost and disruption to traffic flow while guaranteeing safety when uncontrollable HDVs are present.
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17:20-17:40, Paper ThC04.5 | |
>A Set-Theoretic Control Approach to the Trajectory Tracking Problem for Input-Output Linearized Wheeled Mobile Robots |
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Tiriolo, Cristian | Concordia University |
Lucia, Walter | Concordia University |
Keywords: Autonomous vehicles, Feedback linearization, Predictive control for linear systems
Abstract: This paper proposes a set-theoretic receding horizon control scheme to address the trajectory tracking problem for input-constrained differential-drive robots. The proposed solution is derived starting from an input-output linearized description of the robot kinematics and a worst-case characterization of the orientation-dependent input constraint acting on the feedback linearized model. In particular, offline, given a worst-case characterization of the constraint set, we analytically design the smallest robust control invariant region for the tracking error. Moreover, such a region is recursively enlarged by computing a family of robust one-step controllable sets whose union characterizes the controller's domain of attraction. Online, such sets and the knowledge of the current robot's orientation are leveraged to define a non-conservative control law ensuring bounded tracking error. The effectiveness of the proposed strategy is experimentally validated using a Khepera IV robot, and its performance is contrasted with four alternative trajectory tracking algorithms.
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17:40-18:00, Paper ThC04.6 | |
>Optimal Control of Distributed Ensembles with Application to Bloch Equations |
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Chertovskih, Roman | University of Porto |
Pogodaev, Nikolay | Università Degli Studi Di Padova |
Staritsyn, Maxim | Faculty of Engineering, University of Porto |
Aguiar, A. Pedro | Faculty of Engineering, University of Porto |
Keywords: Optimal control, Uncertain systems, Numerical algorithms
Abstract: Motivated by the problem of designing robust composite pulses for Bloch equations in the presence of natural perturbations, we study an abstract optimal ensemble control problem in a probabilistic setting with a general nonlinear performance criterion. The model under study addresses meanfield dynamics described by a linear continuity equation in the space of probability measures. For the resulting optimization problem, we derive an exact representation of the increment of the cost functional in terms of the flow of the driving vector field. Using this representation, a descent method is designed that is free of any internal line search. The method is applied to solve new optimal control problems for distributed ensembles of Bloch equations.
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ThC05 |
Simpor Junior 4912 |
Rigidity Theory, Multi-Agent Formations, and Distributed Localization |
Invited Session |
Chair: Chen, Liangming | Southern University of Science and Technology |
Co-Chair: Sun, Zhiyong | Eindhoven University of Technology (TU/e) |
Organizer: Chen, Liangming | Southern University of Science and Technology |
Organizer: Sun, Zhiyong | Eindhoven University of Technology (TU/e) |
Organizer: Zelazo, Daniel | Technion - Israel Institute of Technology |
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16:00-16:20, Paper ThC05.1 | |
>Cooperative Nearest-Neighbor Control of Multi-Agent Systems: Consensus and Formation Control Problems |
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Almuzakki, Muhammad Zaki | Universitas Pertamina |
Jayawardhana, Bayu | University of Groningen |
Keywords: Cooperative control, Networked control systems, Nonlinear output feedback
Abstract: This letter studies the problem of cooperative nearest-neighbor control of multi-agent systems where each agent can only realize a finite set of control points. Under the assumption that the underlying graph representing the communication network between agents is connected and the interior of the convex hull of all finite actions of each agent contains the zero element, consensus or distance-based formation problems can practically be stabilized by means of nearest-neighbor control approach combined with the well-known consensus control or distributed formation control laws, respectively. Furthermore, we provide the convergence bound for each corresponding error vector which can be computed based on the information of individual agent's finite control points. Finally, we show Monte Carlo numerical simulations that confirm our analysis.
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16:20-16:40, Paper ThC05.2 | |
>Distributed Adaptive Formation Control for Uncertain Point Mass Agents with Mixed Dimensional Space |
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Rosa, Muhammad Ridho | University of Groningen |
Jayawardhana, Bayu | University of Groningen |
Keywords: Distributed control, Constrained control, Adaptive control
Abstract: We propose distance-based distributed adaptive formation control of point mass agents in port-Hamiltonian (pH) framework that can deal with parameter uncertainties and with mixed dimensional space (2D, 3D or mixed 2D/3D). Adaptive control mechanism is subsequently proposed to maintain formation of uncertain pH systems with unknown damping parameters. Numerical simulations are presented for both known and uncertain point mass agents in mixed 2D/3D space.
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16:40-17:00, Paper ThC05.3 | |
>Formation Tracking Control of Heterogeneous Underactuated Planar Agents with Stable Internal Dynamics (I) |
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Tran, Quoc Van | Hanoi University of Science and Technology (HUST) |
Keywords: Networked control systems, Control of networks, Distributed control
Abstract: Distributed formation tracking control of a system of heterogeneous underactuated agents on a 2-D plane is proposed based on the leader-follower approach and using the inter-agent displacements. A typical example of such an agent is an underactuated surface vessel whose planar surge-sway-yaw motion is considered, while only two independent controls are available, thus underactuated. Formation tracking control law is developed to steer certain offset points on the longitudinal axes of the agents, called hand points, to the target formation asymptotically and exponentially fast in the presence of bounded disturbances. A distinct feature of such an underactuated planar vehicle is that its lateral motion representing the non-actuated degree of freedom is unrestricted and can be unstable. Thus, a sufficient condition on the the leader's velocity and the hand points' locations for the stability of the lateral motion of the agents is provided. Simulation results of formation tracking control of underactuated surface vessels support the theoretical analysis.
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17:00-17:20, Paper ThC05.4 | |
>Performance Optimization of Angle-Based Network Localization (I) |
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Liang, Chenyang | Harbin Institute of Technology, Shenzhen |
Chen, Liangming | Southern University of Science and Technology |
Li, Yibei | Nanyang Technological University |
Mei, Jie | Harbin Institute of Technology, Shenzhen |
Xie, Lihua | Nanyang Tech. Univ |
Keywords: Distributed control, Networked control systems, Sensor networks
Abstract: Recent advances in sensor network localization have enabled sensor nodes to localize themselves by using the measurements of inter-node angles. According to our earlier work, the proposed angle-based localization algorithms' performance, particularly, the convergence rate, is relatively poor, which, however, has not been adequately addressed in the existing literature. Motivated by this, this paper aims to improve the performance of angle-based localization algorithms, specifically, the stability margin, convergence rate and robustness against measurement noises. Firstly, we show that the stability margin, convergence rate and robustness of angle-based localization algorithms are commonly determined by one parameter, namely, the minimum eigenvalue of the network's localization matrix. Secondly, we formulate the performance optimization problem as an eigenvalue optimization problem, and show the non-differentiability of the eigenvalue optimization problem. By carefully choosing the decision variable, we utilize interior-point methods to obtain an optimal solution to the eigenvalue optimization problem. Finally, simulation examples validate the improvement of the algorithms' performance.
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17:20-17:40, Paper ThC05.5 | |
>Automated Formation Control Synthesis from Temporal Logic Specifications (I) |
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Qi, Shuhao | Eindhoven University of Technology |
Zhang, Zengjie | Eindhoven University of Technology |
Haesaert, Sofie | Eindhoven University of Technology |
Sun, Zhiyong | Eindhoven University of Technology (TU/e) |
Keywords: Formal Verification/Synthesis, Agents-based systems, Autonomous robots
Abstract: In many practical scenarios, multi-robot systems are envisioned to support humans in executing complicated tasks within structured environments, such as search-and-rescue tasks. We propose a framework for a multi-robot swarm to fulfill complex tasks represented by temporal logic specifications. Given temporal logic specifications on the swarm formation and navigation, we develop a controller with runtime safety and convergence guarantees that drive the swarm to formally satisfy the specification. In addition, the synthesized controller will autonomously switch formations as necessary and react to uncontrollable events from the environment. The efficacy of the proposed framework is validated with a simulation study on the navigation of multiple quadrotor robots.
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17:40-18:00, Paper ThC05.6 | |
>Displacement-Based Formation Control with Measurement Noises (I) |
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Chen, Weiqiang | Harbin Institute of Technology (Shenzhen) |
Chen, Liangming | Southern University of Science and Technology |
Mei, Jie | Harbin Institute of Technology, Shenzhen |
Zhang, Hongwei | Harbin Institute of Technology, Shenzhen |
Keywords: Stochastic systems, Distributed control, Cooperative control
Abstract: Multi-agent formations have many practical applications. Measurement noises are inevitable in multi-agent formations, in which, however, the existing results mainly focus on special types of noises, and the analytical discussion on the effect of general noises is challenging and remains open. This motivates us to study the effect of stochastic measurement noises on displacement-based multi-agent formations, which are described by a general form of stochastic processes with finite second-order moments. First, for the case of unbiased measurement noises, a sufficient and necessary condition is derived for the existence of solutions in the stochastic dynamics of multi-agent formations. Then, several statistical features and convergence of formation errors are analyzed. In particular, for the case of unbiased measurement noises described by zero-mean wide-sense stationary processes, an upper bound on the mean square convergence of formation errors is obtained. Finally, we demonstrate the effectiveness of our theoretical results through a simulation example.
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ThC06 |
Simpor Junior 4911 |
Estimation and Control of Infinite Dimensional Systems I |
Invited Session |
Chair: Demetriou, Michael A. | Worcester Polytechnic Institute |
Co-Chair: Burns, John A | Virginia Tech |
Organizer: Demetriou, Michael A. | Worcester Polytechnic Institute |
Organizer: Burns, John A | Virginia Tech |
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16:00-16:20, Paper ThC06.1 | |
>Infinite-Dimensional Observers for High Order Boundary-Controlled Port-Hamiltonian Systems |
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Toledo Zucco, Jesus Pablo | ONERA |
Wu, Yongxin | FEMTO-ST/ENSMM |
Ramirez, Hector | Universidad Tecnica Federico Santa Maria |
Le Gorrec, Yann | Cnrs, Ensmm, Femto-St / As2m |
Keywords: Distributed parameter systems, Observers for Linear systems, Estimation
Abstract: This letter investigates the design of a class of infinite-dimensional observers for one dimensional (1D) boundary controlled port-Hamiltonian systems (BC-PHS) defined by differential operators of order N≥1. The convergence of the proposed observer depends on the number and location of available boundary measurements. Provided that enough boundary measurements are available, exponential convergence can be assured for the cases N=1 and N=2 and asymptotic convergence for the case N≥1. Furthermore, in the case of partitioned BC-PHS with N=2, such as the Euler-Bernoulli beam, this is shown that exponential convergence can be assured considering less available measurements. The Euler-Bernoulli beam model is used to illustrate the design of the proposed observers and to perform numerical simulations.
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16:20-16:40, Paper ThC06.2 | |
>Anti-Windup Design for a Reaction-Diffusion Equation |
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Shreim, Suha | LAAS-CNRS |
Ferrante, Francesco | Universita Degli Studi Di Perugia |
Prieur, Christophe | CNRS |
Keywords: Distributed parameter systems, Stability of nonlinear systems, Lyapunov methods
Abstract: This paper focuses on the anti-windup design for saturated one-dimensional linear reaction-diffusion equation. The considered open-loop system admits a finite number of unstable poles. We consider a scenario in which the system is controlled via a dynamic output feedback controller ensuring closed-loop exponential stability. Within this setting, a method is proposed to design a dynamic anti-windup compensator to maximize the region of attraction and minimize the effect of external perturbations. More precisely, the sufficient conditions for the local exponential stability of the closed-loop system are derived and expressed in terms of a set of matrix inequalities. Using generalized sector conditions and proper change of variables, the conditions are then recast as an optimization problem solving linear matrix inequalities. A numerical example is provided to showcase the proposed method and highlight its effectiveness on the system performance.
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16:40-17:00, Paper ThC06.3 | |
>Intermittent Adaptive Spatial Field Estimation and Concurrent Evacuation Planning Using Field-Dependent Evacuee Guidance (I) |
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Demetriou, Michael A. | Worcester Polytechnic Institute |
Keywords: Distributed parameter systems
Abstract: This work combines a path-planning scheme used for the evacuation of humans in indoor environments with the real-time estimation of spatially varying fields using adaptive methods. When a hazardous environment is known, then one possible path planning scheme uses level-set methods to guide a human to safety (escape exit) while at the same time minimizes the accumulated amount of the hazardous field modelled as the hazardous substance inhaled. When the field representing the spatial distribution of the hazardous substance in unknown, then an arrested adaptive estimate of the spatial field is proposed in the level-set guidance. The human evacuee viewed as a mobile agent, obtains spatial field measurements and process them in an adaptive learning scheme to obtain an estimate of the spatial field. When a planning period is added in the traveling period, the adaptive scheme obtains the most recent spatial field estimate (arrested adaptation) and uses it as a time-invariant spatial field for path planning.
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17:00-17:20, Paper ThC06.4 | |
>Rejecting an Unknown Matched Disturbance from an Infinite-Dimensional Control System (I) |
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Gurjar, Bhagyashri | Indian Institute of Technology, Bombay |
Sistla, Bhargav Pavan Kumar | Indian Institute of Technology Bombay |
Natarajan, Vivek | Indian Institute of Technology Bombay |
Keywords: Distributed parameter systems
Abstract: In this paper we address the problem of rejecting an unknown disturbance, which is matched with the input, from an infinite-dimensional plant belonging to the class of regular linear systems. The plant input and output are finite-dimensional and the time-derivative of the disturbance is assumed to be bounded with a known bound. In our solution approach to this problem, we drive a stable ODE using the output of the plant. Via a state transformation obtained by solving a Sylvester equation with possibly unbounded operators, we derive an auxiliary ODE in which the disturbance and the input are matched. We then build a nonlinear disturbance observer for the auxiliary ODE, based on the super-twisting sliding mode algorithm, to generate asymptotically accurate estimates for the unknown disturbance. By letting the input to the plant to be the negative of the disturbance estimate obtained, the matched disturbance in the plant can be rejected. In case the plant is unstable, including a stabilizing feedback signal in the input will ensure that the plant state converges to zero asymptotically. Our approach requires the state of the plant to be known. When only the plant output is known, our approach can be implemented using a state observer for the plant and then modifying the disturbance observer suitably. We demonstrate the efficacy of our approach in simulations by taking the plant to be an anti-stable 1D wave equation and assuming output measurement.
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17:20-17:40, Paper ThC06.5 | |
>Neural Operators for Hyperbolic PDE Backstepping Kernels (I) |
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Bhan, Luke | University of California, San Diego |
Shi, Yuanyuan | University of California San Diego |
Krstic, Miroslav | University of California, San Diego |
Keywords: Nonlinear output feedback, Learning, Nonlinear systems
Abstract: We introduce a framework for eliminating the computation of controller gain functions in PDE control. We learn the nonlinear operator from the plant parameters to the control gains with a (deep) neural network. We provide closed-loop stability guarantees (global exponential) under an NN-approximation of the feedback gains. While, in the existing PDE backstepping, finding the gain kernel requires (one offline) solution to an integral equation, the neural operator (NO) approach we propose learns the mapping from the functional coefficients of the plant PDE to the kernel function by employing a sufficiently high number of offline numerical solutions to the kernel integral equation, for a large enough number of the PDE model’s different functional coefficients. We prove the existence of a DeepONet approximation, with arbitrarily high accuracy, of the exact nonlinear continuous operator mapping PDE coefficient functions into gain functions. Once proven to exist, learning of the NO is standard, completed “once and for all” (never online) and the kernel integral equation doesn’t need to be solved ever again, for any new functional coefficient not exceeding the magnitude of the functional coefficients used for training. Simulation illustrations are provided and code is available on github. This framework, eliminating real-time recomputation of gains, has the potential to be game changing for adaptive control of PDEs and gain scheduling control of nonlinear PDEs.
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17:40-18:00, Paper ThC06.6 | |
>Explicit Backstepping Kernel Solutions for Leak Detection in Pipe Flow Networks Containing Loops (I) |
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Wilhelmsen, Nils Christian Aars | NTNU |
Aamo, Ole Morten | NTNU |
Keywords: Backstepping, Distributed parameter systems, Fluid flow systems
Abstract: A recursive procedure to obtain explicit expressions to a set of observer backstepping kernel equations for an interconnection (cascade) of N+1 systems of 2X2 linear hyperbolic PDEs, N > 0 an integer, for use in leak detection in pipe flow networks containing loops is developed. The kernel equations, consisting of two sets each of N+1 pairs of Goursat PDEs defined over a triangular domain, and N(N+1)/2 pairs of Goursat PDEs defined over a square domain, interconnected to each other in an overarching triangular structure, is separated into 2(N+1) systems consisting of k+1 pairs of PDEs over a triangular domain interconnected with (N-k/2)(k+1) pairs of PDEs over a square domain, k={0,1,...,N}. Under the assumption that the mean friction factor of the network may be used in place of individual friction factors for each pipe, it is shown that the solution to each of the simplified kernel equation systems is expressed explicitly in terms of modified Bessel functions of the first kind, and may be constructed recursively. A numerical example is provided to illustrate the results.
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ThC07 |
Simpor Junior 4813 |
Game Theory V |
Regular Session |
Chair: Nguyen, Duong | Arizona State University |
Co-Chair: He, Jianping | Shanghai Jiao Tong University |
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16:00-16:20, Paper ThC07.1 | |
>Differential Game with Mixed Strategies: A Weak Approximation Approach |
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Xu, Tao | Shanghai Jiao Tong University |
Xi, Wang | Shanghai Jiao Tong University |
He, Jianping | Shanghai Jiao Tong University |
Keywords: Game theory, Randomized algorithms, Stochastic systems
Abstract: This paper utilizes the weak approximation method to analyze differential games that involve mixed strategies. Mixed strategies have the potential to produce unique strategic behaviors, whereas traditional models and tools in pure strategy games cannot be directly applied. Based on the stochastic processes with independent increments, we define the mixed strategy without assuming the knowledge of the opponents' strategy and system state. However, this general mixed strategy poses challenges in evaluating game payoff and game value. To overcome these challenges, we utilize the weak approximation method to employ a stochastic differential game to characterize the dynamics of the mixed strategy game. We demonstrate that the game's payoff function can be precisely approximated with an error of the same scale as the step size. Furthermore, we estimate the upper and lower value functions of the weak approximated game to analyze the existence of game value. Finally, we provide numerical examples to illustrate and elaborate on our findings.
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16:20-16:40, Paper ThC07.2 | |
>Information Disclosure about Booster Efficacy in a Non-Stationary Environment |
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Shah, Sohil | Massachusetts Institute of Technology |
Amin, Saurabh | Massachusetts Institute of Technology |
Jaillet, Patrick | Massachusetts Institute of Technology |
Keywords: Game theory, Stochastic systems, Markov processes
Abstract: This paper investigates the dynamic disclosure of information in nonstationary environments. In particular, a planner iteratively discloses information about the efficacy of an immunizing booster shot that stochastically evolves over time amid the long-run spread of an infectious disease whose severity also varies over time. Each time period, a heterogeneous population of agents uses the disclosed information to determine whether they should obtain the booster shot, and then whether to remain isolated or active. The central planner's objective is to ensure that the active population remains above a minimum threshold each period. We characterize a Markov decision process over the state of beliefs and how signalling mechanisms act on them. We highlight the ``greedy" disclosure rule which provides the least amount of information possible subject to the planner maximizing the likelihood of achieving the active population threshold in the current period. Our results demonstrate that the greedy disclosure rule becomes optimal in finite time. We show this for settings where the population's belief over the booster's efficacy becomes more pessimistic than the belief required in the long-run.
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16:40-17:00, Paper ThC07.3 | |
>Safe Equilibrium |
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Ganzfried, Sam | Ganzfried Research |
Keywords: Game theory
Abstract: The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may obtain an extremely low payoff. On the other hand, a maximin strategy assumes that all opposing agents are playing to minimize our payoff (even if it is not in their best interest), and ensures the maximal possible worst-case payoff, but results in exceedingly conservative play. We propose a new solution concept called safe equilibrium that models opponents as behaving rationally with a specified probability and behaving potentially arbitrarily with the remaining probability. We prove that a safe equilibrium exists in all strategic-form games (for all possible values of the rationality parameters), and prove that its computation is PPAD-hard. We present exact algorithms for computing a safe equilibrium in both 2 and n-player games, as well as scalable approximation algorithms.
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17:00-17:20, Paper ThC07.4 | |
>Deception by Motion: The Eater and the Mover Game |
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Rostobaya, Violetta | George Mason University |
Guan, Yue | Georgia Institute of Technology |
Berneburg, James | George Mason University |
Shishika, Daigo | George Mason University |
Dorothy, Michael | US Army Research Laboratory |
Keywords: Game theory
Abstract: This paper studies the idea of ``deception by motion'' through a two-player dynamic game played between a Mover who must reach a goal to retrieve resources, and an Eater who can consume resources from two candidate goals. The Mover seeks to minimize the resource consumption at the true goal it must reach, while the Eater tries to maximize it without knowing which one the true goal is. Unlike existing works on deceptive motion control that measures the deceptiveness through the quality of inference made by a distant observer (an estimator), we incorporate agents' actions to directly measure the efficacy of deception through the outcome of the game. An equilibrium concept is then proposed without the notion of an estimator. We further identify a pair of equilibrium strategies and demonstrate that if the Eater optimizes for the worst-case scenario, hiding the intention (deception by ambiguity) is still effective, whereas trying to fake the true goal (deception by exaggeration) is not.
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17:20-17:40, Paper ThC07.5 | |
>Geometric Convergence of Distributed Heavy-Ball Nash Equilibrium Algorithm Over Time-Varying Digraphs with Unconstrained Actions |
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Nguyen, Duong Thuy Anh | Arizona State University |
Nguyen, Duong | Arizona State University |
Nedich, Angelia | Arizona State University |
Keywords: Game theory
Abstract: This paper presents a new distributed algorithm that leverages heavy-ball momentum and a consensus-based gradient method to find a Nash equilibrium (NE) in a class of non-cooperative convex games with unconstrained action sets. In this approach, each agent in the game has access to its own smooth local cost function and can exchange information with its neighbors over a communication network. The main novelty of our work is the incorporation of heavy-ball momentum in the context of non-cooperative games that operate on fully-decentralized, directed, and time-varying communication graphs, while also accommodating non-identical step-sizes and momentum parameters. Overcoming technical challenges arising from the dynamic and asymmetric nature of mixing matrices and the presence of an additional momentum term, we provide a rigorous proof of the geometric convergence to the NE. Moreover, we establish explicit bounds for the step-size values and momentum parameters based on the characteristics of the cost functions, mixing matrices, and graph connectivity structures. We perform numerical simulations on a Nash-Cournot game to demonstrate accelerated convergence of the proposed algorithm compared to that of the existing methods.
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ThC08 |
Simpor Junior 4812 |
Optimal Control VI |
Regular Session |
Chair: Sun, Jing | University of Michigan |
Co-Chair: Alam, Syed Eqbal | University of New Brunswick |
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16:00-16:20, Paper ThC08.1 | |
>I2LQR: Iterative LQR for Iterative Tasks in Dynamic Environments |
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Zeng, Yifan | Shanghai Jiao Tong University |
He, Suiyi | University of Minnesota-Twin Cities |
Nguyen, Han | University of California, Berkeley |
Li, Yihan | Xi'an Jiaotong University |
Li, Zhongyu | UC Berkeley |
Sreenath, Koushil | University of California, Berkeley |
Zeng, Jun | University of California, Berkeley |
Keywords: Optimal control, Predictive control for nonlinear systems, Robotics
Abstract: This work introduces a novel control strategy called Iterative Linear Quadratic Regulator for Iterative Tasks (i2LQR), which aims to improve closed-loop performance with local trajectory optimization for iterative tasks in a dynamic environment. The proposed algorithm is reference-free and utilizes historical data from previous iterations to enhance the performance of the autonomous system. Unlike existing algorithms, the i2LQR computes the optimal solution in an iterative manner at each timestamp, rendering it well-suited for iterative tasks with changing constraints at different iterations. To evaluate the performance of the proposed algorithm, we conduct numerical simulations for an iterative task aimed at minimizing completion time. The results show that i2LQR achieves an optimized performance with respect to learning-based MPC (LMPC) as the benchmark in static environments, and outperforms LMPC in dynamic environments with both static and dynamics obstacles.
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16:20-16:40, Paper ThC08.2 | |
>Improving Primal Decomposition for Multistage MPC Using an Extended Newton Method |
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Bjorvand, Simen | NTNU |
Jaschke, Johannes | Norwegian University of Science and Technology |
Keywords: Optimal control, Predictive control for nonlinear systems, Robust control
Abstract: Multistage model predictive control is a robust MPC formulation that takes into account parametric uncertainty by constructing a finite set of coupled scenarios. As the amount of scenarios increase so does computational cost and real-time implementation might not be possible. Scenario decomposition has been proposed to distribute computations and make real-time implementation possible, however, typically the subproblems are coordinated using the steepest descent method with slow convergence properties. In this paper a primal decomposition algorithm is improved by the use of a nonsmooth Newtons method for continuous nonsmooth equations. The proposed algorithm is applied to a gas-lift optimization system and compared to the standard primal decomposition method using steepest descent.
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16:40-17:00, Paper ThC08.3 | |
>Robust Model Predictive Control for Enhanced Fast Charging on Electric Vehicles through Integrated Power and Thermal Management |
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Hu, Qiuhao | University of Michigan |
Amini, Mohammad Reza | University of Michigan |
Wiese, Ashley Peter | Ford Motor Company |
Kolmanovsky, Ilya V. | The University of Michigan |
Sun, Jing | University of Michigan |
Keywords: Optimal control, Robust control
Abstract: This paper explores the synergies between integrated power and thermal management (iPTM) and battery charging in an electric vehicle (EV). A multi-objective model predictive control (MPC) framework is developed to optimize the fast charging performance while enforcing the constraints in the power and thermal loops. The approach takes into account the coupling of the battery and cabin thermal management. The case study of a commercial EV demonstrates that the proposed method can effectively meet the requirements of fast charging and thermal management when accurate preview information is available. However, failure to predict the charging event can result in performance degradation with longer charging time. A time-varying weighting strategy is proposed to enhance charging performance in the presence of uncertainty. This strategy leverages the battery state-of-charge (SOC) and adjusts the priority of the multi-objective MPC at different phases during charging. Simulated results using a commercial EV use case show improved robustness in charging time using the proposed strategy.
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17:00-17:20, Paper ThC08.4 | |
>Local Turnpike Properties in Finite Horizon Optimal Control |
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Kruegel, Lisa | University of Bayreuth |
Faulwasser, Timm | TU Dortmund University |
Gruene, Lars | University of Bayreuth |
Keywords: Optimal control, Stability of nonlinear systems
Abstract: In optimal control, it is well known that near-optimal trajectories exhibit a turnpike property if the system is strictly dissipative at the considered equilibrium and additional technical conditions are satisfied. In this paper we extend this result to a system which is merely locally strictly dissipative. For the special case of locally positive definite stage costs we show that there exists upper and lower bounds on the optimization horizon for which a local turnpike property becomes visible. For locally strictly dissipative costs we show that the same holds under a condition on the leaving arc of the local turnpike property. Our theoretical findings are illustrated by numerical examples.
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17:20-17:40, Paper ThC08.5 | |
>Communication-Efficient Allocation of Multiple Indivisible Resources in a Federated Multi-Agent System |
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Alam, Syed Eqbal | University of New Brunswick |
Shukla, Dhirendra | University of New Brunswick |
Keywords: Optimal control, Stochastic optimal control, Agents-based systems
Abstract: A federated multi-agent system is a multi-agent system wherein agents collaborate with a central server to optimize system goals without sharing their private information. We develop a communication-efficient solution to resource allocation problems for a population of agents coupled through multiple indivisible shared resources in a federated multi-agent system. The agents demand resources in a probabilistic way based on their local computation and preferences, and the agents receive either one unit of a resource or do not receive it. The agents are not required to share their cost functions or derivatives of cost functions with other agents or the central server. Optimal control of a population of such agents, subject to capacity constraints, is widely found in many application domains, such as smart energy systems, intelligent transportation systems, and edge computing, to name a few. We present convergence results using multi-time scale stochastic approximation techniques and an example of electric vehicle charging point allocation illustrating the efficacy of the developed solution.
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17:40-18:00, Paper ThC08.6 | |
>Finite Elements with Switch Detection for Direct Optimal Control of Nonsmooth Systems with Set-Valued Step Functions |
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Nurkanovic, Armin | University of Freiburg |
Frey, Jonathan | University of Freiburg |
Pozharskiy, Anton | University of Freiburg |
Diehl, Moritz | University of Freiburg |
Keywords: Optimal control, Switched systems, Numerical algorithms
Abstract: This paper extends the Finite Elements with Switch Detection (FESD) method [Nurkanovic et al.,2022] to optimal control problems with nonsmooth systems involving set-valued step functions. Logical relations and common nonsmooth functions within a dynamical system can be expressed using linear and nonlinear expressions involving step functions. A prominent subclass of these systems are Filippov systems. The set-valued step function can be expressed by the solution map of a linear program, and using its KKT conditions allows one to transform the initial system into an equivalent dynamic complementarity system (DCS). Standard Runge-Kutta (RK) methods applied to DCS have only first-order accuracy. The FESD discretization makes the step sizes degrees of freedom and adds further constraints that ensure exact switch detection to recover the high-accuracy properties that RK methods have for smooth ODEs. We use the novel FESD method for the direct transcription of optimal control problems. All methods and examples in this paper are implemented in the open-source software package NOSNOC.
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ThC09 |
Simpor Junior 4811 |
Optimization I |
Regular Session |
Chair: Sznaier, Mario | Northeastern University |
Co-Chair: Zorzi, Mattia | University of Padova |
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16:00-16:20, Paper ThC09.1 | |
>Peak Estimation of Time Delay Systems Using Occupation Measures |
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Miller, Jared | ETH Zurich |
Korda, Milan | LAAS-CNRS |
Magron, Victor | LAAS, CNRS |
Sznaier, Mario | Northeastern University |
Keywords: Optimization, Delay systems, Algebraic/geometric methods
Abstract: This work proposes a method to compute the maximum value obtained by a state function along trajectories of a Delay Differential Equation (DDE). An example of this task includes finding the maximum number of infected people in an epidemic model with a nonzero incubation period. The variables of this peak estimation problem include the stopping time and the original history (restricted to a class of admissible histories). The original nonconvex DDE peak estimation problem is approximated by an infinite-dimensional Linear Program (LP) in occupation measures, inspired by existing measure-based methods in peak estimation and optimal control. This LP is approximated from above by a sequence of Semidefinite Programs through the moment-Sum-of-Squares hierarchy. Effectiveness of this scheme in providing peak estimates for DDEs is demonstrated with provided examples.
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16:20-16:40, Paper ThC09.2 | |
>Zeroth-Order Optimization for Cooperative Multi-Agent Systems with Diminishing Step Size and Smoothing Radius |
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Zheng, Xinran | University of California San Diego |
Javidi, Tara | University of California, San Diego |
Touri, Behrouz | University of California San Diego |
Keywords: Optimization, Distributed control, Optimization algorithms
Abstract: We study a class of zeroth-order distributed optimization problems, where each agent can control a partial vector and observe a local cost that depends on the joint vector of all agents, and the agents can communicate with each other with time delay. We propose and study a gradient descent-based algorithm using two-point gradient estimators with diminishing smoothing parameters and diminishing step-size and we establish the convergence rate to a first-order stationary point for general nonconvex problems. A byproduct of our proposed method with diminishing step size and smoothing parameters, as opposed to the fixed-parameter scheme, is that our proposed algorithm does not require any information regarding the local cost functions. This makes the solution appealing in practice as it allows optimizing an unknown (black-box) global function. At the same time, the performance will adaptively match the problem instance parameters.
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16:40-17:00, Paper ThC09.3 | |
>Distributed Outer Approximation of the Intersection of Ellipsoids |
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Aldana-López, Rodrigo | Universidad De Zaragoza |
Sebastián, Eduardo | Universidad De Zaragoza |
Aragues, Rosario | Universidad De Zaragoza |
Montijano, Eduardo | Universidad De Zaragoza |
Sagues, Carlos | Universidad De Zaragoza |
Keywords: Optimization, Distributed control, Sensor fusion
Abstract: The outer Löwner-John method is widely used in sensor fusion applications to find the smallest ellipsoid that can approximate the intersection of a set of ellipsoids, described by positive definite covariance matrices modeling the quality of each sensor. We propose a distributed algorithm to solve this problem when these matrices are defined over the network's nodes. This is of particular significance as it is the first decentralized algorithm capable of computing the covariance intersection ellipsoid by combining information from the entire network using only local interactions. The solution is based on a reformulation of the centralized problem, leading to a local protocol based on exact dynamic consensus tools. After reaching consensus, the protocol converges to an outer Löwner-John ellipsoid in finite time, and to the global optimum asymptotically. Formal convergence analysis and numerical experiments are provided to validate the proposal’s advantages.
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17:00-17:20, Paper ThC09.4 | |
>Nesterov Smoothing for Sampling without Smoothness |
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Fan, Jiaojiao | Georgia Institute of Technology |
Yuan, Bo | Georgia Institute of Technology |
Liang, Jiaming | Yale University |
Chen, Yongxin | Georgia Institute of Technology |
Keywords: Optimization, Filtering, Randomized algorithms
Abstract: We study the problem of sampling from a target distribution in mathbb{R}^d whose potential is not smooth. Compared with the sampling problem with smooth potentials, this problem is much less well-understood due to the lack of smoothness. In this paper, we propose a novel sampling algorithm for a class of non-smooth potentials by first approximating them by smooth potentials using a technique that is akin to Nesterov smoothing. We then utilize sampling algorithms on the smooth potentials to generate approximate samples from the original non-smooth potentials. We select an appropriate smoothing intensity to ensure that the distance between the smoothed and un-smoothed distributions is minimal, thereby guaranteeing the algorithm's accuracy. Hence we obtain non-asymptotic convergence results based on existing analysis of smooth sampling. We verify our convergence result on a synthetic example and apply our method to improve the worst-case performance of Bayesian inference on a real-world example.
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17:20-17:40, Paper ThC09.5 | |
>A Weaker Regularity Condition for the Multidimensional Nu-Moment Problem |
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Zhu, Bin | Sun Yat-Sen University |
Zorzi, Mattia | University of Padova |
Keywords: Optimization, Identification, Stochastic systems
Abstract: We consider the problem of finding a d-dimensional spectral density through a moment problem which is characterized by an integer parameter nu. Previous results showed that there exists an approximate solution under the regularity condition nu >= d/2+1. To realize the process corresponding to such a spectral density, one would take nu as small as possible. In this letter we show that this condition can be weaken as nu >= d/2.
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17:40-18:00, Paper ThC09.6 | |
>Set-Valued Regression and Cautious Suboptimization: From Noisy Data to Optimality |
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Eising, Jaap | ETH Zurich |
Cortes, Jorge | University of California, San Diego |
Keywords: Optimization, Learning, Extremum seeking
Abstract: This paper deals with the problem of finding suboptimal values of an unknown function on the basis of measured data corrupted by bounded noise. As a prior, we assume that the unknown function is parameterized in terms of a number of basis functions. Inspired by the informativity approach, we view the problem as the suboptimization of the worst-case estimate of the function. The paper provides closed form solutions and convexity results for this function, which enables us to solve the problem. After this, an online implementation is investigated, where we iteratively measure the function and perform a suboptimization. This nets a procedure that is safe at each step, and which, under mild assumptions, converges to the true optimizer.
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ThC10 |
Roselle Junior 4713 |
Neural Networks I |
Regular Session |
Chair: Ruths, Justin | University of Texas at Dallas |
Co-Chair: Pauli, Patricia | University of Stuttgart |
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16:00-16:20, Paper ThC10.1 | |
>Transformer Neural Networks for Maximum Friction Coefficient Estimation of Tire-Road Contact Using Onboard Vehicle Sensors |
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Schäfke, Hendrik | Leibniz University Hannover |
Lampe, Nicolas | Osnabrück University of Applied Sciences |
Kortmann, Karl-Philipp | Leibniz University Hannover, Institute of Mechatronic Systems |
Keywords: Neural networks, Automotive systems, Estimation
Abstract: For the optimization of advanced driver assistance systems (ADAS) and the implementation of autonomous driving, the perception of the vehicles environment and in particular the maximum friction coefficient is crucial. Since the maximum friction coefficient cannot be measured directly via existing serial sensors, estimating this coefficient based on available sensors is an area of research. In this paper, maximum friction coefficient estimation is presented using transformer neural networks (TNN) based on the input data measured by onboard vehicle sensors. The TNN is applied to both a simulative dataset created with IPG CarMaker and an experimental dataset recorded on a test track, each using a sports utility vehicle (SUV) as the test vehicle. Both datasets contain typical longitudinal and lateral driving maneuvers on different road surfaces. On an independent test dataset, the data-based TNN approach shows improved results in estimating the maximum friction coefficient compared to the model-based approach of an unscented Kalman filter (UKF) and to two other data-based approaches using recurrent artificial neural networks (RANNs) from previous works. In particular, the TNN responds faster and more accurate to jumps of the maximum friction coefficient, especially during lateral driving maneuvers. Moreover, the TNN has both less parameters, and training epochs compared to the RANN.
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16:20-16:40, Paper ThC10.2 | |
>Counter-Example Guided Imitation Learning of Controllers from Temporal Logic Specifications |
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Dang, Thao | VERIMAG |
Donze, Alexandre | Decyphir SAS |
Haque, Inzemamul | Indian Institute of Technology Kanpur |
Kekatos, Nikolaos | Verimag - Univ. Grenoble Alpes |
Saha, Indranil | Indian Institute of Technology Kanpur |
Keywords: Neural networks, Iterative learning control, Formal Verification/Synthesis
Abstract: We present a novel method for imitation learning for control requirements expressed using Signal Temporal Logic (STL). More concretely we focus on the problem of training a neural network to imitate a complex controller. The learning process is guided by efficient data aggregation based on counter-examples and a coverage measure. Moreover, we introduce a method to evaluate the performance of the learned controller via parameterization and parameter estimation of the STL requirements. We demonstrate our approach with a flying robot case study.
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16:40-17:00, Paper ThC10.3 | |
>Lipschitz-Bounded 1D Convolutional Neural Networks Using the Cayley Transform and the Controllability Gramian |
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Pauli, Patricia | University of Stuttgart |
Wang, Ruigang | The University of Sydney |
Manchester, Ian R. | University of Sydney |
Allgöwer, Frank | University of Stuttgart |
Keywords: Neural networks, LMIs
Abstract: We establish a layer-wise parameterization for 1D convolutional neural networks (CNNs) with built-in end-to-end robustness guarantees. In doing so, we use the Lipschitz constant of the input-output mapping characterized by a CNN as a robustness measure. We base our parameterization on the Cayley transform that parameterizes orthogonal matrices and the controllability Gramian of the state space representation of the convolutional layers. The proposed parameterization by design fulfills linear matrix inequalities that are sufficient for Lipschitz continuity of the CNN, which further enables unconstrained training of Lipschitz-bounded 1D CNNs. Finally, we train Lipschitz-bounded 1D CNNs for the classification of heart arrythmia data and show their improved robustness.
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17:00-17:20, Paper ThC10.4 | |
>Hybrid Zonotopes Exactly Represent ReLU Neural Networks |
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Ortiz, Joshua | University of Texas at Dallas |
Vellucci, Alyssa | University of Texas at Dallas |
Koeln, Justin | University of Texas at Dallas |
Ruths, Justin | University of Texas at Dallas |
Keywords: Neural networks, Machine learning, Data driven control
Abstract: We show that hybrid zonotopes offer an equivalent representation of feed-forward fully connected neural networks with ReLU activation functions. Our approach demonstrates that the complexity of binary variables is equal to the total number of neurons in the network and hence grows linearly in the size of the network, regardless of the architecture. We demonstrate the utility of the hybrid zonotope formulation through three case studies including nonlinear function approximation, MPC closed-loop reachability and verification, and robustness of classification on the MNIST dataset.
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17:20-17:40, Paper ThC10.5 | |
>Neural Network Observer for Lateral Vehicle Model with Varying Sampled and Delayed Output |
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Abdl Ghani, Hasan | ESIGELEC |
Laghmara, Hind | INSA Rouen Normandie |
Ahmed Ali, Sofiane | IBISC, Evry-Val-d’Essonne University, Universite Paris-Saclay, E |
Ainouz, Samia | INSA Rouen Normandie |
Keywords: Neural networks, Observers for nonlinear systems, Autonomous vehicles
Abstract: This research offers a neural network adaptive observer (NNAO) architecture for nonlinear lateral vehicle dynamics with variable sampled delayed output. A radial basis function (RBF) neural network is used to approximate the system's unknown part, and a new weight updating mechanism is provided. A closed-loop output predictor is used to offer inter-sample output estimate while dealing with variable samples, and a closed-loop integral compensation is used to deal with variable delay. The convergence of the proposed observer is proved using Lyapunov function and small gain arguments. Simulation tests confirm the NNAO's estimate algorithm's accuracy in estimating yaw rate, longitudinal speed, and particularly the excellent performance of the estimation of lateral speed.
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17:40-18:00, Paper ThC10.6 | |
>Adaptive Estimation of the Pennes' Bio-Heat Equation - II: A NN-Based Implementation for Real-Time Applications |
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Cappellini, Guglielmo | Sapienza University of Rome |
Trappolini, Giovanni | Sapienza University of Rome |
Staffetti, Ernesto | Universidad Rey Juan Carlos |
Cristofaro, Andrea | Sapienza University of Rome |
Vendittelli, Marilena | Sapienza University of Rome |
Keywords: Neural networks, Observers for nonlinear systems, Uncertain systems
Abstract: This is the companion paper of a two-part work on the observation of the heat transfer phenomenon in biological tissues. In particular, we are interested in real-time estimation of the temperature in the interior of a spatial domain of interest using measurements at its boundary. The prevailing model for heat transfer in biological tissues, pioneered by Pennes, relies on a parabolic reaction-diffusion partial differential equation. However, neither the observation problem has been fully explored nor have the available solutions proved suitable for real-time applications. In the companion paper, we propose the design of an observer whose formal properties, however, cannot be easily reflected in its practical performance, due to computational issues arising with the use of common numerical solvers. The difficulties are mostly related to the integration of a system of coupled PDEs/ODE, required by the algorithm. In this paper, we propose an alternative implementation of the observer that makes use of deep neural networks for predicting the PDEs state, thus avoiding the online integration. Preliminary results show that this approach is very effective in solving the considered problem and is amenable to extension to other classes of PDEs and to higher dimensions.
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ThC11 |
Roselle Junior 4712 |
Autonomous Systems II |
Regular Session |
Chair: Menon, Prathyush P | Faculty of Environment, Science and Economy |
Co-Chair: Clark, Andrew | Washington University in St. Louis |
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16:00-16:20, Paper ThC11.1 | |
>Multi Agent Systems Learn to Safely Move Indoor Environment |
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Suppa, Martina | University of Pavia |
Hajkarim, Mohammad Hossein | University of Exeter |
Menon, Prathyush P | Faculty of Environment, Science and Economy |
Ferrara, Antonella | University of Pavia |
Keywords: Autonomous systems, Machine learning, Robotics
Abstract: This letter presents a path-planning algorithm for a fleet of autonomous agents operating in a bounded indoor environment with static and moving obstacles. The proposed algorithm uses a combination of Modified Artificial Potential Field (MAPF) and Reinforcement Learning (RL) to determine safe paths for the agents to their respective goal locations. The proposed approach ensures avoiding collision with the obstacles and among the agents. The better performance of our proposed method, suitable for a real-world operation, is illustrated by comparing it with multiple RL and MAPF concepts. In addition to simulations, we carry out practical experiments using multiple open-source flying development platforms in an indoor VICON lab environment to demonstrate the efficacy of the proposed approach.
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16:20-16:40, Paper ThC11.2 | |
>Convex Optimization-Based Policy Adaptation to Compensate for Distributional Shifts |
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Hashemi, Navid | University of Southern California |
Ruths, Justin | University of Texas at Dallas |
Deshmukh, Jyotirmoy | University of Southern California |
Keywords: Autonomous systems, Neural networks, Markov processes
Abstract: In many real-world cyber-physical systems, control designers often model the dynamics of the physical components using stochastic dynamical equations, and the design optimal control policies for the model. At any given time, a stochastic difference equation essentially models the distribution on next states conditioned on the state and controller action at that time. Due to shifts in this distribution, modeling assumptions on the stochastic dynamics made during initial control design may no longer be valid when the system is deployed in the real-world. In safety-critical systems, this can be particularly problematic; even if the system follows the designed control trajectory that was deemed safe and optimal, it may reach unsafe states due to the distribution shift. In this paper, we address the following problem: suppose we obtain an optimal control trajectory in the training environment, how do we ensure that in the real system this optimal trajectory is tracked with minimal error? In other words, we wish to adapt an optimal trained policy to distribution shifts in the environment. We show that this problem can be cast as a nonlinear optimization problem solvable using heuristic optimization methods. However, a convex relaxation of this problem allows us to learn policies that track the optimal trajectory with much better error performance and faster computation times. We demonstrate the efficacy of our approach on two different case studies: optimal path tracking using a Dubin’s car model, and collision avoidance using both a linear and nonlinear model for adaptive cruise control.
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16:40-17:00, Paper ThC11.3 | |
>Efficient Sum of Squares-Based Verification and Construction of Control Barrier Functions by Sampling on Algebraic Varieties |
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Zhang, Hongchao | Washington University in St. Louis |
Li, Zhouchi | Worcester Polytechnic Institute |
Dai, Hongkai | Toyota Research Institute |
Clark, Andrew | Washington University in St. Louis |
Keywords: Autonomous systems, Nonlinear systems, Algebraic/geometric methods
Abstract: Safety is a critical property of control systems in vital applications such as manufacturing, energy, and autonomous vehicles. Control barrier functions have been proposed for safe control, however, verifying the safety guarantees of a given CBF and constructing CBFs to satisfy safety constraints are computationally challenging. In this paper, we propose a new approach to addressing these challenges, in which the global safety properties of CBFs are characterized based on a finite set of sample points. Specifically, we propose new algorithms for verifying CBFs for polynomial systems by solving a system of linear equalities and sum-of-squares constraints at a set of points sampled on an algebraic variety induced by the CBF. We extend this approach to high-order CBFs as well as systems with actuation constraints. Turning to the problem of constructing CBFs, we propose an algorithm that first selects a finite set of samples, and then computes a CBF such that the samples lie on the boundary of the safe region by solving a mixed-integer convex program. We prove that, if the number of samples is sufficiently large and a CBF exists, then our approach returns a function that satisfies necessary conditions of a CBF. We evaluate our approach on a linear cruise control scenario and a nonlinear quadrotor UAV, and find that both the verification and synthesis algorithms significantly outperform another state-of-the-art SOS-based algorithm.
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17:00-17:20, Paper ThC11.4 | |
>Optimal Decision-Making for Autonomous Agents Via Data Composition |
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Garrabé, Émiland | University of Salerno |
Lamberti, Martina | University of Salerno (student) |
Russo, Giovanni | University of Salerno |
Keywords: Autonomous systems, Optimal control, Information theory and control
Abstract: We consider the problem of designing agents able to compute optimal decisions by composing data from multiple sources to tackle tasks involving: (i) tracking a desired behavior while minimizing an agent-specific cost; (ii) satisfying safety constraints. After formulating the control problem, we show that this is convex under a suitable assumption and find the optimal solution. The effectiveness of the results, which are turned in an algorithm, is illustrated on a connected cars application via in-silico and in-vivo experiments with real vehicles and drivers. All the experiments confirm our theoretical predictions and the deployment of the algorithm on a real vehicle shows its suitability for in-car operation.
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17:20-17:40, Paper ThC11.5 | |
>Fast, Smooth, and Safe: Implicit Control Barrier Functions through Reach-Avoid Differential Dynamic Programming |
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Ramesh Kumar, Athindran | Princeton University |
Hsu, Kai-Chieh | Princeton University |
Ramadge, Peter J. | Princeton Univ |
Fernández Fisac, Jaime | Princeton University |
Keywords: Autonomous systems, Optimal control
Abstract: Safety is a central requirement for autonomous system operation across domains. Hamilton-Jacobi (HJ) reachability analysis can be used to construct ``least-restrictive'' safety filters that result in infrequent, but often extreme, control overrides. In contrast, control barrier function (CBF) methods apply smooth control corrections to guard the system against an often conservative safety boundary. This paper provides an online scheme to construct an implicit CBF through HJ reach-avoid differential dynamic programming in a receding-horizon framework, enabling smooth safety filtering with infinite-time safety guarantees. Simulations with the Dubins car and 5D bicycle dynamics demonstrate the scheme's ability to preserve safety smoothly without the conservativeness of handcrafted CBFs.
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17:40-18:00, Paper ThC11.6 | |
>Guidance for Terminal Direction and Final Time Constrained-Approach towards a Moving Target |
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A, Vivek | Indian Institute of Technology Madras |
Ghosh, Satadal | Indian Institute of Technology Madras |
Keywords: Aerospace, Autonomous systems
Abstract: Approaching a moving target at a desired time along a desired orientation is an essential requirement for many applications. Most works that address this issue in the literature are developed considering a stationary target. Extending such guidance strategies against moving targets using the concept of predicted intercept point could degrade its performance. Instead, considering the engagement against a lower-speed moving but nonmaneuvering target directly, in this paper, a proportional navigation-based integrated guidance strategy is developed to address this problem of simultaneous control of terminal angle and final time. The desired terminal angle is achieved by suitably selecting the navigation gain and manipulating the lateral acceleration applied. At the same time, the final time requirement is satisfied by changing the purser's speed suitably. The proposed guidance scheme is validated through numerical simulations for different terminal requirements starting from same initial engagement geometry.
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ThC12 |
Roselle Junior 4711 |
Decentralized Control |
Regular Session |
Chair: Chen, Ben M. | Chinese University of Hong Kong |
Co-Chair: Hadjicostis, Christoforos N. | University of Cyprus |
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16:00-16:20, Paper ThC12.1 | |
>A Strong Duality Result for Cooperative Decentralized Constrained POMDPs |
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Khan, Nouman | University of Michigan, Ann Arbor |
Subramanian, Vijay G. | University of Michigan |
Keywords: Decentralized control, Cooperative control, Constrained control
Abstract: The work studies cooperative decentralized constrained POMDPs with asymmetric information. Using an extension of Sion's Minimax theorem for functions with positive infinity and results on weak-convergence of measures, strong duality and existence of a saddle point are established for the setting of infinite-horizon expected total discounted costs when the observations lie in a countable space, the actions are chosen from a finite space, the immediate constraint costs are bounded, and the immediate objective cost is bounded from below.
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16:20-16:40, Paper ThC12.2 | |
>OA-ECBVC: A Cooperative Collision-Free Encirclement and Capture Approach in Cluttered Environments |
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Wang, Xinyi | The Chinese University of Hong Kong |
Ding, Yulong | Tongji University |
Chen, Yizhou | The Chinese University of Hong Kong |
Han, Ruihua | The University of Hong Kong |
Xi, Lele | Hebei University of Science and Technology |
Chen, Ben M. | Chinese University of Hong Kong |
Keywords: Decentralized control, Autonomous systems, Control applications
Abstract: This article investigates the practical scenarios of chasing an adversarial evader in an unbounded environment with cluttered obstacles. We propose a Voronoi-based decentralized algorithm for multiple pursuers to encircle and capture the evader by reacting to collisions. An efficient approach is presented for constructing an obstacle-aware evader-centered bounded Voronoi cell (OA-ECBVC), which strictly ensures collision avoidance in various obstacle scenarios when pursuing the evader. The evader can be efficiently enclosed in a convex hull given random initial configurations. Furthermore, to cooperatively capture the evader, each pursuer continually compresses the boundary of its OA-ECBVC to quickly reduce the movement space of the evader while maintaining encirclement. Our OA-ECBVC algorithm is validated in various simulated environments with different dynamic systems of robots. Real-time performance of resisting uncertainties shows the superior reliability of our method for deployment on multiple robot platforms.
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16:40-17:00, Paper ThC12.3 | |
>Automatic Decomposition of Reward Machines for Decentralized Multiagent Reinforcement Learning |
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Smith, Sophia | The University of Texas at Austin |
Neary, Cyrus | The University of Texas at Austin |
Topcu, Ufuk | The University of Texas at Austin |
Keywords: Decentralized control, Automata, Learning
Abstract: In cooperative multiagent reinforcement learning (MARL), a team of agents learns to work together to complete a task. Centralized approaches to MARL quickly become intractable as the number of agents increases, necessitating decentralized learning algorithms which take advantage of task decompositions to train the agents individually. However, these task decompositions typically require careful human engineering. In this work, we develop algorithms to automatically decompose a team task into a collection of subtasks that can be used for decentralized reinforcement learning. We use reward machines—structured representations of reward functions—to encode team tasks and to automatically generate task decompositions that enforce the following three properties. 1) Task Consistency: We generate decompositions that are consistent with the team’s task—if the agents individually learn to accomplish their subtasks, we guarantee that the composition of their learned behaviors will accomplish the original task. 2) Minimized Coordination: Inter-agent coordination during task execution can be costly. We minimize the coordination that’s necessary to execute the decomposed tasks, which simplifies the decentralized learning problem by reducing each agent’s interdependencies with its teammates. 3) Fairly Distributed: We maximize a weighted sum that balances the total utility of the agents and the fairness of the decomposition, which we define in terms of the distribution of assigned subtasks between the agents. Experimental results in three-agent and five-agent MARL tasks show the method’s novel capabilities. The algorithm automatically generates task decompositions that are consistent with the team task, that reduce unnecessary coordination between the agents, and that take the agent’s utility over subtasks into account. When used to define decentralized objectives, the generated task decompositions result in team policies that efficiently complete the task. Meanwhile, baseline decompositions yield policies that fail to complete the task.
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17:00-17:20, Paper ThC12.4 | |
>Predator-Prey Interactions through Heterogeneous Coverage Control Using Reaction-Diffusion Processes |
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Lin, Ruoyu | University of California, Irvine |
Egerstedt, Magnus | University of California, Irvine |
Keywords: Decentralized control, Cooperative control, Robotics
Abstract: A predator-prey interaction scheme based on a heterogeneous cooperative control strategy driven by reaction-diffusion processes is investigated in this paper, where the heterogeneity is understood along five modalities in terms of the dynamics of predator and prey. The predators are modeled as individual agents whereas the prey are modeled as space-time dependent densities. A decentralized coverage controller for predators with heterogeneous mobility, encoded by multiplicatively weighted Voronoi cells, is derived so that the predators can optimally react to the time-varying prey distributions. The predator-prey interaction scheme can be adopted in diverse application scenarios. An experiment of deploying a multi-robot system across a two-dimensional domain pictorially representing a forest in which ideally modeled wildfires need to be put out demonstrates the efficacy of the proposed scheme.
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17:20-17:40, Paper ThC12.5 | |
>Harnessing HARQ Retransmissions for Fast Average Consensus Over Unreliable Communication Channels |
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Makridis, Evagoras | University of Cyprus |
Charalambous, Themistoklis | University of Cyprus |
Hadjicostis, Christoforos N. | University of Cyprus |
Keywords: Decentralized control, Delay systems, Discrete event systems
Abstract: In this work, we introduce a new consensus mechanism by incorporating a Hybrid Repeat reQuest (HARQ) error control protocol into the Ratio Consensus (RC) algorithm to achieve fast discrete-time asymptotic average consensus in the presence of packet retransmissions (information delays), and packet-dropping links (information loss) over directed networks. Using this consensus mechanism (hereinafter referred to as HARQ-RC), each transmitting node decides whether to retransmit packets (containing values of consensus variables) to its out-neighbors by utilizing their HARQ feedback signals. Under this protocol, each receiving node may detect the corrupted part of the received packet, and by combining successfully received information from previous retransmission trials, it may recover the information of the packet. This mechanism leads in a lower number of retransmission trials compared to standard ARQ mechanism, and hence the consensus iterations converge faster to the average consensus value. By introducing the weighted adjacency matrix that models the HARQ-based information exchange between nodes, we show that the nodes are guaranteed to reach asymptotic average consensus using the HARQ-RC mechanism despite the information delays and losses. The effectiveness of the HARQ-RC over bad communication links, with respect to achieving faster convergence to the average consensus value, is demonstrated under different simulation scenarios.
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17:40-18:00, Paper ThC12.6 | |
>A Fully Asynchronous Newton Tracking Method for Decentralized Optimization |
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Pan, Zhaoye | Shanghai University of Finance and Economics |
Liu, Huikang | Shanghai University of Finance and Economics |
Keywords: Decentralized control, Delay systems, Optimization algorithms
Abstract: We consider fully asynchronous decentralized optimization over a directed graph.While various algorithms have been proposed, real-world applications require relaxing the assumption and considering communication networks with asynchronous and heterogeneous nodes. To meet these challenges, we propose an efficient and robust Newton tracking mechanism for fully asynchronous optimization. Our proposed mechanism can be adapted to different asynchronous first-order methods as required by the practical context. Through the theoretical analysis we demonstrate the R-linear rate of our method and derive an explicit expression of decaying factor under local conditions. Furthermore, numerical comparison with existing algorithms support the efficiency and robustness of our method.
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ThC13 |
Roselle Junior 4613 |
Networked Control Systems III |
Regular Session |
Chair: Nesic, Dragan | University of Melbourne |
Co-Chair: He, Changran | The Chinese University of Hong Kong |
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16:00-16:20, Paper ThC13.1 | |
>A Multi-Processor Implementation for Networked Control Systems |
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Maass, Alejandro I. | Universidad De O'Higgins |
Wang, Wei | The University of Melbourne |
Nesic, Dragan | University of Melbourne |
Tan, Ying | The University of Melbourne |
Postoyan, Romain | CNRS, CRAN, Université De Lorraine |
Keywords: Networked control systems, Hybrid systems, Stability of nonlinear systems
Abstract: We study nonlinear networked control systems (NCS) with a multi-processor emulation-based controller. We start with a stable and centralised NCS commonly considered in the literature. Then, we show how to implement the centralised controller over multiple processors inspired by parallel computing techniques, so that stability is preserved (semi-globally and practically) under sufficiently fast computations. An example illustrates the main results.
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16:20-16:40, Paper ThC13.2 | |
>Scheduling and Control of Networked Systems: A Sparsity Approach |
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Dasgupta, Anubhab | Indian Institute of Technology Kharagpur |
Kundu, Atreyee | Indian Institute of Technology Kharagpur |
Keywords: Networked control systems, Linear systems, Optimization
Abstract: This paper deals with the design of scheduling logic and control logic for networked control systems (NCSs) with limited communication resources. We consider an NCS with (N) plants that communicate with remotely located controllers over a shared band-limited communication network. Due to a limited capacity of the network, at most (M::(
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16:40-17:00, Paper ThC13.3 | |
>Distributed and Anytime Algorithm for Network Optimization Problems with Separable Structure |
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Mestres, Pol | University of California, San Diego |
Cortes, Jorge | University of California, San Diego |
Keywords: Networked control systems, Optimization, Cooperative control
Abstract: This paper considers the problem of designing a dynamical system to solve constrained optimization problems in a distributed way and in an anytime fashion (i.e., such that the feasible set is forward invariant). For problems with separable objective function and constraints, we design an algorithm with the desired properties and establish its convergence. Simulations illustrate our results.
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17:00-17:20, Paper ThC13.4 | |
>Leader-Following Consensus of Multiple Uncertain Rigid Body Systems by a Sampled-Data Adaptive Distributed Observer |
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He, Changran | The Chinese University of Hong Kong |
Huang, Jie | The Chinese University of Hong Kong |
Keywords: Networked control systems, Nonlinear systems, Sampled-data control
Abstract: In this paper, we study the leader-following attitude consensus problem for multiple uncertain rigid body systems by a sampled-data adaptive distributed observer. Unlike the existing sampled-data distributed observer, which can only asymptotically estimate the state of the leader, the sampled-data adaptive distributed observer can estimate both the state and the system matrix of the leader exponentially. We synthesize a distributed control law utilizing sampled-data communications to solve the leader-following attitude consensus problem for multiple uncertain rigid body systems based on the sampled-data adaptive distributed observer. Compared with a distributed control law that uses continuous-time communications, the distributed control law utilizing sampled-data communications consumes fewer communication resources and is more robust to communication failures.
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17:20-17:40, Paper ThC13.5 | |
>Transactive Multi-Agent Systems Over Flow Networks |
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Chen, Yijun | University of Sydney |
Salehi, Zeinab | The Australian National University |
Petersen, Ian R. | Australian National University |
Ratnam, Elizabeth | The Australian National University |
Shi, Guodong | The University of Sydney |
Keywords: Networked control systems, Optimization, Agents-based systems
Abstract: This paper presents insights into the implementation of transactive multi-agent systems over decentralized flow networks. Agents have local resource demand and supply and are interconnected through a flow network to support resource sharing while respecting capacity constraints. We establish a competitive market with a pricing mechanism that internalizes flow capacity constraints into agents' decisions. We demonstrate the existence and equivalence of competitive equilibrium and social welfare equilibrium under convexity assumptions. We introduce a social acceptance sharing problem and propose a method to solve it by prescribing socially admissible utility functions. We provide a pedagogical example for linear-quadratic multi-agent systems. Extensive experiments validate our results.
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17:40-18:00, Paper ThC13.6 | |
>Distributed Safety Verification for Multi-Agent Systems |
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Wang, Han | University of Oxford |
Papachristodoulou, Antonis | University of Oxford |
Margellos, Kostas | University of Oxford |
Keywords: Networked control systems, Nonlinear systems, Optimization algorithms
Abstract: The control barrier function (CBF) framework is known to be a powerful tool for safe controller design and safety analysis. Given a dynamical system and a CBF, the system is safe if the CBF-induced constraints are satisfied for every state inside an invariant set, which is a subset of the safe set. We propose a safety verification algorithm for networked nonlinear multi-agent systems. In our proposed algorithm, we independently sample scenarios from the invariant set, and subsequently quantify safety for the multi-agent system by solving a scenario program in a distributed manner. Both the scenario sampling and safety verification algorithms are fully distributed. The efficacy of our algorithms is demonstrated by an example on multi-robot collision avoidance.
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ThC14 |
Roselle Junior 4612 |
Nonlinear System Identification |
Regular Session |
Chair: Maruta, Ichiro | Kyoto University |
Co-Chair: Jha, Mayank Shekhar | University of Lorraine |
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16:00-16:20, Paper ThC14.1 | |
>Out of Distribution Detection Via Domain-Informed Gaussian Process State Space Models |
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Marco, Alonso | University of California Berkeley |
Morley, Elias | University of California, Berkeley |
Tomlin, Claire J. | UC Berkeley |
Keywords: Nonlinear systems identification, Machine learning, Intelligent systems
Abstract: In order for robots to safely navigate in unseen scenarios using learning-based methods, it is important to accurately detect out-of-training-distribution (OoD) situations online. Recently, Gaussian process state-space models (GPSSMs) have proven useful to discriminate unexpected observations by comparing them against probabilistic predictions. However, the capability for the model to correctly distinguish between in- and out-of-training distribution observations hinges on the accuracy of these predictions, primarily affected by the class of functions the GPSSM kernel can represent. In this paper, we propose (i) a novel approach to embed existing domain knowledge in the kernel and (ii) an OoD online runtime monitor, based on receding-horizon predictions. Domain knowledge is provided in the form of a dataset, collected either in simulation or by using a nominal model. Numerical results show that the informed kernel yields better regression quality with smaller datasets, as compared to standard kernel choices. We demonstrate the effectiveness of the OoD monitor on a real quadruped navigating an indoor setting, which reliably classifies previously unseen terrains.
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16:20-16:40, Paper ThC14.2 | |
>Nonlinear Bayesian Identification for Motor Commutation: Applied to Switched Reluctance Motors |
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van Meer, Max | Eindhoven University of Technology |
González, Rodrigo A. | Eindhoven University of Technology |
Witvoet, Gert | TNO Technical Sciences |
Oomen, Tom | Eindhoven University of Technology |
Keywords: Mechatronics, Identification for control, Identification
Abstract: Switched Reluctance Motors (SRMs) enable power-efficient actuation with mechanically simple designs. This paper aims to identify the nonlinear relationship between torque, rotor angle, and currents, to design commutation functions that minimize torque ripple in SRMs. This is achieved by conducting specific closed-loop experiments using purposely imperfect commutation functions and identifying the nonlinear dynamics via Bayesian estimation. A simulation example shows that the presented method is robust to position-dependent disturbances, and experiments suggest that the identification method enables the design of commutation functions that significantly increase performance. The developed approach enables accurate identification of the torque-current-angle relationship in SRMs, without the need for torque sensors, an accurate linear model, or an accurate model of position-dependent disturbances, making it easy to implement in production.
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16:40-17:00, Paper ThC14.3 | |
>Neural Network-Based Nonlinear System Identification for Generating Stochastic Models with Distribution Estimation |
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Yamada, Keito | Kyoto University |
Maruta, Ichiro | Kyoto University |
Fujimoto, Kenji | Kyoto University |
Keywords: Nonlinear systems identification, Neural networks, Subspace methods
Abstract: This paper proposes a nonlinear system identification method for constructing models that provide not only point estimates but also distribution. The method is based on a nonlinear system identification method using the concepts of bottleneck structured neural networks and subspace system identification, and further applies the concept of variational autoencoders. The validity of the proposed method is confirmed through numerical examples.
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17:00-17:20, Paper ThC14.4 | |
>Sparse Neural Networks with Skip-Connections for Identification of Aluminum Electrolysis Cell |
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Lundby, Erlend | NTNU |
Robinson, Haakon | NTNU - Norwegian University of Science and Technology |
Rasheed, Adil | Norwegian University of Science and Technology |
Halvorsen, Ivar Johan | SINTEF Digital |
Gravdahl, Jan Tommy | Norwegian Univ. of Science & Tech |
Keywords: Nonlinear systems identification, Neural networks, Electrochemical processes
Abstract: Neural networks are rapidly gaining interest in nonlinear system identification due to the model's ability to capture complex input-output relations directly from data. However, despite the flexibility of the approach, there are still concerns about the safety of these models in this context, as well as the need for large amounts of potentially expensive data. Aluminum electrolysis is a highly nonlinear production process, and most of the data must be sampled manually, making the sampling process expensive and infrequent. In the case of infrequent measurements of state variables, the accuracy and open-loop stability of the long-term predictions become highly important. Standard neural networks struggle to provide stable long-term predictions with limited training data. In this work, we investigate the effect of combining concatenated skip-connections and the sparsity-promoting ell_1 regularization on the open-loop stability and accuracy of forecasts with short, medium, and long prediction horizons. The case study is conducted on a high-dimensional and nonlinear simulator representing an aluminum electrolysis cell's mass and energy balance. The proposed model structure contains concatenated skip connections from the input layer and all intermittent layers to the output layer, referred to as InputSkip. ell_1 regularized InputSkip is called sparse InputSkip. The results show that sparse InputSkip outperforms dense and sparse standard feedforward neural networks and dense InputSkip regarding open-loop stability and long-term predictive accuracy. The results are significant when models are trained on datasets of all sizes (small, medium, and large training sets) and for all prediction horizons (short, medium, and long prediction horizons.)
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17:20-17:40, Paper ThC14.5 | |
>Redundancy-Aware Physics Informed Neural Networks (R-PINNs) Based Learning of Nonlinear Algebraic Systems with Non-Measurable States |
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Jha, Mayank Shekhar | University of Lorraine |
Garnier, Hugues | University of Lorraine |
Theilliol, Didier | Universite De Lorraine |
Keywords: Nonlinear systems identification, Neural networks, Fault detection
Abstract: The paper presents Redundancy-Aware Physics Informed Neural Networks (R-PINNs) for learning of unknown model parameters of nonlinear algebraic systems in continuous time with non-measurable state variables. R-PINNs accomplish the learning task in presence of non-measurable states of the system by incorporating input-output representation of the textit{a priori} available physics based laws, generally in form of nonlinear differential (partial) equations within the NN based learning procedure, leading to learning of a set of optimal parameters that determine the optimal mapping between input-output data while adhering to the known physics. Analytical Redundancy Relationships (ARRs) are able to express input-output representation of system using solely the measured/known variables by exploring the redundancy within the analytical structure of the system. The paper proposes a methodology that includes ARR derivation and suitable integration within PINNs framework to develop R-PINNs. Mathematically rigorous novel proofs on uniform and ultimate boundedness (UUB) of the output and parametric estimation errors in Lyapunov sense is provided. Finally a DC motor enabled friction drive system based simulation study is presented to demonstrate the effectiveness of the approach.
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17:40-18:00, Paper ThC14.6 | |
>Universal Approximation Property of Hamiltonian Deep Neural Networks |
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Zakwan, Muhammad | EPFL |
d'Angelo, Massimiliano | Sapienza Università Di Roma |
Ferrari-Trecate, Giancarlo | Ecole Polytechnique Fédérale De Lausanne |
Keywords: Neural networks, Machine learning
Abstract: This paper investigates the universal approximation capabilities of Hamiltonian Deep Neural Networks (HDNNs) that arise from the discretization of Hamiltonian Neural Ordinary Differential Equations. Recently, it has been shown that HDNNs enjoy, by design, non-vanishing gradients, which provide numerical stability during training. However, although HDNNs have demonstrated state-of-the- art performance in several applications, a comprehensive study to quantify their expressivity is missing. In this regard, we provide a universal approximation theorem for HDNNs and prove that a portion of the flow of HDNNs can approximate arbitrary well any continuous function over a compact domain. This result provides a solid theoretical foundation for the practical use of HDNNs.
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ThC15 |
Roselle Junior 4611 |
Robust Control II |
Regular Session |
Chair: Chakrabortty, Aranya | North Carolina State University |
Co-Chair: Ebenbauer, Christian | RWTH Aachen University |
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16:00-16:20, Paper ThC15.1 | |
>Game-Theoretic Mixed H2/Hinf Control with Sparsity Constraint for Multi-Agent Control Systems |
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Lian, Feier | North Carolina State University |
Chakrabortty, Aranya | North Carolina State University |
Duel-Hallen, Alexandra | North Carolina State University |
Keywords: Robust control, Optimization algorithms, Game theory
Abstract: A mixed H2 /Hinf control problem under a sparsity constraint is investigated for multi-agent control systems (MAS) to provide robustness against model uncertainty and to reduce the communication cost. First, proximal alternating linearized minimization (PALM) is employed to develop a centralized social optimization algorithm, which is guaranteed to converge to a globally optimal sparse controller. Next, we investigate a noncooperative game that accommodates different control performance criteria of the agents and propose a best-response dynamics algorithm based on PALM. A special case of this game produces a partially distributed social optimization solution. We validate the proposed algorithms using a network with open-loop-unstable nodes and demonstrate superiority of the PALM-based method to a previously investigated sparsity-constrained mixed H2/Hinf controller.
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16:20-16:40, Paper ThC15.2 | |
>A Pontryagin-Based Game-Theoretic Approach for Robust Nonlinear Model Predictive Control |
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Pagone, Michele | Politecnico Di Torino |
Zino, Lorenzo | Politecnico Di Torino |
Novara, Carlo | Politecnico Di Torino |
Keywords: Robust control, Predictive control for nonlinear systems, Game theory
Abstract: A Pontryagin-based differential game approach to solve a class of robust Nonlinear Model Predictive Control is proposed. The methodology defines an optimal control policy that takes into account non-accurate predictions of the system dynamics due to modeling errors and/or unknown exogenous disturbance, which may seriously compromise the controller performances. To this end, we propose a Pontryagin-based solution to the nonlinear min-max problem, which can be viewed as a zero-sum differential game, where the two players are the controlled input and the system's uncertainty/external disturbance. We show that, under suitable assumptions on system's dynamics, the game admits a Nash equilibrium, whose knowledge drastically decreases the high algorithmic complexity usually required for min-max optimization schemes. Finally, the theoretical results are confirmed by numerical simulations, performed on the Van der Pol nonlinear oscillator.
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16:40-17:00, Paper ThC15.3 | |
>Fractional-Order Position Control for the Fully-Actuated Hexa-Rotor: SITL Simulations in the PX4 Firmware |
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Montes de Oca Rebolledo, Andres | Centro De Investigaciones En Optica |
Flores, Alejandro | Centro De Investigaciones En Óptica A.C |
Rakotondrabe, Micky | ENIT Tarbes, INPT, University of Toulouse |
Flores, Gerardo | Center for Research in Optics |
Keywords: Robust control, Stability of nonlinear systems
Abstract: This paper presents a fractional-order controller for the fully-actuated Hexa-rotor under external disturbances applied to the position and attitude dynamics. We proved that the closed-loop system equilibrium point for the positioning subsystem is globally exponentially stable. Furthermore, the controller provides extraordinary robustness to the system when affected by exogenous and aggressive disturbances. The system's stability is also validated through MATLAB and software in the loop simulations. One of the paper's contributions, apart from the control design, is the implementation of the controller in the PX4 firmware, the most popular open-source autopilot code used worldwide for flying drones. The code is available for download and implemented in real drones. Finally, we have implemented the control algorithm in the PX4-firmware alongside a virtual environment in Gazebo and compared it with the standard PX4-firmware controller. The results considerably outperform the traditional PID controller programmed in the PX4 firmware.
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17:00-17:20, Paper ThC15.4 | |
>Parameterized Barrier Functions to Guarantee Safety under Uncertainty |
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Alan, Anil | University of Michigan |
Molnar, Tamas G. | California Institute of Technology |
Ames, Aaron D. | California Institute of Technology |
Orosz, Gabor | University of Michigan |
Keywords: Robust control, Uncertain systems, Lyapunov methods
Abstract: Deploying safety-critical controllers in practice necessitates the ability to modulate uncertainties in control systems. In this context, robust control barrier functions—in a variety of forms—have been used to obtain safety guarantees for uncertain systems. Yet the differing types of uncertainty experienced in practice have resulted in a fractured landscape of robustification—with a variety of instantiations depending on the structure of the uncertainty. This paper proposes a framework for generalizing these variations into a single form: parameterized barrier functions (PBFs), which yield safety guarantees for a wide spectrum of uncertainty types. This leads to controllers that enforce robust safety guarantees while their conservativeness scales by the parameterization. To illustrate the generality of this approach, we show that input-to-state safety (ISSf) is a special case of the PBF framework, whereby improved safety guarantees can be given relative to ISSf.
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17:20-17:40, Paper ThC15.5 | |
>Robust Constraint-Following Control for Uncertain Mechanical Systems with Generalized Udwadia-Kalaba Approach |
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Zhu, Zicheng | National University of Singapore |
Ma, Jun | The Hong Kong University of Science and Technology (Guangzhou) |
Wang, Wenxin | National University of Singapore |
Xian, Yuanjie | Hefei University of Technology |
Sun, Hao | Hefei University of Technology |
Zhao, Han | Hefei University of Technology |
Lee, Tong Heng | National University of Singapore |
Keywords: Robust control, Uncertain systems, Lyapunov methods
Abstract: In this letter, we propose a robust constraint-following control approach for uncertain mechanical systems under both equality and inequality constraints. Particularly, both the global and local inequality constraints are systematically incorporated into the Udwadia-Kalaba (U-K) equation leveraging the diffeomorphism technique, wherein a novel smooth approximation of the local inequality constraints is proposed to address the non-differentiability resulting from its spatiotemporal dependence nature. Based on this development, the generalized U-K equation is mathematically established. With this, we develop a robust constraint-following control strategy to ensure satisfying system performance in the presence of uncertainties and various constraints. Moreover, by Lyapunov minimax approach, the proposed control strategy guarantees both uniform boundedness (UB) and uniform ultimate boundedness (UUB) of the system. Finally, numerical simulations on the lateral motion control of an autonomous vehicle demonstrate the effectiveness of the proposed approach.
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17:40-18:00, Paper ThC15.6 | |
>A Structure Exploiting SDP Solver for Robust Controller Synthesis |
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Gramlich, Dennis | RWTH Aachen |
Holicki, Tobias | University of Stuttgart |
Scherer, Carsten W. | University of Stuttgart |
Ebenbauer, Christian | RWTH Aachen University |
Keywords: Robust control, Uncertain systems, Numerical algorithms
Abstract: In this paper, we revisit structure exploiting SDP solvers dedicated to the solution of Kalman-Yakubovic-Popov semi-definite programs (KYP-SDPs). These SDPs inherit their name from the KYP Lemma and they play a crucial role in e.g. robustness analysis, robust state feedback synthesis, and robust estimator synthesis for uncertain dynamical systems. Off-the-shelve SDP solvers require O(n^6) arithmetic operations per Newton step to solve this class of problems, where n is the state dimension of the dynamical system under consideration. Specialized solvers reduce this complexity to O(n^3). However, existing specialized solvers do not include semi-definite constraints on the Lyapunov matrix, which is necessary for controller synthesis. In this paper, we show how to incorporate such constraints in structure exploiting KYP-SDP solvers.
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ThC16 |
Peony Junior 4512 |
Smart Grid I |
Regular Session |
Chair: Bianchini, Gianni | Università Di Siena |
Co-Chair: Zhang, Hongwei | Harbin Institute of Technology, Shenzhen |
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16:00-16:20, Paper ThC16.1 | |
>Bridging Transient and Steady-State Performance in Voltage Control: A Reinforcement Learning Approach with Safe Gradient Flow |
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Feng, Jie | University of California San Diego |
Cui, Wenqi | University of Washington |
Cortes, Jorge | University of California, San Diego |
Shi, Yuanyuan | University of California San Diego |
Keywords: Smart grid, Decentralized control, Machine learning
Abstract: Deep reinforcement learning approaches are becoming appealing for the design of nonlinear controllers for voltage control problems, but the lack of stability guarantees hinders their real-world deployment. This paper constructs a decentralized RL-based controller for inverter-based real-time voltage control in distribution systems. It features two components: a transient control policy and a steady-state performance optimizer. The transient policy is parameterized as a neural network, and the steady-state optimizer represents the gradient of the long-term operating cost function. The two parts are synthesized through a safe gradient flow framework, which prevents the violation of reactive power capacity constraints. We prove that if the output of the transient controller is bounded and monotonically decreasing with respect to its input, then the closed-loop system is asymptotically stable and converges to the optimal steady-state solution. We demonstrate the effectiveness of our method by conducting experiments with IEEE 13-bus and 123-bus distribution system test feeders.
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16:20-16:40, Paper ThC16.2 | |
>Distributed Robust Secondary Frequency Control of Inverter-Based Microgrids under Time-Varying Communication Delays |
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Gholami, Milad | University of Siena |
Bianchini, Gianni | Università Di Siena |
Vicino, Antonio | Univ. Di Siena |
Keywords: Smart grid, Distributed control, Agents-based systems
Abstract: This paper presents a robust secondary control strategy for frequency synchronization and active power sharing for inverter-based microgrids. The problem is addressed in a multi-agent fashion where the local controllers of the distributed generators play the role of agents, and communication is affected by time-varying delays. The approach is fully distributed and based on a synergic combination of linear consensus and integral sliding-mode control. Lyapunov analysis is presented to assess the stability properties of the closed loop. Delay dependent stability conditions are expressed as a set of linear matrix inequalities whose solution yields appropriate control gains such that frequency restoration is achieved despite delays and active power sharing constraints. Simulations confirm the effectiveness of the proposed control strategy.
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16:40-17:00, Paper ThC16.3 | |
>Resilient Control of DC Microgrids against FDI Attacks on Communication Links |
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Liu, Qifen | Southwest Jiaotong University |
Zhang, Hongwei | Harbin Institute of Technology, Shenzhen |
Keywords: Smart grid, Distributed control, Resilient Control Systems
Abstract: The intrusion of cyber attacks on communication network in microgrids will deteriorate the control performance. And it is even more difficult to effectively extract unknown attacks to obtain correct transmitted information for a direct current (DC) microgrid. In this paper, a resilient controller is designed to mitigate the adverse effects of cyber attacks, where the DC microgrids could restore their control objectives, including current sharing and voltage regulation. Furthermore, the restriction on the number of healthy neighbors is relaxed in this proposed control scheme. The effectiveness of this resilient controller is illustrated by numerical examples.
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17:00-17:20, Paper ThC16.4 | |
>Constraints on OPF Surrogates for Learning Stable Local Volt/Var Controllers |
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Yuan, Zhenyi | University of California, San Diego |
Cavraro, Guido | National Renewable Energy Laboratory |
Cortes, Jorge | University of California, San Diego |
Keywords: Smart grid, Control of networks, Stability of nonlinear systems
Abstract: We consider the problem of learning local Volt/Var controllers in distribution grids (DGs). Our approach starts from learning separable surrogates that take both local voltages and reactive powers as arguments and predict the reactive power setpoints that approximate optimal power flow (OPF) solutions. We propose an incremental control algorithm and identify two different sets of slope conditions on the local surrogates such that the network is collectively steered toward desired configurations asymptotically. Our results reveal the trade-offs between each set of conditions, with coupled voltage-power slope constraints allowing arbitrary shape of surrogate functions but risking limitations on exploiting generation capabilities, and reactive power slope constraints taking full advantage of generation capabilities but constraining the shape of surrogate functions. Simulations on the IEEE 37-bus feeder illustrate their respective advantages in two DG scenarios.
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17:20-17:40, Paper ThC16.5 | |
>Voltage Constrained Heavy Duty Vehicle Electrification: Formulation and Case Study (I) |
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Shukla, Apurv | Texas A&M |
El Helou, Rayan | TAMU |
Xie, Le | Texas A&M University |
Keywords: Smart grid, Modeling, Transportation networks
Abstract: The electrification of heavy-duty vehicles (HDEVs) is a rapidly emerging avenue for decarbonization of energy and transportation sectors. In this paper, we propose the first analytically tractable model that considers the effect of optimally scheduling HDEVs on the power grid. Our model captures the impacts of increased vehicle electrification on the power grid infrastructure, with particular focus on HDEVs. We jointly model transportation and energy networks coupling them through the demand generated for charging requirements of HDEVs. We obtain optimal routing schedules, dispatches satisfying mobility constraints of HDEV while minimizing voltage violation in the power network. We then provide a case-study utilizing a synthetic representation of the 2000-bus Texas transmission grid, realistic representations of multiple distribution grids in Travis county, Texas, as well as transit data pertaining to HDEVs, to uncover the consequences of HDEV electrification, and crystalize the limitations imposed by existing transportation and electric grid infrastructure. We then show how our modeling approach mitigates the introduction of voltage violations in several ways including reduction in the voltage magnitude, geographical dispersion of voltage violations and worst-case voltage violations at critical nodes.
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17:40-18:00, Paper ThC16.6 | |
>Robust Online EV Charging Scheduling with Statistical Feasibility (I) |
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Jiang, Wenqian | The Chinese University of Hong Kong, Shenzhen |
Liang, Jinhao | The Chinese University of Hong Kong, Shenzhen |
Lu, Chenbei | Tsinghua University |
Wu, Chenye | The Chinese University of Hong Kong, Shenzhen |
Keywords: Smart grid, Robust adaptive control, Data driven control
Abstract: With the worldwide adoption of electric vehicles (EVs), charging stations are becoming the bottleneck in delivering high-quality charging service to EVs. Compared to conventional fuel vehicles, EVs require more time to charge at charging stations until their energy requirements are fulfilled. Furthermore, the distribution network capacities frequently limit charging resources at a charging station. As a result, charging station operators must optimize EVs' charging scheduling and allocate the limited charging resources efficiently. Due to the high uncertainty of future EVs' arrival and charging demands, station operators typically schedule the arrived EVs' charging solely based on the charging requirements of these EVs, while disregarding future arrivals. Such a scheduling policy is simple to implement, but it may result in high service drop rate, particularly for charging stations with high occupancy levels. To that end, we develop an EV charging schedule model that includes a reserved charging rate, as well as a robust sample-based approach that incorporates the concept of statistical feasibility to help minimize the service drop rate. Numerical studies further verify the effectiveness of our suggested method.
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ThC17 |
Peony Junior 4511 |
Iterative Learning Control II |
Regular Session |
Chair: Rogers, Eric | University of Southampton |
Co-Chair: Kong, Zhaodan | University of California, Davis |
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16:00-16:20, Paper ThC17.1 | |
>Monotonic Model Improvement Self-Play Algorithm for Adversarial Games |
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Thathigari, Poorna Syama Sundar | Indian Institute of Technology Tirupati |
Vasam, Manjunath | Indian Institute of Technology Tirupati |
Joseph, Ajin George | Indian Institute of Technology Tirupati |
Keywords: Iterative learning control, Optimal control, Discrete event systems
Abstract: The problem of solving strategy games has intrigued the scientific community for centuries. In this paper, we consider two-player adversarial zero-sum symmetric games with zero information loss. Here, both players are continuously attempting to make decisions that will change the current game state to his/her advantage and hence the gains of one player are always equal to the losses of the other player. In this paper, we propose a model improvement self-play algorithm, where the agent iteratively switches roles to subdue the current adversary strategy. This monotonic improvement sequence leads to the ultimate development of a monolithic, competent absolute no-loss policy for the game environment. This tactic is the first of its kind in the setting of two-player adversarial games. Our approach could perform competitively and sometimes expertly in games such as 4x4 tic-tac-toe, 5x5 domineering, cram, and dots & boxes with a minimum number of moves.
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16:20-16:40, Paper ThC17.2 | |
>Repetitive Process Based Higher-Order Iterative Learning Control Law Design |
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Maniarski, Robert | University of Zielona Góra |
Paszke, Wojciech | University of Zielona Gora |
Chu, Bing | University of Southampton |
Rogers, Eric | University of Southampton |
Keywords: Iterative learning control, Stability of linear systems, LMIs
Abstract: This paper uses the repetitive process setting to develop new results on the design of higher-order learning control laws. The basic idea of higher-order iterative learning control is to use information from a finite number of previous trials instead of just the last trial to update the control input for application on the subsequent trial, with the primary objective of improving the error convergence performance. The sufficient conditions ensuring the convergence of the resulting control scheme are established with repetitive process setting and utilizing non-unit memory repetitive process models. Also, the corresponding control law gains are derived from a set of linear matrix inequality constraints. Finally, an example is used to demonstrate the properties of the new design.
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16:40-17:00, Paper ThC17.3 | |
>Iterative Learning Control of Discrete Systems with Actuator Backlash Using a Weighted Sum of Previous Trial Control Signals |
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Pakshin, Pavel | Arzamas Polytechnic Institute of R.E. Alekseev Nizhny Novgorod S |
Emelianova, Julia | Arzamas Polytechnic Institute of R.E. Alekseev NizhnyNovgorod St |
Rogers, Eric | University of Southampton |
Galkowski, Krzysztof | Univ. of Zielona Gora |
Keywords: Iterative learning control
Abstract: This paper considers iterative learning control design for discrete dynamics in the presence of backlash in the actuators. A new control design for this problem is developed based on the stability theory for nonlinear repetitive processes. An example demonstrates the effectiveness of the new design where the system model is constructed from data collected from frequency response tests on a physical system.
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17:00-17:20, Paper ThC17.4 | |
>Iterative Learning Embedded Model Reference Adaptive Control for Perturbed Nonlinear MIMO Systems |
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Zhang, Heng | ShanghaiTech University |
Zhang, Qilong | ShanghaiTech University |
Liu, Song | ShanghaiTech University |
Wang, Yang | Shanghai Technology Unversity |
Keywords: Iterative learning control, Adaptive control, Uncertain systems
Abstract: This paper presents a novel adaptive iterative learning control (ILC) framework for achieving high-performance trajectory tracking in uncertain nonlinear systems perturbed by external disturbances. The proposed scheme, referred to as IL-MRAC, combines two components inspired by indirect ILC and classical model reference adaptive control (MRAC), respectively. The key idea behind the proposed scheme is to first develop an input signal for a stabilized nominal model of the plant in ILC-loop, then inject the signal into the MRAC-Loop as the reference signal. This bypasses the unrealistic identical initialization condition required by conventional ILC methods and ingeniously transfers the problems brought by the initial errors, model uncertainties, and external disturbances to a powerful adaptive controller and handled in the time domain. Meanwhile, by including the well-trained inputs obtained in the iteration domain as reference signals, the adaptive controller gains the ability to directly track the desired trajectory. The convergence of the scheme is rigorously proven, and numerical examples and high-fidelity simulations demonstrate its effectiveness and superiority.
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17:20-17:40, Paper ThC17.5 | |
>Efficient Re-Synthesis of Control Barrier Function Via Safe Exploration (I) |
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Zehfroosh, Ashkan | University of California Davis |
Kong, Zhaodan | University of California, Davis |
Vougioukas, Stavros | University of California, Davis |
Keywords: Lyapunov methods, Optimal control, Iterative learning control
Abstract: This paper presents an efficient approach to incremental learning and updating of a valid control barrier function (CBF) so that it renders new explored safe area as its safe zone. For that purpose, we assume having access to sensor information (e.g. LiDAR sensor) that enables us to predict if a given location is immediately unsafe (e.g. close to a obstacle) or not. Using the sensor information, a set of predicted explorations over the potential safe regions is generated. The exploration data is then used to learn a valid CBF with enlarged safe zone. Toward this goal, we propose two methods: the first one is less conservative, as it possibly ends up with a larger safe zone, but it relies on a nonlinear optimization problem. A more computationally efficient alternative only requires Linear Programming at the cost of being more conservative.
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17:40-18:00, Paper ThC17.6 | |
>Reinforcement Learning for Stochastic Max-Plus Linear Systems |
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Subramanian, Vignesh | Georgia Institute of Technology |
Farhadi, Farzaneh | Newcastle University |
Soudjani, Sadegh | Newcastle University |
Keywords: Discrete event systems, Stochastic systems, Iterative learning control
Abstract: This paper studies the design of control policies for Discrete Event Systems under uncertainties. We capture the timing of the events using the framework of max-plus-linear systems in which the time between consecutive events depends on random delays with unknown distributions. Our policy synthesis approach is with respect to a cost function, and it can be extended directly to satisfy safety specifications on the timing of events. The main novelty of our approach is to translate the system evolution to a Markov decision process (MDP) that has an uncountable state space and develop a stochastic optimisation problem under the evolution of the MDP. To tackle the unknown distribution of uncertainties (thus unknown transition probabilities in the MDP), we employ model-free reinforcement learning to perform optimisations and find control policies for the system. Our implementation results on the 9-dimensional model of a railway network show superiority of our learning approach in comparison with the stochastic model predictive control approach.
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ThC18 |
Peony Junior 4412 |
Stability of Nonlinear Systems II |
Regular Session |
Chair: Susca, Mircea | Technical University of Cluj-Napoca |
Co-Chair: van den Eijnden, Sebastiaan | Eindhoven University of Technology |
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16:00-16:20, Paper ThC18.1 | |
>Locally Homogeneous Finite-Time Stabilization of Quasi-Linear Systems |
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Ayamou, Mericel | Univ. Lille |
Polyakov, Andrey | Inria, Univ. Lille |
Espitia, Nicolas | CRIStAL, CNRS |
Keywords: Stability of nonlinear systems, Lyapunov methods, Constrained control
Abstract: In this paper, an algorithm of a local finite-time control design is developed for a class of quasi-linear systems. The design procedure is essentially based on the concept of generalized homogeneity and the convex embedding technique. The adjustment of control parameters is realized by solving a system of linear matrix inequalities (LMIs). Theoretical results are supported by numerical simulations.
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16:20-16:40, Paper ThC18.2 | |
>Small Gain Theorems for Infinite Networks of Discontinuous Dynamical Systems and Applications |
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Pavlichkov, Svyatoslav | Technical University of Kaiserslautern |
Bajcinca, Naim | University of Kaiserslautern |
Keywords: Stability of nonlinear systems, Lyapunov methods, Decentralized control
Abstract: We prove two small gain theorems for uniform asymptotic, uniform finite-time and uniform fixed-time stability of infinite networks of interconnected nonlinear systems with discontinuous right-hand sides. Their applicability to decentralized control problems is demonstrated on an example of infinite networks of mechanical systems described by lower-triangular form systems with discontinuous dynamics and power integrators.
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16:40-17:00, Paper ThC18.3 | |
>Robust Finite-Time Stabilization of Stochastic Parabolic PDE Systems Via Non-Fragile Spatial Sampled-Data Control |
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Hu, Xiaofang | China University of Geosciences |
Song, Feida | China University of Geosciences, School of Automation |
Wang, Leimin | China University of Geosciences |
Keywords: Stability of nonlinear systems, Lyapunov methods, Delay systems
Abstract: This paper addresses the robust finite-time stabilization (FTS) issue for stochastic parabolic PDE systems via non-fragile spatial sampled-data control scheme. First, a class of distributed parameter systems characterized by the delayed stochastic parabolic partial differential equation is developed for analyzing the effects of stochastic disturbance, structural uncertainty, and discrete delay on the system performance. Then, a non-fragile spatial sampled-data control scheme is established by setting sampling points in the spatial domain, which effectively saves communication resources and ensures that the closed-loop system maintains good performance when the controller is perturbed. Moreover, based on the partial differential equation theory, stochastic analysis approach, and the extended Wirtinger's inequality technique, several criteria are provided to ensure the robust FTS of stochastic parabolic PDE systems in the mean square sense. Lastly, a numerical example is provided to verify the feasibility of the suggested stabilization criteria and control scheme.
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17:00-17:20, Paper ThC18.4 | |
>On an Integral Variant of Incremental Input/Output-To-State Stability and Its Use As a Notion of Nonlinear Detectability |
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Schiller, Julian D. | Leibniz University Hannover |
Müller, Matthias A. | Leibniz University Hannover |
Keywords: Stability of nonlinear systems, Lyapunov methods, Estimation
Abstract: We propose a time-discounted integral variant of incremental input/output-to-state stability (i-iIOSS) together with an equivalent Lyapunov function characterization. Continuity of the i-iIOSS Lyapunov function is ensured if the system satisfies a certain continuity assumption involving the Osgood condition. We show that the proposed i-iIOSS notion is a necessary condition for the existence of a robustly globally asymptotically stable observer mapping in a time-discounted “L^2-to-L^infty” sense. In combination, our results provide a general framework for a Lyapunov-based robust stability analysis of observers in continuous time, which in particular is crucial for the use of optimization-based state estimators (such as moving horizon estimation).
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17:20-17:40, Paper ThC18.5 | |
>Projection-Based Controllers with Inherent Dissipativity Properties |
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Chu, Hoang | Eindhoven University of Technology |
van den Eijnden, Sebastiaan | Eindhoven University of Technology |
Heemels, W.P.M.H. | Eindhoven University of Technology |
Keywords: Stability of nonlinear systems, Lyapunov methods, Hybrid systems
Abstract: Projection-based Controllers (PBCs) are currently gaining traction in both scientific and engineering communities. In PBCs, the input-output signals of the controller are kept in sector-bounded sets by means of projection. In this paper, we will show how this projection operation can be used to induce useful passivity or general dissipativity properties for broad classes of (unprojected) nonlinear controllers that otherwise would not have these properties. The induced dissipativity properties of PBC will be exploited to guarantee asymptotic stability of negative feedback interconnections of passive nonlinear plants and suitably designed PBC, under mild conditions. Generalizations to so-called (q,s,r)-dissipativity will be presented as well. To illustrate the effectiveness of PBC control design via these passivity-based techniques, one numerical example is provided.
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17:40-18:00, Paper ThC18.6 | |
>Maximizing the Exponential Decay Rate for Finite Dimensional Bilinear Systems Using Passivity-Based Controllers |
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Mihaly, Vlad Mihai | Technical University of Cluj-Napoca |
Susca, Mircea | Technical University of Cluj-Napoca |
Dobra, Petru | Technical University of Cluj |
Keywords: Stability of nonlinear systems, Lyapunov methods, LMIs
Abstract: Passivity-based controllers which ensure the asymptotic stability of the closed-loop system can be developed with the aid of the Krasovskii passivity notion. However, there are no available design procedures to impose a set of performances. The main focus of the current paper is to formulate an optimization problem whose solution provides the parameters of a Krasovskii passivity-based controller (K-PBC) which ensures local exponential stability with a maximized lower bound of the decay rate. After a convexification procedure we obtain a linear programming problem with linear matrix inequality constraints. The numerical example underlines the advantage of the proposed method by emphasizing the difference between an optimized and a default controller obtained without optimization.
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ThC19 |
Peony Junior 4411 |
Predictive Control for Linear Systems I |
Regular Session |
Chair: Werner, Herbert | Hamburg University of Technology |
Co-Chair: Shu, Zhan | University of Alberta |
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16:00-16:20, Paper ThC19.1 | |
>On Stability Analysis of Predictive Flocking Using N-Paths |
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Hastedt, Philipp | Hamburg University of Technology |
Werner, Herbert | Hamburg University of Technology |
Keywords: Predictive control for linear systems, Agents-based systems, Distributed control
Abstract: Most publications in the field of model predictive flocking (MPF) present frameworks without providing stability analyses for the proposed schemes. In those providing stability results, one specific line of reasoning is based on the geometric properties of the optimal state sequences, so-called N-paths. This method is used in several publications to show stability for centralized and distributed MPF schemes. In this paper, we critically discuss this line of reasoning and point out several errors in the N-path-based analysis. As incorrect statements in assumptions and lemmas cause the lines of reasoning to break, this raises the question of whether the N-path-based line of reasoning is suitable for the MPF stability analysis in general.
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16:20-16:40, Paper ThC19.2 | |
>On Complexity Reduction in a Variable Terminal Set Setpoint-Tracking MPC Scheme |
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Gheorghe, Bogdan | University Politehnica of Bucharest |
Stoican, Florin | Universitatea Nationala De Stiinta Si Tehnologie POLITEHNICA BUC |
Prodan, Ionela | Grenoble Institute of Technology (Grenoble INP) - Esisar |
Keywords: Predictive control for linear systems, Algebraic/geometric methods, Numerical algorithms
Abstract: We applied and adapted the linear encodings from [1] to the feasible-reference tracking model predictive control (MPC) formulation from [2] to reduce its computational cost. The improvements come from avoiding to explicitly use the vertex-based representation of the variable terminal set in testing its inclusion in the constraint set. We considered both polytopic and zonotopic formulations. For the later we have also proposed a positive invariant (PI) zonotopic approximation of the maximal PI set.
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16:40-17:00, Paper ThC19.3 | |
>A Software Package for MPC Design and Tuning: MPT+ |
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Holaza, Juraj | Slovak University of Technology in Bratislava |
Galčíková, Lenka | Faculty of Chemical and Food Technology, Slovak University of Te |
Oravec, Juraj | Slovak University of Technology in Bratislava |
Kvasnica, Michal | Slovak University of Technology in Bratislava |
Keywords: Predictive control for linear systems, Control software, Robust control
Abstract: The industrial implementation of the model predictive control (MPC) is driven by the necessity to design, tune, and validate the constructed control policy. We present a novel software toolbox for advanced model predictive control (MPC) design extending the Multi-Parametric toolbox (MPT). Particularly, MPTplus introduces several advanced MPC controller design methods, including memory-efficient explicit Tube MPC design, Tube MPC controller with the limited rate of control actions, and a polynomial approximation of the 1-, Inf-norm-based explicit control law. The benefits of the proposed toolbox are demonstrated using the both, numerical simulations and the laboratory implementation on the device with a fast dynamics.
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17:00-17:20, Paper ThC19.4 | |
>Hybrid Cost Function Distributed MPC for Vehicle Platoons with Stability and String Stability Properties |
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Pauca, Ovidiu | Faculty of Automatic Control and Computer Engineering, “Gheorghe |
Lazar, Mircea | Eindhoven University of Technology |
Caruntu, Constantin F. | Gheorghe Asachi Technical University of Iasi |
Keywords: Predictive control for linear systems, Cooperative control, Autonomous vehicles
Abstract: Distributed MPC schemes for control of vehicle platoons typically employ a p-norms-based cost function to achieve stability and string stability. Quadratic cost functions yield smoother trajectories, but they are not aligned with string stability conditions. Hence, in this paper, we develop distributed MPC controllers for vehicle platoons based on a hybrid cost function, which combines infinity norms and quadratic forms. Sufficient conditions for global platoon stability and leader-follower string stability are derived for the developed hybrid cost function and applied to lateral dynamics control. Simulation results show that the hybrid cost function yields lateral position errors that are 10 times smaller (for the maximum error) compared with an infinity norms-based cost function.
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17:20-17:40, Paper ThC19.5 | |
>Distributed Source Seeking Using a Bi-Level Distributed Model Predictive Control Algorithm |
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Gao, Xinzhou | University of Alberta |
Shu, Zhan | University of Alberta |
Keywords: Predictive control for linear systems, Distributed control, Cooperative control
Abstract: This paper presents a novel distributed source seeking algorithm, called Bi-Level Distributed Model Predictive Control (BLMPC), to locate the source using a group of agents. During the process, the source emits a signal that the agents use to guide their movements, and the agents utilize the signal collaboratively with BLMPC to generate continuous estimation of the source location and move accordingly. BLMPC employs a bi-level structure involving an upper distributed optimization level to estimate the source location and a lower MPC level to control the agents with time-varying goals. This structure ensures that the formation center of agents converges to a small neighborhood around the signal source's location theoretically. The effectiveness of the proposed approach is illustrated by simulations.
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17:40-18:00, Paper ThC19.6 | |
>Robust Closed-Loop State Predictor for Unstable Systems with Input Delay |
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Nikiforov, Vladimir O. | ITMO University |
Gerasimov, Dmitry | ITMO University |
Keywords: Predictive control for linear systems, Linear systems, Robust control
Abstract: The paper addresses the problem of the safe implementation of a state predictor used for stabilization of linear time-invariant systems with input delay. To this end, we design an observer generating an estimate of the state prediction error, i.e., the estimate of the difference between the inaccessible true state prediction and the state prediction estimate elaborated by a state predictor. This estimate is used as feedback in the closed-loop state predictor. The robustness of the proposed closed-loop predictor with respect to parametric perturbations is proved and illustrated by simulation results. Robustness with respect to approximation errors caused by limited accuracy of a numerical solver is discussed and illustrated by simulation results.
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ThC20 |
Orchid Junior 4312 |
Robotics and Nonholonomic Systems |
Regular Session |
Chair: Schenato, Luca | University of Padova |
Co-Chair: Anahory Simões, Alexandre | IE University |
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16:00-16:20, Paper ThC20.1 | |
>Visibility-Constrained Control of Multirotor Via Reference Governor |
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Kim, Dabin | Seoul National University |
Pezzutto, Matthias | Université Libre De Bruxelles |
Schenato, Luca | University of Padova |
Kim, H. Jin | Seoul National University |
Keywords: Robotics, Vision-based control, Autonomous robots
Abstract: For safe vision-based control applications, perception-related constraints have to be satisfied in addition to other state constraints. In this paper, we deal with the problem where a multirotor equipped with a camera needs to maintain the visibility of a point of interest while tracking a reference given by a high-level planner. We devise a method based on reference governor that, differently from existing solutions, is able to enforce control-level visibility constraints with theoretically assured feasibility. To this end, we design a new type of reference governor for linear systems with polynomial constraints which is capable of handling time-varying references. The proposed solution is implemented online for the real-time multirotor control with visibility constraints and validated with simulations and an actual hardware experiment.
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16:20-16:40, Paper ThC20.2 | |
>Safe Control of Euler-Lagrange Systems with Limited Model Information |
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Wang, Yujie | University of Wisconsin-Madison |
Xu, Xiangru | University of Wisconsin-Madison |
Keywords: Robotics, Constrained control, Nonlinear systems
Abstract: This work presents a new safe control framework for Euler-Lagrange (EL) systems with limited model information, external disturbances, and measurement uncertainties. The EL system is decomposed into two subsystems called the proxy subsystem and the virtual tracking subsystem. An adaptive safe controller based on barrier Lyapunov functions is designed for the virtual tracking subsystem to ensure the boundedness of the safe velocity tracking error, and a safe controller based on control barrier functions is designed for the proxy subsystem to ensure controlled invariance of the safe set defined either in the joint space or task space. Theorems that guarantee the safety of the proposed controllers are provided. In contrast to existing safe control strategies for EL systems, the proposed method requires much less model information and can ensure safety rather than input-to-state safety. Simulation results are provided to illustrate the effectiveness of the proposed method.
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16:40-17:00, Paper ThC20.3 | |
>An Embedded MPC for High-Speed Trajectory Tracking of Piezoelectric Actuators with Implementation on an ARM Microprocessor |
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Dong, Fei | Beihang University |
Zuo, Wenguang | Beihang University |
Xie, Hongyang | Beihang University |
Wang, Xinyu | Beihang University |
Hu, Qinglei | Beihang University |
Keywords: Predictive control for linear systems, Mechatronics, MEMs and Nano systems
Abstract: This work studies the problem of high-speed trajectory tracking for a piezoelectric actuator (PEA) subject to constraints on both the displacement output and control input via a resource-limited embedded processor. To ensure tracking performance, an extremely high control frequency of 10kHz is recommended. In response, we propose an embedded model predictive control (MPC) algorithm and deploy it on a low-cost STM32F407 ARM microprocessor operating at 168MHz. Specifically, a fast coordinate ascent algorithm is designed to online solve the constrained quadratic programming (QP) problem derived from the MPC, and a delayed Kalman filter (KF) is introduced to compensate for the computation latency. Through hardware-in-the-loop (HIL) simulations, we demonstrate the feasibility and effectiveness of our embedded MPC algorithm.
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17:00-17:20, Paper ThC20.4 | |
>A Delta-Persistently-Exciting Formation Controller for Non-Holonomic Systems Over Directed Graphs |
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Dutta, Maitreyee | IIT Bombay |
Loria, Antonio | CNRS |
Panteley, Elena | CNRS |
Srikant, Sukumar | Indian Institute of Technology Bombay |
Nuño, Emmanuel | University of Guadalajara |
Keywords: Nonholonomic systems, Lyapunov methods, Distributed control
Abstract: We study a formation control problem of nonholonomic vehicles which consists in making a group of them gather around a given rendezvous set-point and acquire a common orientation. This task may be regarded as part of a more complex maneuver, e.g., requiring the robots to advance in a scouting mission on a path composed of straight lines and occasional turns. The control approach relies on addressing separately the problems of stabilization (on the plane) and of orientation consensus. For the former we use individual controllers involving smooth time-varying terms and for the latter we use distributed consensus control, under the assumption that the robots form a directed graph that contains a spanning tree.
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17:20-17:40, Paper ThC20.5 | |
>Hamel Equations and Quasivelocities for Nonholonomic Systems with Inequality Constraints |
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Anahory Simões, Alexandre | IE University |
Colombo, Leonardo Jesus | Spanish National Research Council |
Keywords: Nonholonomic systems, Variational methods
Abstract: In this paper we derive Hamel equations for the motion of nonholonomic systems subject to inequality constraints in quasivelocities. As examples, the vertical rolling disk hitting a wall and the Chaplygin sleigh with a knife edge constraint hitting a circular table are shown to illustrate the theoretical results.
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17:40-18:00, Paper ThC20.6 | |
>Circumnavigation Control of Non-Holonomic Vehicle System with Distance-Rate Measurements (I) |
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Zou, Yao | University of Science and Technology Beijing |
Zhong, Liangyin | University of Science and Technology Beijing |
Zhu, Bing | Beihang University |
Sun, Liang | University of Science and Technology Beijing |
He, Wei | University of Science and Technology Beijing |
Keywords: Nonholonomic systems
Abstract: This article studies the circumnavigation problem of a non-holonomic vehicle independent of the global coordinate. Specifically, the vehicle circumnavigates an unknown stationary target with anticipated distance and velocity. However, the position information (i.e., absolute position and positive position) is not available to the vehicle. Instead, the vehicle can just obtain the distance rate relative to the target. We propose a generic continuous and bounded control algorithm based on only the distance-rate measurement. It is demonstrated using Poincar´e-Bendixon Criterion that the proposed control algorithm in this article ensures the asymptotically stable circumnavigation. Simulation is finally given to verify the effectiveness of the proposed control algorithm.
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ThC21 |
Orchid Junior 4311 |
Predictive Control for Nonlinear Systems III |
Regular Session |
Chair: Dimarogonas, Dimos V. | KTH Royal Institute of Technology |
Co-Chair: Zhang, Lixian | Harbin Institute of Technology |
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16:00-16:20, Paper ThC21.1 | |
>Transient Performance of MPC for Tracking |
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Koehler, Matthias | University of Stuttgart |
Kruegel, Lisa | University of Bayreuth |
Gruene, Lars | University of Bayreuth |
Müller, Matthias A. | Leibniz University Hannover |
Allgöwer, Frank | University of Stuttgart |
Keywords: Predictive control for nonlinear systems
Abstract: We analyse the closed-loop performance of a model predictive control (MPC) for tracking formulation with artificial references. It has been shown that such a scheme guarantees closed-loop stability and recursive feasibility for any externally supplied reference, even if it is unreachable or time-varying. The basic idea is to consider an artificial reference as an additional decision variable and to formulate generalised terminal ingredients with respect to it. In addition, its offset is penalised in the MPC optimisation problem, leading to closed-loop convergence to the best reachable reference. In this letter, we provide a transient performance bound on the closed loop using MPC for tracking. We employ mild assumptions on the offset cost and scale it with the prediction horizon. In this case, an increasing horizon in MPC for tracking recovers the infinite horizon optimal solution.
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16:20-16:40, Paper ThC21.2 | |
>Stability Analysis of Nonlinear Model Predictive Control with Progressive Tightening of Stage Costs and Constraints |
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Baumgärtner, Katrin | University of Freiburg |
Zanelli, Andrea | ETH Zurich |
Diehl, Moritz | University of Freiburg |
Keywords: Predictive control for nonlinear systems, Stability of nonlinear systems, Optimal control
Abstract: We consider a stage-varying nonlinear model predictive control (NMPC) formulation and provide a stability result for the corresponding closed-loop system under the assumption that cost and constraints are progressively tightening. We illustrate the generality of the stage-varying formulation pointing out various approaches proposed in the literature that can be cast as stage-varying and progressively tightening optimal control problems.
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16:40-17:00, Paper ThC21.3 | |
>Corridor MPC for Multi-Agent Inspection of Orbiting Structures |
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Marchesini, Gregorio | KTH Royal Institute of Technology |
Roque, Pedro | KTH Royal Institute of Technology |
Dimarogonas, Dimos V. | KTH Royal Institute of Technology |
Keywords: Predictive control for nonlinear systems, Sampled-data control, Aerospace
Abstract: In this work, we propose an extension of the previously introduced Corridor Model Predictive Control scheme for high-order and distributed systems, with an application for on-orbit inspection. To this end, we leverage high order control barrier function (HOCBF) constraints as a suitable control approach to maintain each agent in the formation within a safe corridor from its reference trajectory. The recursive feasibility of the designed MPC scheme is tested numerically, while suitable modifications of the classical HOCBF constraint definition are introduced such that safety is guaranteed both in sampled and continuous time. The designed controller is validated through computer simulation in a realistic inspection scenario of the International Space Station.
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17:00-17:20, Paper ThC21.4 | |
>Asynchronous Fuzzy Control for a Class of Constrained Fuzzy Stochastic Switching Systems Via Bumpless MPC (I) |
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Li, Bo | Harbin Institute of Technology |
Weng, Rui | Harbin Institute of Technology |
Cai, Bo | Harbin Institute of Technology |
Keywords: Predictive control for nonlinear systems, Switched systems, Markov processes
Abstract: This paper addresses the problem of bumpless stabilization for a class of T-S fuzzy hidden Markovian jump systems with bounded inputs and states. The asynchronous scenario between the real mode and the observed one under consideration is described by hidden Markovian chains. Moreover, the stabilizing controller dependent on both the fuzzy rule and the observed mode is constructed. By virtue of the bumpless model predictive control, the controller not only maintains the system within constraints but also reduces excessive bumps of system states in switching instants. Then, relying on the stochastic stability criteria, a numerically attainable receding horizon optimization problem is established to obtain the recursive feasible and stabilizing controller with the smooth evolution of states by introducing some mathematical techniques. Finally, demonstrating the validity and potential of the developed control strategy is achieved through the presentation of a numerical example.
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17:20-17:40, Paper ThC21.5 | |
>Transition-Dependent Robust MPC for Stochastic Switched Systems (I) |
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Wu, Tong | Harbin Institute of Technology |
Zhu, Yimin | Harbin Institute of Technology |
Yang, Jianan | Harbin Institute of Technology |
Han, Yuejiang | Harbin Institute of Technology |
Zhang, Lixian | Harbin Institute of Technology |
Keywords: Switched systems, Predictive control for nonlinear systems, Stochastic optimal control
Abstract: This study is concerned with the robust MPC for discrete-time stochastic switched systems subject to constraints on states and control inputs. Aiming at achieving optimal control synthesis under the requirement of bumpless transfer control (BTC), the min-max MPC formulation is extended to the transition-dependent paradigm, and a weighted performance index is optimized in the receding horizon, such that the abrupt variation in feedback gains can be mitigated. Meanwhile, a class of more general stochastic switching signals is considered, where the sojourn time may follow any distribution, and the recursive feasibility and mean-square stability are theoretically guaranteed. Compared with existing studies on switched MPC or BTC, this work avoids the assumption of the Markov property on mode switching and reduces conservatism by exploiting the statistical information of sojourn time. An illustrative example is provided to show the potential of the obtained results.
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17:40-18:00, Paper ThC21.6 | |
>Obstacle Avoidance in Dynamic Environments Via Tunnel-Following MPC with Adaptive Guiding Vector Fields |
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Dahlin, Albin | Chalmers University of Technology |
Karayiannidis, Yiannis | Lund University |
Keywords: Robotics, Predictive control for nonlinear systems, Constrained control
Abstract: This paper proposes a motion control scheme for robots operating in a dynamic environment with concave obstacles. A Model Predictive Controller (MPC) is constructed to drive the robot towards a goal position while ensuring collision avoidance without direct use of obstacle information in the optimization problem. This is achieved by guaranteeing tracking performance of an appropriately designed receding horizon path. The path is computed using a guiding vector field defined in a subspace of the free workspace where each point in the subspace satisfies a criteria for minimum distance to all obstacles. The effectiveness of the control scheme is illustrated by means of simulation.
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ThC22 |
Orchid Junior 4212 |
Stochastic Systems III |
Regular Session |
Chair: Xue, Bai | Institute of Software, Chinese Academy of Sciences |
Co-Chair: Hoshino, Kenta | Kyoto University |
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16:00-16:20, Paper ThC22.1 | |
>Adaptive Identification under Saturated Output Observations with Possibly Correlated and Unbounded Input Signals |
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Zhang, Lantian | Academy of Mathematics and Systems Science, Chinese Academy of S |
Guo, Lei | Academy of Mathematics and Systems Science, Chinese Academy of S |
Keywords: Stochastic systems, Nonlinear systems identification, Adaptive systems
Abstract: In this work, we consider adaptive identification and prediction problems for stochastic dynamical systems with saturated output observations, which arise from various problems in science and technology as well as in social and economic systems. A new adaptive algorithm is introduced, which avoids the projection operators used in the related existing work. More importantly, unlike most previous works that require independent and identically distributed conditions as well as bounded conditions on system signals, it is shown that the global convergence of the average regret and strong consistency of the parameter estimates can be established under possibly unbounded, correlated, and non-stationary signal conditions. A numerical example is also given to illustrate the effectiveness of the proposed adaptive algorithm.
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16:20-16:40, Paper ThC22.2 | |
>Input-To-State Stability in Probability |
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Culbertson, Preston | Caltech |
Cosner, Ryan | California Institute of Technology |
Tucker, Maegan | California Institute of Technology |
Ames, Aaron D. | California Institute of Technology |
Keywords: Stochastic systems, Stability of nonlinear systems, Robotics
Abstract: Input-to-State Stability (ISS) is fundamental in mathematically quantifying how stability degrades in the presence of bounded disturbances. If a system is ISS, its trajectories will remain bounded, and will converge to a neighborhood of an equilibrium of the undisturbed system. This graceful degradation of stability in the presence of disturbances describes a variety of real-world control implementations. Despite its utility, this property requires the disturbance to be bounded and provides invariance and stability guarantees only with respect to this worst-case bound. In this work, we introduce the concept of ``ISS in probability (ISSp)'' which generalizes ISS to discrete-time systems subject to unbounded stochastic disturbances. Using tools from martingale theory, we provide Lyapunov conditions for a system to be exponentially ISSp, and connect ISSp to stochastic stability conditions found in literature. We exemplify the utility of this method through its application to a bipedal robot confronted with step heights sampled from a truncated Gaussian distribution.
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16:40-17:00, Paper ThC22.3 | |
>Safe Probabilistic Invariance Verification for Stochastic Discrete-Time Dynamical Systems |
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Yu, Yiqing | Department of Information Science, School of Mathematical Scienc |
Wu, Taoran | Institute of Software CAS |
Xia, Bican | Peking University, China |
Wang, Ji | National University of Defense Technology |
Xue, Bai | Institute of Software, Chinese Academy of Sciences |
Keywords: Stochastic systems, Stability of nonlinear systems
Abstract: Ensuring safety through set invariance has proven a useful method in a variety of applications in robotics and control. In this paper, we focus on the safe probabilistic invariance verification problem for discrete-time dynamical systems subject to stochastic disturbances over the infinite time horizon. Our goal is to compute the lower and upper bounds of the liveness probability for a given safe set and set of initial states. This probability represents the likelihood that the system will remain within the safe set for all time. To address this problem, we draw inspiration from stochastic barrier certificates for safety verification and build upon the findings in cite{xue2021reach}, where an equation was presented for exact probability analysis. We present two sets of optimizations and demonstrate their effectiveness through two examples, using semi-definite programming tools.
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17:00-17:20, Paper ThC22.4 | |
>Stochastic Approximation for Nonlinear Discrete Stochastic Control: Finite-Sample Bounds for Exponentially Stable Systems |
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Nguyen, Huy Hoang | Georgia Institute of Technology |
Maguluri, Siva Theja | Georgia Institute of Technology |
Keywords: Stochastic systems, Optimization, Lyapunov methods
Abstract: We consider a nonlinear discrete stochastic control system, and our goal is to design a feedback control policy in order to lead the system to a prespecified state. We adopt a stochastic approximation viewpoint of this problem. It is known that by solving the corresponding continuous-time deterministic system, and using the resulting feedback control policy, one ensures almost sure convergence to the prespecified state in the discrete system. In this paper, we adopt such a control mechanism and provide its finite-sample convergence bounds whenever a Lyapunov function is known for the continuous system. In particular, we establish the rate Obr{1/varepsilon} to guarantee that the mean square error is less than varepsilon where the Lyapunov function for the continuous system is non-smooth and gives exponential rates. Our proof relies on constructing a Lyapunov function for the discrete system based on the given Lyapunov function for the continuous system, and then appropriately smoothing the given function using the Moreau envelope. We present a numerical experiment in the selector control example to validate the established rate.
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17:20-17:40, Paper ThC22.5 | |
>First Hitting Time Guarantees for Contractive Nonlinear Systems |
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Huang, Julien | University of Oxford |
Roberts, Stephen | University of Oxford |
Calliess, Jan-Peter | University of Oxford |
Keywords: Nonlinear systems identification, Stochastic systems, Finance
Abstract: We derive tight probabilistic bounds on the first hitting time of general classes of nonlinear autoregressive systems that can be linked to mean reverting stochastic processes. The obtained results are formulated such that they can be readily applied to models identified by machine learning techniques such as deep learning. As an application to finance, we show how our results can be utilised to inform statistical arbitrage trading strategies for which we provide probabilistic performance guarantees.
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17:40-18:00, Paper ThC22.6 | |
>Finite-Horizon Optimal Control of Continuous-Time Stochastic Systems with Terminal Cost of Wasserstein Distance |
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Hoshino, Kenta | Kyoto University |
Keywords: Stochastic systems, Stochastic optimal control, Mean field games
Abstract: This study addresses an stochastic optimal control problem for continuous-time systems with aimed at steering a probability distribution of the terminal state towards a desired probability distribution. The problem formulation incorporates the Wasserstein distance, a metric of the space of probability measures, in the cost functional. We provide an optimality condition for this optimal control problem in the form of Pontryagin's minimal principle. The condition is obtained by carefully examining properties of the Wasserstein distance. Consequently, we obtain the optimality condition described by the forward-backward stochastic differential equation and the Kantorovich potential, which appears in optimal transport theory.
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ThC23 |
Orchid Junior 4211 |
Fault-Tolerant Systems |
Regular Session |
Chair: Wang, Jianliang | Hangzhou Innovation Institute of Beihang University |
Co-Chair: Xu, Feng | Tsinghua University |
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16:00-16:20, Paper ThC23.1 | |
>Input Set Design for Active Fault Diagnosis and Control |
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Xu, Feng | Tsinghua University |
Keywords: Fault diagnosis, Fault tolerant systems, Linear systems
Abstract: This paper aims to implement integrated active fault diagnosis and control. The main novelty is that a novel online input set design method is proposed such that any input inside the input set can facilitate active fault diagnosis. At each time instant, an optimal input is selected from the input set such that an output-tracking control objective is minimized. Based on this idea, integrated active fault diagnosis and control is finally implemented by designing input sets and optimal inputs step by step. At the end of this paper, a four-tank system is used to illustrate the effectiveness of the proposed method.
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16:20-16:40, Paper ThC23.2 | |
>A Hybrid Diagnosis for Gas Starvation Faults in Proton Exchange Membrane Fuel Cells |
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Sani, Mukhtar | CEA Grenoble |
Piffard, Maxime | CEA |
Heiries, Vincent | CEA |
Keywords: Fault diagnosis, Machine learning, Simulation
Abstract: Fuel cell technology is recognized as a green energy alternative for the transport sector and stationary power applications, boasting high current density and zero emissions. Nonetheless, broad adoption and commercial viability of the technology is limited by its low durability and reliability. These limitations can be addressed by developing and implementing a fuel cell management system. In this paper, gas starvation faults in proton exchange membrane fuel cells (PEMFCs) have been studied. The causes, consequences, and the fault indicators (features) are identified. The sensitivities of fault indicators and how they affect the performance have been evaluated. Subsequently, a hybrid fault diagnosis method that combines residual-based fault detection with data-driven fault isolation has been proposed. Fault detection is achieved using a physics-based white-box model while fault isolation is achieved using a data-driven approach. Two supervised machine learning classifiers, namely the k-nearest neighbor (kNN) and the support vector machine (SVM) have been developed. The performances of these methods are compared in terms of their accuracy and computation time. Moreover, the effect of additional indicators has been evaluated. The results show that starvation faults on the PEMFC can be detected and isolated efficiently and correctly, thanks to the fault indicators and the hybrid nature of the diagnostic method. Also, from the presented results, it can be deduced that the kNN classifier has outperformed the SVM classifier.
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16:40-17:00, Paper ThC23.3 | |
>Improved Proportional-Integral Observer-Based Fault-Tolerant Control for MASs against Unbounded FDIA |
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Wang, Bo-Qun | University of Science and Technology Beijing |
Guo, Xiang-Gui | University of Science and Technology Beijing |
Wang, Jianliang | Hangzhou Innovation Institute of Beihang University |
Ding, Da-Wei | University of Science and Technology Beijing |
Wang, Heng | University of Science and Technology Beijing |
Keywords: Fault tolerant systems, Attack Detection, Networked control systems
Abstract: An improved proportional-integral observer (PIO) based fault-tolerant control problem is addressed for multiagent systems (MASs) with disturbance under unbounded false data injection attack (FDIA) over an undirected graph. The FDIAs are modeled as a class of unbounded attack signals. Notably, an augmented descriptor system is formulated by letting the FDIA be an auxiliary state vector. Then, an improved PIO is constructed to achieve the estimation of process faults and FDIA simultaneously. A compensation term is incorporated into the PIO to attenuate the effects of external disturbances and thus improving the accuracy of the PIO. Besides, an improved PIO-based fault-tolerant secure control scheme against unbounded FDIA is developed to achieve consensus even in the presence of process faults. Finally, the effectiveness and advantages of the proposed control strategy is verified through a simulation result.
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17:00-17:20, Paper ThC23.4 | |
>Systematic Synthesis of Passive Fault-Tolerant Augmented Neural Lyapunov Control Laws for Nonlinear Systems |
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Grande, Davide | University College London |
Fenucci, Davide | National Oceanography Centre |
Peruffo, Andrea | TU Delft |
Anderlini, Enrico | University College London |
Phillips, Alex B | University of Southampton |
Giles, Thomas | University College London |
Salavasidis, Georgios | University of Southampton |
Keywords: Fault tolerant systems, Lyapunov methods, Machine learning
Abstract: Performance and closed-loop stability of control systems can be jeopardised by actuator faults. Actuator redundancy in combination with appropriate control laws can increase the resiliency of a system to both loss of efficiency or jamming. Passive Fault-Tolerant Control (FTC) systems aim at designing a unique control law with guaranteed stability in both nominal and faulty scenarios. In this work, a novel machine learning-based method is devised to systematically synthesise control laws for systems affected by actuator faults, whilst formally certifying the closed-loop stability. The learning architecture trains two Artificial Neural Networks, one representing the control law, and the other resembling a Control Lyapunov Function (CLF). In parallel, a Satisfiability Modulo Theory solver is employed to certify that the obtained CLF formally guarantees the Lyapunov conditions. The method is showcased for two scenarios, one encompassing the stabilisation of an inverted pendulum with redundant actuators, whilst the other covers the control of an Autonomous Underwater Vehicle. The framework is shown capable of synthesising both linear and nonlinear control laws with minimal hyperparameter tuning and within limited computational resources.
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17:20-17:40, Paper ThC23.5 | |
>Robust Fault-Tolerant Control Based on L∞ Design for Discrete-Time Systems with Parameter Uncertainty |
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Fu, Shui | Dalian University of Technology |
Wang, Rui | Dalian University of Technology |
Tang, Wentao | Dalian University of Technology |
Sun, Xi-Ming | Dalian University of Technology |
Keywords: Fault tolerant systems, Robust control, Fault diagnosis
Abstract: 该文提出一种鲁棒容错控制器 具有参数不确定性的离散时间系统。一、国家和 故障由观察者根据 L∞ 设计估计。这 证明了L∞观测器的稳定性,误差系统为 对未知干扰的鲁棒性。然后,在过错的基础上和 状态估计, L∞ 技术设计鲁棒 容错控制器可恢复系统性能 受执行器故障影响。 基于所提方法,补偿状态可以限定为 设计的L∞指数,保证了系统的安全性。 最后,将所提出的鲁棒容错控制器应用于 双旋翼航空发动机系统模型仿真及其 有效性得到验证。
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17:40-18:00, Paper ThC23.6 | |
>Adaptive Finite Time Prescribed Performance Fault Tolerant Control for Spacecraft Attitude Maneuver (I) |
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Yang, Ze | Harbin Institute of Technology |
Yang, Baoqing | Harbin Institute of Technology |
Ji, Ruihang | National University of Singapore |
Ma, Jie | Harbin Institute of Technology |
Keywords: Fault tolerant systems, Fault diagnosis, Adaptive control
Abstract: In this paper, an active fault tolerant control method for spacecraft against actuator faults, uncertainties and disturbances is investigated. First, an adaptive iterative learning observer with improved adaptive law is proposed, which greatly improves the accuracy and speed of fault estimation. Then, a novel adaptive finite time prescribed performance fault tolerant controller is proposed, which has flexible performance constraints according to faults and control references, with better robustness and lower conservatism, breaking the limitation of fixed performance constraint. Next, an online optimal control allocation strategy is designed to achieve high-performance actuator allocation under saturation and fault constraints. Finally, through numerical simulation, the effectiveness and robustness of the proposed scheme are illustrated by comparing with existing methods.
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ThC24 |
Orchid Main 4201AB |
Switched Systems II |
Regular Session |
Chair: Sun, Zhendong | Academy of Mathematics & Systems Science, CAS |
Co-Chair: Nair, Girish N. | University of Melbourne |
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16:00-16:20, Paper ThC24.1 | |
>Inhomogeneous Singular Linear Switched Systems in Discrete Time: Solvability, Reachability, and Controllability Characterizations (I) |
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Sutrisno, Sutrisno | University of Groningen and Diponegoro Unversity |
Trenn, Stephan | University of Groningen |
Keywords: Switched systems, Differential-algebraic systems, Linear systems
Abstract: In this paper we study a novel solvability notion for discrete-time singular linear switched systems with inputs. We consider the existence and uniqueness of a solution on arbitrary finite time intervals with arbitrary inputs and arbitrary switching signals, and furthermore, we pay special attention to strict causality, i.e. the current state is only allowed to depend on past values of the state and the input. A necessary and sufficient condition for this solvability notion is then established. Furthermore, a surrogate switched system (an ordinary switched system that has equivalent input-output behavior) is derived for any solvable system. By utilizing those surrogate systems, we are able to characterize the reachability and controllability properties of the original singular systems using a geometric approach.
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16:20-16:40, Paper ThC24.2 | |
>Analysis and Synthesis of Switched Linear Systems with Random Mode-Dependent Sojourn-Time |
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Cai, Bo | Harbin Institute of Technology |
Xu, Kaixin | Harbin Institute of Technology |
Lu, Shengao | Harbin Institute of Technology |
Liang, Ye | Harbin Institute of Technology |
Zhang, Lixian | Harbin Institute of Technology |
Keywords: Switched systems, Stochastic systems, Stability of linear systems
Abstract: This paper concentrates on the issues of stability and stabilization for a class of switched linear systems with a new class of switching signals in discrete-time domain. The considered switching signals are of general random mode-dependent sojourn-time (RMST) property. Compared with the dwell-time switching or Markov chain often studied in the literature, it is capable of describing the mode-dependent sojourn-time consisting of a fixed part and a random part with the known expectation. By fully considering the characteristics of RMST, the criteria of stability and stabilization are derived for the underlying systems. Further, the results are extended to the asynchronously switched stabilizing control for RMST switched systems. A numerical example is provided to demonstrate the effectiveness and potential of the theoretical results.
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16:40-17:00, Paper ThC24.3 | |
>Stabilizing Design of Third-Order Continuous-Time Switched Linear Systems |
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Wang, Miaomiao | Chinese Academy of Sciences |
Sun, Zhendong | Shandong University of Science and Technology |
Keywords: Switched systems, Stability of hybrid systems
Abstract: In this work, we address both the state feedback stabilization problem and the dynamic output feedback stabilization problem for third-order continuous-time switched linear systems. Based on the controllability normal form decomposition approach, we prove that any controllable system is state feedback stabilizable, and the rate of convergence could be arbitrarily pre-assigned. Furthermore, for observable switched systems, we propose a reduced-order observer that could asymptotically estimate the unmeasured states. The dynamic output feedback stabilization problem is solved by designing a common switching law that stabilizes both the state and the observer. The design process is completely constructive.
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17:00-17:20, Paper ThC24.4 | |
>Comparison Theorem for Infinite-Dimensional Linear Impulsive Systems |
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Bivziuk, Vladyslav | University of Illinois Urbana-Champaign |
Dashkovskiy, Sergey | University of Wuerzburg |
Slyn'ko, Vitalii | S.P. Timoshenko Institute of Mechanics |
Keywords: Stability of hybrid systems, Stability of linear systems, Lyapunov methods
Abstract: We consider a linear impulsive system in an infinite-dimensional Banach space. It is assumed that the moments of impulsive action satisfy the averaged dwell-time condition and the linear operator on the right side of the differential equation generates an analytic semigroup in the state space. Using commutator identities, we prove a comparison theorem that reduces the problem of asymptotic stability of the original system to the study of a simpler system with constant dwell-times. An illustrative example of a linear impulsive system of parabolic type in which the continuous and discrete dynamics are both unstable is given.
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17:20-17:40, Paper ThC24.5 | |
>Asymptotically Optimal Finite-Dimensional Approximations for Linear Filtering with Infinite-Dimensional Measurements |
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Varley, Maxwell | University of Melbourne |
Molloy, Timothy L. | Australian National University |
Nair, Girish N. | University of Melbourne |
Keywords: Kalman filtering, Stochastic systems, Filtering
Abstract: This work proposes a novel approach to approximate optimal linear filters for discrete-time linear Gaussian systems with infinite-dimensional measurements and finite-dimensional states. Assuming scalar-valued states for simplicity, we formulate the problem in terms of optimally selecting N points at which to sample the infinite-dimensional measurement, in order to minimize the mean-squared filtering error. We show that for large N , this problem can be expressed using the notion of an asymptotic point density function from the field of high-resolution quantization theory. To the best of the authors’ knowledge, this method has not been considered in infinite-dimensional filtering previously. This leads to a characterization in terms of an Urysohn integral equation, which can be solved numerically to yield an asymptotically optimal N -point filter. The mean-square approximation error is proportional to N−4, which is faster than the typical N−2 decay of high-resolution quantization and suggests that this approximation method will be useful even for moderate or small N. These properties are verified by simulations based on a linearized pinhole camera measurement model.
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17:40-18:00, Paper ThC24.6 | |
>Symbolic Models for Interconnected Impulsive Systems (I) |
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Belamfedel Alaoui, Sadek | University Mohammed VI Polytechnic |
Saoud, Adnane | CentraleSupelec |
Jagtap, Pushpak | Indian Institute of Science |
Swikir, Abdalla | Technical University of Munich |
Keywords: Formal Verification/Synthesis, Large-scale systems, Hybrid systems
Abstract: In this paper, we present a compositional methodology for constructing symbolic models of nonlinear interconnected impulsive systems. Our approach relies on the concept of "alternating simulation function" to establish a relationship between concrete subsystems and their symbolic models. Assuming some small-gain type conditions, we develop an alternating simulation function between the symbolic models of individual subsystems and those of the nonlinear interconnected impulsive systems. To construct symbolic models of nonlinear impulsive subsystems, we propose an approach that depends on incremental input-to-state stability and forward completeness properties. Finally, we demonstrate the advantages of our framework through a case study.
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ThC25 |
Lotus Junior 4DE |
Quantum Information and Control |
Regular Session |
Chair: Wisniewski, Rafal | Aalborg University |
Co-Chair: Nurdin, Hendra I | UNSW Australia |
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16:00-16:20, Paper ThC25.1 | |
>Beyond Common Randomness: Quantum Resources in Decentralized Control |
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Deshpande, Shashank | IIT Bombay |
Kulkarni, Ankur A. | Indian Institute of Technology Bombay |
Keywords: Quantum information and control, Decentralized control, Stochastic systems
Abstract: Ananthram and Borkar showed that there exist strategies that are consistent with the requirements of a decentralized information structure but are unattainable through the use of common randomness. This opens the question of discovering physically realisable mechanisms that provide access to this region of the strategic space. In our previous work we introduced a class of quantum strategies that allow such access in a two-agent setting. In this paper, we consider the problem of optimal allocation of a k-partite quantum resource amongst n agents, k
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16:20-16:40, Paper ThC25.2 | |
>Dynamical Mode Decomposition for Infinite-Dimensional Open Quantum Systems; Liouvillian Spectral Analysis and Parameter Estimation |
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Kato, Yuzuru | Future University Hakodate |
Nakao, Hiroya | Tokyo Institute of Technology |
Keywords: Quantum information and control, Nonlinear systems identification
Abstract: Dynamic mode decomposition (DMD) is a data-driven method for the estimation, prediction, and control of complex dynamical systems, which has gained much attention in the fields of nonlinear dynamics and fluid mechanics. A DMD method for quantum spin systems, described by a linear dynamical system of a finite-dimensional set of observables, has been proposed recently. In this study, we propose two DMD methods applicable to infinite-dimensional open quantum systems, which use time-series data obtained by quantum state tomography. First, we propose a kernel DMD method for a data-driven spectral analysis of the Liouville superoperator. Second, we propose a method for the parameter estimation of the Liouville superoperator, which incorporates prior knowledge of the model structure into DMD. The proposed methods can accurately reconstruct the system dynamics and show that DMD frameworks can be applicable to infinite-dimensional open quantum systems.
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16:40-17:00, Paper ThC25.3 | |
>Quantum Pontryagin Neural Networks in Gamkrelidze Form Subjected to the Purity of Quantum Channels |
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Binandeh Dehaghani, Nahid | University of Porto |
Aguiar, A. Pedro | Faculty of Engineering, University of Porto |
Wisniewski, Rafal | Aalborg University |
Keywords: Quantum information and control, Optimal control, Neural networks
Abstract: We investigate a time and energy minimization optimal control problem for open quantum systems, whose dynamics is governed through the Lindblad (or Gorini-Kossakowski-Sudarshan-Lindblad) master equation. The dissipation is Markovian time-independent, and the control is governed by the Hamiltonian of a quantum-mechanical system. We are specifically interested to study the purity in a dissipative system constrained by state and control inputs. We deal with the state constraints through Gamkrelidze revisited method, while handling control constraints through the idea of saturation functions and system extensions. This is the first time that quantum purity conservation is formulated in such framework. We obtain the necessary conditions of optimality through the Pontryagin Minimum Principle. Finally, the resulted boundary value problem is solved by a Physics-Informed Neural Network (PINN) approach, a technique that is also new in quantum control context. We show that these PINNs play an effective role in learning optimal control actions.
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17:00-17:20, Paper ThC25.4 | |
>Asymptotic Stability of Non-Demolition Quantum Trajectories with Measurement Imperfections |
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Bompais, Mael | University Paris Saclay |
Amini, Nina H. | CNRS, L2S, CentraleSupelec |
Keywords: Quantum information and control, Stochastic systems, Estimation
Abstract: We consider the question of asymptotic stability of quantum trajectories undergoing quantum non-demolition imperfect measurement, that is to say the convergence of the estimated trajectory towards the true trajectory whose parameters and initial state are not necessarily known. We give conditions on the estimated initial state and regions of validity for the estimated parameters so that this convergence is ensured. We illustrate these results through numerical simulations on the physical example [1] and discuss the asymptotic stability for a more realistic general case where decoherence acts on the system. In this case, the evolution is described by new Kraus operators which do not satisfy the quantum non-demolition property.
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17:20-17:40, Paper ThC25.5 | |
>Robust Quantum Coding for Thermal Noise Via Dissipative Dynamics |
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Nishino, Kazuki | The University of Tokyo |
Ohki, Kentaro | Kyoto University |
Tsumura, Koji | The University of Tokyo |
Keywords: Quantum information and control
Abstract: This paper proposes an improved quantum coding method based on Markovian dissipative dynamics that is robust against thermal noise. A method for correcting information errors is indispensable for the practical use of quantum information devices, and stabilizer codes for quantum systems have been devised. One of the quantum coding methods, namely, quantum coding based on Markovian dissipative dynamics, has a favorable feature that it does not require strict time control, however it is known that these methods are susceptible to thermal noise. In this paper, we propose a quantum coding method that incorporates a new mechanism to correct the disturbance of the quantum state caused by thermal noise into the quantum coding method using dissipative dynamics. We also analyze the stability of the proposed quantum dynamics in the quantum state corresponding to the target code word. Numerical experiments confirm the effectiveness of the proposed method.
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17:40-18:00, Paper ThC25.6 | |
>Markovian Embeddings of Non-Markovian Quantum Systems: Coupled Stochastic and Quantum Master Equations for Non-Markovian Quantum Systems |
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Nurdin, Hendra I | UNSW Australia |
Keywords: Quantum information and control
Abstract: Quantum Markov models are employed ubiquitously in quantum physics and in quantum information theory due to their relative simplicity and analytical tractability. In particular, these models are known to give accurate approximations for a wide range of quantum optical and mesoscopic systems. However, in general, the validity of the Markov approximation entails assumptions regarding properties of the system of interest and its environment, which may not be satisfied or accurate in arbitrary physical systems. Therefore, developing useful modelling tools for general non-Markovian quantum systems for which the Markov approximation is inappropriate or deficient is an undertaking of significant importance. This work considers non-Markovian principal quantum systems that can be embedded in a larger Markovian quantum system with one or more compound baths consisting of an auxiliary quantum system and a quantum white noise field, and derives a set of coupled stochastic and quantum master equations for embedded non-Markovian quantum systems. The case of a purely Hamiltonian coupling between the principal and auxiliary systems as a closed system without coupling to white noises is included as a special case. The results are expected to be of interest for (open-loop and feedback) control of continuous-time non-Markovian systems and studying reduced models for numerical simulation of such systems. They may also shed more light on the general structure of continuous-time non-Markovian quantum systems.
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ThC26 |
Orchid Main 4301AB |
Geometric Methods |
Regular Session |
Chair: Iori, Tomoyuki | Osaka University |
Co-Chair: Duffaut Espinosa, Luis Augusto | University of Vermont |
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16:00-16:20, Paper ThC26.1 | |
>LMI-Based Stability Analysis of a Geometric PID-Type Attitude Control Law |
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Aslam, Farooq | Institute of Space Technology |
Khan, Hafiz Zeeshan Iqbal | Institute of Space Technology, Islamabad |
Haydar, Muhammad Farooq | Animal Dynamics Ltd |
Akhtar, Suhail | Institute of Space Technology |
Riaz, Jamshed | Department of Aeronautics and Astronautics, Institute of Space T |
Keywords: Algebraic/geometric methods, LMIs, Aerospace
Abstract: This paper presents an analytical framework for analyzing the stability of a geometric PID controller, with a prescribed structure, for attitude control on the Special Orthogonal Group SO(3). A key feature of the proposed approach is the use of linear matrix inequalities (LMIs) to formulate sufficient conditions which ensure that the closed-loop tracking error system is almost globally asymptotically stable (AGAS). To this end, a candidate Lyapunov function is considered which is slightly more general than those traditionally employed in the SO(3) literature. In particular, the Lyapunov function contains terms which couple the attitude and velocity errors with the integrator state, as well as matrix gains for four of the six Lyapunov function coefficients. The LMI-based stabilization conditions are then cast as a feasibility problem which can be used to search for Lyapunov function coefficients that confirm AGAS for a given PID controller with matrix gains. Using the proposed approach, control designers can use linearized models of the attitude kinematics and dynamics to tune the PID gains, and then solve a semidefinite programming problem to obtain AGAS guarantees for the corresponding geometric nonlinear PID controller. The effectiveness of this method is demonstrated on a practical problem involving the design and analysis of a geometric PID controller for a hexacopter UAV with local performance requirements specified in terms of rise time, settling time, gain and phase margins, and closed-loop bandwidth.
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16:20-16:40, Paper ThC26.2 | |
>Functional Derivatives of Chen-Fliess Series with Applications to Optimal Control |
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Duffaut Espinosa, Luis Augusto | University of Vermont |
Gray, W. Steven | Old Dominion University |
Perez Avellaneda, Ivan | University of Vermont |
Keywords: Algebraic/geometric methods, Nonlinear systems, Optimal control
Abstract: Functional optimization problems, such as those appearing in optimal control, are often stated in terms of finding the critical points of a variational derivative. The first goal of this paper is to describe the Frechet derivative of a Chen-Fliess series and to provide an algebraic tool for computing it. The second goal is to show how to characterize and compute critical points of this Frechet derivative both analytically and numerically. The former requires a certain shuffle separability property of the generating series for the Frechet derivative and employs the concept of a nullable series. Finally, some simple examples are provided to show how these ideas can be applied to solve quadratic optimal control problems entirely in the context of Chen-Fliess series.
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16:40-17:00, Paper ThC26.3 | |
>Pose-Following with Dual Quaternions |
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Arrizabalaga, Jon | Technical University of Munich (TUM) |
Ryll, Markus | Technical University Munich |
Keywords: Algebraic/geometric methods, Nonlinear systems
Abstract: This work focuses on pose-following, a variant of path-following in which the goal is to steer the system’s position and attitude along a path with a moving frame attached to it. Full body motion control, while accounting for the additional freedom to self-regulate the progress along the path is an appealing trade-off. Towards this end, we extend the well-established dual quaternion based pose-tracking method into a pose-following control law. Specifically, we derive the equations of motion for the full pose error between the geometric reference and the rigid body in the form of a dual quaternion and dual twist, and subsequently, formulate an almost globally asymptotically stable control law. The global attractivity of the presented approach is validated in a spatial example, while its benefits over pose-tracking are showcased through a planar case-study.
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17:00-17:20, Paper ThC26.4 | |
>Optimal Active Sensing Control for Two-Frame Systems |
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Benhamou, Jonas | Safran/Mines Paris |
Bonnabel, Silvere | Mines ParisTech |
Chapdelaine, Camille | SAFRAN SA |
Keywords: Algebraic/geometric methods, Observers for nonlinear systems, Autonomous robots
Abstract: This paper provides a complete characterization of the trajectories that maximize the information collected by a moving vehicle, through sensors' measurements, for the recently introduced class of nonlinear ``two-frame systems". The information is quantified in terms of the trace of the observability Gramian (OG) along a trajectory. In general, this quantity nontrivially depends on the control inputs and the state trajectory, resulting in a difficult optimal control problem. Herein, we leverage the property of invariant filtering that Jacobians are state-trajectory independent, that is, only depend on the control inputs, which enables us to mathematically derive optimal trajectories in closed form. We illustrate the results numerically on problems from robotics such as 3D robot localization, and 2D simultaneous localization and mapping.
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17:20-17:40, Paper ThC26.5 | |
>Symbolic-Numeric Computation of Integrals in Successive Galerkin Approximation of Hamilton-Jacobi-Bellman Equation |
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Iori, Tomoyuki | Osaka University |
Keywords: Algebraic/geometric methods, Optimal control, Computational methods
Abstract: This paper proposes an efficient symbolic-numeric method to compute integrals in the successive Galerkin approximation (SGA) of the Hamilton-Jacobi-Bellman (HJB) equation. By approximating its solution with a linear combination of basis functions, the HJB equation is reduced to a linear equation comprising integrals that include the basis functions. By choosing the Hermite polynomials as the basis functions, their recursive structure is inherited by the integrals. The recurrence relations of the integrals are computed using the symbolic computation and Mellin transform of differential operators. The integrals can then be computed using recursive substitutions, which are more accurate and require less computational cost than numerical integrations. A numerical example is provided to demonstrate the efficiency of the proposed method compared to other numerical integration methods.
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17:40-18:00, Paper ThC26.6 | |
>Global Controllability Criteria and Motion Planning of Regular Affine Systems with Drifts |
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Ji, Zhengping | Academy of Mathematics and Systems Science, Chinese Academy of S |
Zhang, Xiao | Academy of Mathematics and Systems Science, Chinese Academy of S |
Cheng, Daizhan | Chinese Academy of Sciences |
Keywords: Algebraic/geometric methods, Time-varying systems, Nonholonomic systems
Abstract: In this article, we give a condition for the global controllability of affine nonlinear control systems with drifts on Euclidean spaces. Under regularity assumptions, the condition is necessary and sufficient in the codimension-1 and codimension-2 cases, and holds for systems of higher codimensions under mild restrictions. We then investigate motion planning problems for codimension-1 affine systems, and give proof of the global existence of the lift to control curves for certain drifted systems using the homotopy continuation method.
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