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WeA01 |
Orchid Main 4202-4306 |
Nonstandard Linear-Quadratic Decision Making |
Tutorial Session |
Chair: Basar, Tamer | Univ of Illinois, Urbana-Champaign |
Co-Chair: Zhang, Huanshui | Shandong University of Science and Technology |
Organizer: Basar, Tamer | Univ of Illinois, Urbana-Champaign |
Organizer: Zhang, Huanshui | Shandong University of Science and Technology |
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10:00-10:20, Paper WeA01.1 | |
>Variations Around the Standard LQG Model (I) |
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Basar, Tamer | Univ of Illinois, Urbana-Champaign |
Keywords: Stochastic systems, Game theory
Abstract: ct This talk will provide an introduction to the tutorial session by first recalling the basic elements and assumptions of the standard LQG model, and then identifying several variations around it. One of these variations is placement of memory restrictions on the controllers, which brings in a signaling element into controller design. Here linearity of optimal controller is retained for some classes of such problems (which will be identified), but for most it does not (also to be discussed). Another variation is failure of channels according to some probability law, yet another one is adversarial intrusion into transmission of information (which leads to a stochastic zero-sum game), and yet a third one is introduction of bandwidth limitations, which necessitates quantization of the signals transmitted. Optimal designs for all these variations will be presented. Also to be discussed is what is known as rational expectation models (arising particularly in economics) where the evolution of a decision process depends on future expectations of a decision-maker on that evolution, which can also be handled within the linear quadratic framework with Gaussian statistics, though quite different from the basic LQG framework. Yet another topic to be covered is incentive designs, again in the linear-quadratic framework, where now there are (at least) two decision-makers with different objective functions, where one has the capability to (partially) shape the objective of the other one toward his own benefit. The talk will conclude with variations in the direction of other types of stochastic dynamic games as a segue to the next talk in the session.
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10:20-11:00, Paper WeA01.2 | |
>Advances in Linear-Quadratic Stochastic Differential Games (I) |
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Moon, Jun | Hanyang University |
Keywords: Stochastic systems, Game theory, Mean field games
Abstract: Since the seminal paper of Fleming and Souganidis, stochastic differential games have been playing a central role in mathematical control theory, as they can be applied to model the general decision-making process between interacting players under stochastic uncertainties. Two different types of stochastic differential games can be formulated depending on the role of the interacting players. Specifically, when the interaction of the players can be described in a symmetric way, it is called the Nash differential game. On the other hand, the Stackelberg differential game can be used to formulate the nonsymmetric leader-follower hierarchical decision-making process between the players. This talk consists of two parts, studying various recent results on LQ stochastic Nash and Stackelberg differential games. In the first part, the rigorous mathematical formulation on LQ stochastic Nash and Stackelberg differential games will be covered within various different frameworks, including systems with random-coefficients, games of mean-field type, Markov-jump systems, and systems with delay, where we will also provide several different notions of Nash and Stackelberg equilibria depending on the underlying information structures. In the second part, we will address the detailed mathematical approaches to and analyses of the LQ stochastic differential games formulated in the first part, and present their explicit Nash/Stackelberg equilibrium solutions expressed by Riccati differential equations. Some examples including numerical solvability of the corresponding Riccati differential equations will also be discussed to illustrate the theoretical results of this talk.
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11:00-11:20, Paper WeA01.3 | |
>Progress on Nonstandard LQ Control and Applications in Networked Control Systems (I) |
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Zhang, Huanshui | Shandong University of Science and Technology |
Keywords: Networked control systems, Optimal control
Abstract: The linear quadratic (LQ) control is the core of modern control theory, which has attracted great attention since the 1950s. However, there still exist some challenging fundamental problems that need to be addressed, which have also posed obstacles in areas of networked control systems (NCSs) and other related areas. For example, the stochastic LQR with time-delay has never been properly solved even for the most basic case of single input delay, although the delay-free case has been fully addressed by J. Bismut in the 70’s. As a result, control of NCSs faces fundamental difficulty in the cases of simultaneous packet loss and delay of control or state. Another problem is irregular LQ control, i. e., the related Riccati equation is irregular which leads to the LQ controller not being solvable even though it exists. This arises when the weighting matrix of control is semi-positive or indefinite. Irregular LQR has been a long-standing problem since the 70's. In this talk, we will first identify the challenges in the LQ control; second, we will address these challenges by establishing the unity of LQ control with forward and backward differential/difference equations (FBDEs). Finally, by solving the FBDEs, we will present the solutions to various problems identified, including irregular LQ control, stochastic LQ control with delay, optimal control and stabilization in NCSs with asymmetric information and/or with simultaneous packet loss and delay. (This talk is based on joint work of the speaker with Juanjuan Xu of Shandong University)
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11:20-12:00, Paper WeA01.4 | |
>Stochastic Linear-Quadratic Optimal Control Problems – Some Recent Results (I) |
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Yong, Jiongmin | University of Central Florida |
Sun, Jingrui | Southern University of Science and Technology |
Keywords: Stochastic systems, Game theory
Abstract: For linear-quadratic (LQ, for short) optimal control problems, there are several notions closely related: Existence of optimal control, two-point boundary value problem (optimality system), and (differential/algebraic) Riccati equation. An impression that people have is that these three notions are roughly equivalent. However, it is too vague. The purpose of this two-part talk is to clarify the relation among the above notions for stochastic LQ problems with deterministic coefficients. We introduce open-loop and closed-loop solvability of LQ problems. The following results will be presented: (i) The open-loop solvability is equivalent to solvability of the optimality system (which is now a forward-backward stochastic differential equation) plus the convexity of the cost functional; (ii) The closed-loop solvability is equivalent to the solvability of the Riccati equation; (iii) Open-loop and closed-loop solvability are not equivalent, in general, and they are equivalent for the infinite horizon LQ problems; (iv) There are corresponding results for two-person zero-sum differential games of LQ setting in terms of open-loop and closed-loop saddle points; (v) If the LQ optimal control problem has a closed-loop optimal strategy, and the problem also has an open-loop optimal control which admits a closed-loop representation, then the open-loop optimal control coincides with the outcome of the closed-loop optimal strategy; (vi) The conclusion of (v) continue to hold for open-loop and closed-loop saddle points of two-person zero-sum LQ differential games; However, it is not true, in general, for Nash equilibria of non-zero-sum differential games. This talk is divided into two parts: Part I will cover (i)—(iii), and Part II will cover (iv)—(vi). (This talk is based on the joint work of the speaker with Jingrui Sun of Southern University of Science and Technology, China.)
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WeA02 |
Melati Main 4001AB-4104 |
Learning-Based Control I: Policy Learning and Optimization |
Invited Session |
Chair: Müller, Matthias A. | Leibniz University Hannover |
Co-Chair: Meyn, Sean P. | Univ. of Florida |
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 WeA02.1 | |
>Differentiable Sparse Optimal Control |
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Shima, Ryotaro | Toyota Central R&D Labs |
Moriyasu, Ryuta | Toyota Central R&D Labs |
Kawaguchi, Sho | Toyota Industries Corporation |
Kashima, Kenji | Kyoto University |
Keywords: Optimal control, Machine learning, Computer-aided control design
Abstract: This paper develops a framework for differentiating sparse optimal control inputs with respect to cost parameters. The difficulty lies in the non-smoothness induced by a sparsity-enhancing regularizer. To avoid this, we identify the optimal inputs as a unique zero point of a function using the proximal technique. This enables us to characterize the differentiability and employ the implicit function theorem. We also demonstrate the effectiveness of our approach using a numerical example of inverse optimal control.
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10:20-10:40, Paper WeA02.2 | |
>An Efficient Off-Policy Reinforcement Learning Algorithm for the Continuous-Time LQR Problem (I) |
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Lopez, Victor G. | Leibniz University Hannover |
Müller, Matthias A. | Leibniz University Hannover |
Keywords: Iterative learning control, Data driven control, Optimal control
Abstract: In this paper, an off-policy reinforcement learning algorithm is designed to solve the continuous-time linear quadratic regulator (LQR) problem using only input-state data measured from the system. Different from other algorithms in the literature, we propose the use of a specific persistently exciting input as the exploration signal during the data collection step. We then show that, using this persistently excited data, the solution of the matrix equation in our algorithm is guaranteed to exist and to be unique at every iteration. Convergence of the algorithm to the optimal control input is also proven. Moreover, we formulate the policy evaluation step as the solution of a Sylvester-transpose equation, which increases the efficiency of its solution. A method to determine an initial stabilizing policy using only measured data is proposed. Finally, the advantages of the proposed method are tested via simulation.
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10:40-11:00, Paper WeA02.3 | |
>No-Regret Bayesian Optimization with Gradients Using Local Optimality-Based Constraints: Application to Closed-Loop Policy Search (I) |
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Makrygiorgos, Georgios | University of California, Berkeley |
Paulson, Joel | The Ohio State University |
Mesbah, Ali | University of California, Berkeley |
Keywords: Optimization
Abstract: Bayesian optimization (BO) has emerged as a data-efficient method for global optimization of expensive black-box functions, which commonly arise in learning-based control applications. Recent work has shown that BO can be augmented with gradient measurements to further improve its convergence behavior. These approaches mostly rely on standard acquisition functions and indirectly incorporate gradient information into a probabilistic surrogate model of the performance function to improve its local predictions. This paper presents a new strategy to simultaneously exploit performance (zeroth-order) and gradient (first-order) data within a single constrained acquisition optimization. This is done by enforcing a set of black-box constraints that mimic the necessary optimality conditions for the original global optimization problem. We establish how the incorporation of these constraints restricts the allowable search space of BO, leading to less exploration than zeroth-order BO. The performance of the proposed method is demonstrated for closed-loop policy search via reinforcement learning on a benchmark LQR problem.
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11:00-11:20, Paper WeA02.4 | |
>Scenario Optimization with Constraint Relaxation in a Non-Convex Setup: A Flexible and General Framework for Data-Driven Design (I) |
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Garatti, Simone | Politecnico Di Milano |
Campi, M. C. | Universita' Di Brescia |
Keywords: Uncertain systems, Randomized algorithms, Statistical learning
Abstract: The scenario approach, originally developed as a computational tool for robust problems, has through the years developed into a solid, general, framework for data-driven decision making and design. One main driving force that has fostered this process has certainly been the increasing generality of the considered schemes. In this paper, we move a further step forward in this process. By leveraging some recent results in the wake of the so-called wait-and-judge paradigm, we fully develop a scheme for scenario optimization with constraint relaxation in a non-convex setup, so greatly expanding previous achievements valid under a convexity assumption. We show that a purely data-driven, and yet tight and informative, quantification of the solution robustness is possible regardless of the mechanism through which uncertainty is generated. The generality of this new non-convex setup provides an extremely versatile scheme for data-driven design that can be applied to a variety of problems ranging from mixed-integer optimization to design in abstract spaces.
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11:20-11:40, Paper WeA02.5 | |
>On-Policy Data-Driven Linear Quadratic Regulator Via Model Reference Adaptive Reinforcement Learning (I) |
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Borghesi, Marco | University of Bologna |
Bosso, Alessandro | University of Bologna |
Notarstefano, Giuseppe | University of Bologna |
Keywords: Data driven control, Optimal control, Adaptive control
Abstract: In this paper, we address a data-driven linear quadratic optimal control problem in which the regulator design is performed on-policy by resorting to approaches from reinforcement learning and model reference adaptive control. In particular, a continuous-time identifier of the value function is used to generate online a reference model for the adaptive stabilizer. By introducing a suitably selected dithering signal, the resulting policy is shown to achieve asymptotic convergence to the optimal gain while the controlled plant reaches asymptotically the behavior of the optimal closed-loop system.
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11:40-12:00, Paper WeA02.6 | |
>Learning Optimal Policies in Mean Field Models with Kullback-Leibler Regularization (I) |
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Busic, Ana | Inria |
Meyn, Sean P. | Univ. of Florida |
Cammardella, Neil | University of Florida |
Keywords: Machine learning, Distributed control, Stochastic optimal control
Abstract: The theory and application of mean field games has grown significantly since its origins less than two decades ago. This paper considers a special class in which the game is cooperative, and the cost includes a control penalty defined by Kullback-Leibler divergence, as commonly used in reinforcement learning and other fields. Its use as a control cost or regularizer is often preferred because this leads to an attractive solution. This paper considers a particular control paradigm called Kullback-Leibler Quadratic (KLQ) optimal control, and arrives at the following conclusions: 1. in application to distributed control of electric loads, a new modeling technique is introduced to obtain a simple Markov model for each load (the `agent' in mean field theory). 2. It is argued that the optimality equations may be solved using Monte-Carlo techniques---a specialized version of stochastic gradient descent (SGD). 3. The use of averaging minimizes the asymptotic covariance in the SGD algorithm; the form of the optimal covariance is identified for the first time.
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WeA03 |
Melati Junior 4010A-4111 |
Safe Planning and Control with Uncertainty Quantification I |
Invited Session |
Chair: Gao, Yulong | University of Oxford |
Co-Chair: Gatsis, Konstantinos | 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 WeA03.1 | |
>Koopman-Inspired Implicit Backward Reachable Sets for Unknown Nonlinear Systems |
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Balim, Haldun | ETH Zurich |
Aspeel, Antoine | University of Michigan |
Liu, Zexiang | University of Michigan |
Ozay, Necmiye | Univ. of Michigan |
Keywords: Constrained control, Hybrid systems
Abstract: Koopman liftings have been successfully used to learn high dimensional linear approximations for autonomous systems for prediction purposes, or for control systems for leveraging linear control techniques to control nonlinear dynamics. In this paper, we show how learned Koopman approximations can be used for state-feedback correct-by-construction control. To this end, we introduce the Koopman over-approximation, a (possibly hybrid) lifted representation that has a simulation-like relation with the underlying dynamics. Then, we prove how successive application of controlled predecessor operation in the lifted space leads to an implicit backward reachable set for the actual dynamics. Finally, we demonstrate the approach on two nonlinear control examples with unknown dynamics.
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10:20-10:40, Paper WeA03.2 | |
>Exact Characterization of the Convex Hulls of Reachable Sets (I) |
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Lew, Thomas | Stanford |
Bonalli, Riccardo | Laboratoire Des Signaux Et Systèmes |
Pavone, Marco | Stanford University |
Keywords: Uncertain systems, Optimal control, Predictive control for nonlinear systems
Abstract: We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing over-approximation tools tend to be conservative or computationally expensive. In this work, we exactly characterize the convex hulls of reachable sets as the convex hulls of solutions of an ordinary differential equation from all possible initial values of the disturbances. This finite-dimensional characterization unlocks a fast sampling-based method to accurately over-approximate reachable sets. We give applications to neural feedback loop analysis and robust model predictive control.
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10:40-11:00, Paper WeA03.3 | |
>Logical Zonotopes: A Set Representation for the Formal Verification of Boolean Functions (I) |
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Alanwar, Amr | Technical University of Munich |
Jiang, Frank J. | Royal Institute of Technology |
Amin, Samy | Constructor University |
Johansson, Karl H. | KTH Royal Institute of Technology |
Keywords: Formal Verification/Synthesis, Discrete event systems, Computational methods
Abstract: A logical zonotope, which is a new set representation for binary vectors, is introduced in this paper. A logical zonotope is constructed by XOR-ing a binary vector with a combination of other binary vectors called generators. Such a zonotope can represent up to 2^n binary vectors using only n generators. It is shown that logical operations over sets of binary vectors can be performed on the zonotopes' generators and, thus, significantly reduce the computational complexity of various logical operations (e.g., XOR, NAND, AND, OR, and semi-tensor products). Similar to traditional zonotopes' role in the formal verification of dynamical systems over real vector spaces, logical zonotopes can efficiently analyze discrete dynamical systems defined over binary vector spaces. We illustrate the approach and its ability to reduce the computational complexity in two use cases: (1) encryption key discovery of a linear feedback shift register and (2) safety verification of a road traffic intersection protocol.
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11:00-11:20, Paper WeA03.4 | |
>Scalable Forward Reachability Analysis of Multi-Agent Systems with Neural Network Controllers (I) |
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Gates, Oliver | University of Oxford |
Newton, Matthew | University of Oxford |
Gatsis, Konstantinos | University of Oxford |
Keywords: Machine learning, Neural networks, Robust control
Abstract: Neural networks (NNs) have been shown to learn complex control laws successfully, often with performance advantages or decreased computational cost compared to alternative methods. Neural network controllers (NNCs) are, however, highly sensitive to disturbances and uncertainty, meaning that it can be challenging to make satisfactory robustness guarantees for systems with these controllers. This problem is exacerbated when considering multi-agent NN-controlled systems, as existing reachability methods often scale poorly for large systems. This paper addresses the problem of finding overapproximations of forward reachable sets for discrete-time uncertain multi-agent systems with distributed NNC architectures. We first reformulate the dynamics, making the system more amenable to reachablility analysis. Next, we take advantage of the distributed architecture to split the overall reachability problem into smaller problems, significantly reducing computation time. We use quadratic constraints, along with a convex representation of uncertainty in each agent's model, to form semidefinite programs, the solutions of which give overapproximations of forward reachable sets for each agent. Finally, the methodology is tested on two realistic examples: a platoon of vehicles and a power network system.
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11:20-11:40, Paper WeA03.5 | |
>Distributionally Robust Optimization Using Cost-Aware Ambiguity Sets |
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Schuurmans, Mathijs | KU Leuven |
Patrinos, Panagiotis | KU Leuven |
Keywords: Optimization, Statistical learning
Abstract: We present a novel framework for distributionally robust optimization (DRO), called cost-aware DRO (CADRO). The key idea of CADRO is to exploit the cost structure in the design of the ambiguity set to reduce conservatism. Particularly, the set specifically constrains the worst-case distribution along the direction in which the expected cost of an approximate solution increases most rapidly. We prove that CADRO provides both a high-confidence upper bound and a consistent estimator of the out-of-sample expected cost, and show empirically that it produces solutions that are substantially less conservative than existing DRO methods, while providing the same guarantees.
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11:40-12:00, Paper WeA03.6 | |
>Bounding Optimality Gaps for Non-Convex Optimization Problems: Applications to Nonlinear Safety-Critical Systems (I) |
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Akella, Prithvi | California Institute of Technology |
Ames, Aaron D. | California Institute of Technology |
Keywords: Randomized algorithms, Optimization algorithms, Nonlinear systems
Abstract: Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of their sub-optimality have been long sought after. To that end, by leveraging recent work in risk-aware verification, we provide two algorithms to (1) probabilistically bound the optimality gaps of solutions reported by novel percentile optimization techniques, and (2) probabilistically bound the maximum optimality gap reported by percentile approaches for repetitive applications, e.g. Model Predictive Control (MPC). Notably, our results work for a large class of optimization problems. We showcase the efficacy and repeatability of our results on a few, benchmark non-convex optimization problems and the utility of our results for controls in a Nonlinear MPC setting.
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WeA04 |
Simpor Junior 4913 |
Control of Connected and Autonomous Vehicles in Mixed Traffic |
Invited Session |
Chair: Cicic, Mladen | CNRS, GIPSA-Lab |
Co-Chair: Delle Monache, Maria Laura | University of California, Berkeley |
Organizer: Cicic, Mladen | UC Berkeley |
Organizer: Delle Monache, Maria Laura | University of California, Berkeley |
Organizer: Miao, Fei | University of Connecticut |
Organizer: Pasquale, Cecilia | University of Genova |
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10:00-10:20, Paper WeA04.1 | |
>Cyber-Attack Detection Framework for Connected Vehicles in V2X Networks Based on an Iterative UFIR Filter (I) |
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Jiang, Kai | Nanyang Technological University |
Ju, Zhiyang | Beihang University |
Huang, Lingying | Nanyang Technological University |
Su, Rong | Nanyang Technological University |
Keywords: Attack Detection, Estimation, Transportation networks
Abstract: Connected vehicles have great advantages in driving safety and energy efficiency under the support of vehicle-to-everything (V2X) networks, while they are also vulnerable to malicious cyber-attacks. To enhance the cyber security of connected vehicles, a cyber-attack detection framework is proposed based on multi-source information fusion specifically for the vehicle localization system. In this framework, an iterative unbiased finite impulse response (UFIR) filter is utilized to estimate the vehicle position with low computational load, based on the vehicle dynamics model and information from the inertial measurement system (IMU), GPS, and V2X networks. In addition, a discriminator module is developed to analyze the residuals between estimations and position information from different sources for cyber-attack detection. Finally, multiple simulation cases are implemented to validate the effectiveness of the proposed framework.
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10:20-10:40, Paper WeA04.2 | |
>Connected and Automated Vehicles in Mixed-Traffic: Learning Human Driver Behavior for Effective On-Ramp Merging (I) |
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Senthil Kumar, Nishanth Venkatesh | Cornell University |
Le, Viet-Anh | University of Delaware |
Dave, Aditya | Cornell University |
Malikopoulos, Andreas A. | Cornell University |
Keywords: Traffic control, Optimal control, Machine learning
Abstract: Highway merging scenarios featuring mixed traffic conditions pose significant modeling and control challenges for connected and automated vehicles (CAVs) interacting with incoming on-ramp human-driven vehicles (HDVs). In this paper, we present an approach to learn an approximate information state (AIS) model of CAV-HDV interactions. Thus, the CAV learns the behavior of an incoming HDV using the AIS model and uses it to generate a control strategy for merging. First, we validate the efficacy of this framework on real-world data by using it to predict the behavior of an HDV in situations with other HDVs extracted from the Next-Generation Simulation repository. Then, we generate simulation data for HDV-CAV interactions in a highway merging scenario using a standard inverse reinforcement learning approach. Without assuming a prior knowledge of the generating model, we show that our AIS model learns to predict the future trajectory of the HDV using only observations. Subsequently, we generate safe merging control policies for a CAV when merging with HDVs that demonstrate a spectrum of driving behaviors, from aggressive to conservative. We establish the effectiveness of the proposed approach by performing numerical simulations.
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10:40-11:00, Paper WeA04.3 | |
>Exploring CAV-Based Traffic Control for Improving Traffic Conditions in the Face of Bottlenecks (I) |
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Vishnoi, Suyash | The University of Texas at Austin |
Ji, Junyi | Vanderbilt University |
Bahavarnia, MirSaleh | Vanderbilt University |
Zhang, Yuhang | Vanderbilt University |
Taha, Ahmad | Vanderbilt University |
Claudel, Christian G. | UT Austin |
Work, Daniel B. | Vanderbilt University |
Keywords: Traffic control, Control applications, Autonomous vehicles
Abstract: This work investigates traffic control via controlled connected and automated vehicles (CAVs) using novel controllers derived from the linear-quadratic regulator (LQR) theory. CAV-platoons are modeled as moving bottlenecks impacting the surrounding traffic with their speeds as control inputs. An iterative controller algorithm based on the LQR theory is proposed along with a variant that allows for penalizing abrupt changes in platoon speeds. The controllers use the Lighthill-Whitham-Richards (LWR) model implemented using an extended cell transmission model (CTM) which considers the capacity drop phenomenon for a realistic representation of traffic in congestion. The effectiveness of the proposed traffic control algorithms is tested using a traffic control example and compared with existing proportional-integral (PI)- and model predictive control (MPC)- based controllers from the literature. A case study using the TransModeler traffic microsimulation software is conducted to test the usability of the proposed controller in a realistic setting. It is observed that the proposed controller works well in both settings to mitigate the impact of the jam caused by a fixed bottleneck. The computation time required by the controller is also small making it suitable for real-time control.
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11:00-11:20, Paper WeA04.4 | |
>Optimal Control of Autonomous Vehicles for Flow Smoothing in Mixed Autonomy Traffic (I) |
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Alanqary, Arwa | University of California, Berkeley |
Gong, Xiaoqian | Arizona State University |
Keimer, Alexander | UC Berkeley |
Seibold, Benjamin | Temple University |
Piccoli, Benedetto | Rutgers University - Camden |
Bayen, Alexandre | University of California, Berkeley |
Keywords: Traffic control, Optimal control
Abstract: This article studies the optimal control of autonomous vehicles over a given time horizon to smooth traffic. We model the dynamics of a mixed-autonomy platoon as a system of non-linear ODEs, where the acceleration of human-driven vehicles is governed by a car-following model, and the acceleration of autonomous vehicles is to be controlled. We formulate the car-following task as an optimal control problem and propose a computational method to solve it. Our approach uses an adjoint formulation to compute gradients of the optimization problem explicitly, resulting in more accurate and efficient numerical computations. The gradients are then used to solve the problem using gradient-based optimization solvers. We consider an instance of the problem with the objective of improving the fuel efficiency of the vehicles in the platoon. The effectiveness of the proposed approach is demonstrated through numerical experiments. We apply the proposed approach to different scenarios of lead vehicle trajectories and platoon sizes. The results suggest that introducing an AV can produce significant energy savings for the platoon. It also reveals that the solution is agnostic to the platoon size thus the fuel saving is mainly due to optimizing the trajectory of the AV.
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11:20-11:40, Paper WeA04.5 | |
>Robust Decentralised Proof-Of-Position Algorithms for Smart City Applications (I) |
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Manzano Kharman, Aida | Imperial College London |
Ferraro, Pietro | University College Dublin |
Quinn, Anthony | Imperial College London |
Shorten, Robert | Imperial College London |
Keywords: Agents-based systems, Automotive systems, Smart cities/houses
Abstract: Motivated by the ever growing use of location-based services, we present a decentralised class of algorithms called Tree-Proof-of-Position (T-PoP). Most of the current proofs of location are centralised, thus forgoing verifiablity and privacy for the users. Decentralised solutions also exist, but they suffer from drawbacks that make them unsuitable for realistic, adversarial use cases. T-PoP algorithms rely on the web of interconnected devices in a smart city to establish how likely it is that an agent is in their claimed position. T-PoP operates under adversarial assumptions, where some agents are incentivised to be dishonest. We present a theoretical model for T-PoP and its security properties, and we validate this model through a large number of Monte-Carlo simulations. We specifically focus on two instances of T-PoP and analyse their security and reliability properties under a range of adversarial conditions. Use-cases and applications are discussed towards the end of the paper.
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11:40-12:00, Paper WeA04.6 | |
>A Dynamic Population Game Model of Non-Monetary Bottleneck Congestion Management under Elastic Demand Using Karma (I) |
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Elokda, Ezzat | ETH Zurich |
Cenedese, Carlo | ETH Zurich |
Zhang, Kenan | EPFL |
Censi, Andrea | ETH Zurich |
Bolognani, Saverio | ETH Zurich |
Frazzoli, Emilio | ETH Zürich |
Keywords: Traffic control, Game theory, Mean field games
Abstract: The morning commute bottleneck congestion problem has classically been modelled as a static game in which commuters act strategically based on their immediate Value of Time (VOT). This has restricted existing congestion mitigation techniques to rely on essentially monetary incentives to affect the static costs of the commuters. In contrast, a dynamic model enables characterizing the strategic trade-off between immediate and future resource access rights and inspires the design of new classes of fair, non-monetary congestion mitigation schemes. In this paper, we show how the recently proposed Dynamic Population Game (DPG) framework can be leveraged to study a non-monetary economy for bottleneck congestion management based on karma, a non-tradable mobility credit. Our DPG model allows to consider an elastic demand of commuters that only travel if congestion is reduced, and we show that a Stationary Nash Equilibrium (SNE) is guaranteed to exist despite of the dynamic participation of these commuters. Through numerical case studies we illustrate how our tools can assist policy makers in taking informed decisions about complex policy outcomes. In particular, we show how the dynamic karma scheme is robust to a potentially detrimental rebound effect that would manifest in a static monetary scheme.
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WeA05 |
Simpor Junior 4912 |
Decentralized Optimization and Learning |
Invited Session |
Chair: Yuan, Kun | Peking University |
Co-Chair: You, Keyou | Tsinghua University |
Organizer: Yuan, Kun | Peking University |
Organizer: You, Keyou | Tsinghua University |
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10:00-10:20, Paper WeA05.1 | |
>Smoothing Gradient Tracking for Decentralized Optimization Over the Stiefel Manifold with Non-Smooth Regularizers (I) |
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Wang, Lei | Academy of Mathematics and Systems Science, Chinese Academy of S |
Liu, Xin | Academy of Mathematics and Systems Science, Chinese Academy of S |
Keywords: Optimization, Decentralized control, Machine learning
Abstract: Recently, decentralized optimization over the Stiefel manifold has attracted tremendous attentions due to its wide range of applications in various fields. Existing methods rely on the gradients to update variables, which are not applicable to the objective functions with non-smooth regularizers, such as sparse PCA. In this paper, to the best of our knowledge, we propose the first decentralized algorithm for non-smooth optimization over Stiefel manifolds. Our algorithm approximates the non-smooth part of objective function by its Moreau envelope, and then existing algorithms for smooth optimization can be deployed. We establish the convergence guarantee with the iteration complexity of O (epsilon^{-4}). Numerical experiments conducted under the decentralized setting demonstrate the effectiveness and efficiency of our algorithm.
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10:20-10:40, Paper WeA05.2 | |
>Gradient Tracking with Multiple Local SGD for Decentralized Non-Convex Learning (I) |
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Ge, Songyang | The Chinese University of Hong Kong, Shenzhen |
Chang, Tsung-Hui | The Chinese University of Hong Kong, Shenzhen |
Keywords: Optimization algorithms, Machine learning, Distributed control
Abstract: The stochastic Gradient Tracking (GT) method for distributed optimization, is known to be robust against the inter-client variance caused by data heterogeneity. However, the stochastic GT method can be communication-intensive, requiring a large number of communication rounds of message exchange for convergence. To address this challenge, this paper proposes a new communication-efficient stochastic GT algorithm called the Local Stochastic GT (LSGT) algorithm, which adopts the local stochastic gradient descent (local SGD) technique in the GT method. With LSGT, each agent can perform multiple SGD updates locally within each communication round. Although it is not known previously whether the stochastic GT method can benefit from the local SGD, we establish the conditions under which our proposed LSGT algorithm enjoys the linear speedup brought by local SGD. Compared with the existing work, our analysis requires less restrictive conditions on the mixing matrix and algorithm stepsize. Moreover, it reveals that the local SGD does not only reserve the resilience of the stochastic GT method against the data heterogeneity but also speeds up reducing the tracking error reduction in the optimization process. The experimental results demonstrate that the proposed LSGT exhibits improved convergence speed and robust performance in various heterogeneous environments.
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|
10:40-11:00, Paper WeA05.3 | |
>Achieving Linear Speedup with Network-Independent Learning Rates in Decentralized Stochastic Optimization (I) |
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Yuan, Hao | Peking University |
Alghunaim, Sulaiman A. | Kuwait University |
Yuan, Kun | Peking University |
Keywords: Optimization, Machine learning, Decentralized control
Abstract: Decentralized stochastic optimization has become a crucial tool for addressing large-scale machine learning and control problems. In decentralized algorithms, all computing nodes are connected through a network topology, and each node communicates only with its direct neighbors. Decentralized algorithms can significantly reduce communication overhead by eliminating the need for global communication. However, existing research on the linear speedup analysis of decentralized stochastic algorithms is limited to the condition of network-dependent learning rates, which rarely holds in practice since the network connectivity is typically unknown to each node. As a result, it remains an open question whether a linear speedup bound can be achieved using network-independent learning rates. This paper provides an affirmative answer. By utilizing a new analysis framework, we prove D-SGD and Exact-Diffusion, two representative decentralized stochastic algorithms, can achieve linear speedup with network-independent learning rates. Simulations are provided to validate our theories.
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|
11:00-11:20, Paper WeA05.4 | |
>Fully Stochastic Distributed Convex Optimization on Time-Varying Graph with Compression (I) |
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Yau, Chung-Yiu | The Chinese University of Hong Kong |
Wai, Hoi-To | The Chinese University of Hong Kong |
Keywords: Optimization algorithms, Communication networks, Machine learning
Abstract: This paper develops a fully stochastic proximal primal-dual (FSPPD) algorithm for distributed convex optimization. At each iteration, the distributed algorithm has agents communicating on a randomly drawn graph and applies random sparsification on the transmitted messages, while the agents only have access to a stochastic gradient oracle. To our best knowledge, this is the first compression-enabled distributed stochastic gradient algorithm on random graphs utilizing the primal-dual framework. With diminishing step size, we show that the FSPPD algorithm converges almost surely to an optimal solution of the strongly convex optimization problem. Numerical experiments are provided to verify our results.
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|
11:20-11:40, Paper WeA05.5 | |
>Asynchronous Byzantine-Robust Stochastic Aggregation with Variance Reduction for Distributed Learning (I) |
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Zhu, Zehan | Zhejiang University |
Huang, Yan | Zhejiang University |
Zhao, Chengcheng | Zhejiang University |
Xu, Jinming | Zhejiang University |
Keywords: Optimization algorithms, Cyber-Physical Security, Machine learning
Abstract: We consider Byzantine-robust distributed learning with asynchronous participation of clients at a certain probability, where Byzantine clients can send malicious messages to the server. Instead of relying on traditional robust aggregation rules, such as Krum and Median, that can only tolerate a limited proportion of Byzantine clients, we propose an asynchronous Byzantine-robust stochastic aggregation method that employs regularization-based techniques to mitigate Byzantine attacks, and adopts variance-reduced techniques to eliminate the effect of stochastic noise of gradient sampling. Leveraging a properly designed Lyapunov function, we show that the proposed algorithm converges linearly to an error ball that is independent of stochastic gradient variance. Extensive experiments are conducted to show its efficacy in dealing with Byzantine attacks compared to the existing counterparts.
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11:40-12:00, Paper WeA05.6 | |
>Linear Model Predictive Control under Continuous Path Constraints Via Parallelized Primal-Dual Hybrid Gradient Algorithm (I) |
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Li, Zishuo | Tsinghua University |
Yang, Bo | Tsinghua University |
Li, Jiayun | Tsinghua University |
Yan, Jiaqi | Tokyo Institute of Technology |
Mo, Yilin | Tsinghua University |
Keywords: Predictive control for linear systems, Optimization algorithms, Constrained control
Abstract: In this paper, we consider a Model Predictive Control (MPC) problem of a continuous-time linear time-invariant system subject to continuous-time path constraints on the states and the inputs. By leveraging the concept of differential flatness, we can replace the differential equations governing the system with linear mapping between the states, inputs, and flat outputs (including their derivatives). The flat outputs are then parameterized by piecewise polynomials, and the model predictive control problem can be equivalently transformed into a Semi-Definite Programming (SDP) problem via Sum-of-Squares (SOS), ensuring constraint satisfaction at every continuous-time interval. We further note that the SDP problem contains a large number of small-size semi-definite matrices as optimization variables. To address this, we develop a Primal-Dual Hybrid Gradient (PDHG) algorithm that can be efficiently parallelized to speed up the optimization procedure. Simulation results on a quadruple-tank process demonstrate that our formulation can guarantee strict constraint satisfaction, while the standard MPC controller based on the discretized system may violate the constraint inside a sampling period. Moreover, the computational speed superiority of our proposed algorithm is collaborated by numerical simulation.
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WeA06 |
Simpor Junior 4911 |
Estimation I |
Regular Session |
Chair: Dunik, Jindrich | University of West Bohemia |
Co-Chair: Anil Meera, Ajith | Radboud University Nijmegen |
|
10:00-10:20, Paper WeA06.1 | |
>Adaptive Noise Covariance Estimation under Colored Noise Using Dynamic Expectation Maximization |
|
Anil Meera, Ajith | Radboud University Nijmegen |
Lanillos, Pablo | Spanish National Research Council |
Keywords: Estimation, Biologically-inspired methods, Observers for Linear systems
Abstract: The accurate estimation of the noise covariance matrix (NCM) in a dynamic system is critical for state estimation and control, as it has a major influence in their optimality. Although a large number of NCM estimation methods have been developed, most of them assume the noises to be white. However, in many real-world applications, the noises are colored (e.g., they exhibit temporal autocorrelations), resulting in suboptimal solutions. Here, we introduce a novel brain-inspired algorithm that accurately and adaptively estimates the NCM for dynamic systems subjected to colored noise. Particularly, we extend the Dynamic Expectation Maximization algorithm to perform both online noise covariance and state estimation by optimizing the free energy objective. We mathematically prove that our NCM estimator converges to the global optimum of this free energy objective. Using randomized numerical simulations, we show that our estimator outperforms nine baseline methods with minimal noise covariance estimation error under colored noise conditions. Notably, we show that our method outperforms the best baseline (Variational Bayes) in joint noise and state estimation for high colored noise. We foresee that the accuracy and the adaptive nature of our estimator make it suitable for online estimation in real-world applications.
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10:20-10:40, Paper WeA06.2 | |
>Sharp Performance Bounds for PASTA |
|
Marchi, Matteo | University of California, Los Angeles |
Bunton, Jonathan | University of California, Los Angeles |
Gas, Yskandar | University of California, Los Angeles |
Gharesifard, Bahman | University of California, Los Angeles |
Tabuada, Paulo | University of California at Los Angeles |
Keywords: Estimation, Control applications, Robust control
Abstract: LiDAR is a standard sensor choice for self-localization and SLAM of indoor autonomous robots. While there are many methods to estimate a robot's location using LiDAR measurements, most rely on algorithms that solve a generic LiDAR scan matching problem. When safety is a concern, these algorithms must provide a bound on the localization error to enable safety enforcing controllers, such as those based on Control Barrier Functions. Unfortunately, most existing scan matching algorithms offer no formal guarantees, and are tailored to structured, high-resolution 3D point clouds. In this paper, we present an improved theoretical analysis for a low-cost alternative to these methods named PASTA (Provably Accurate Simple Transformation Alignment), originally introduced in [8]. We provide a formal worst-case error guarantee on the localization error and show, experimentally, that it is tight. This characterization of the localization error simplifies the use of high-dimensional perception data for safety-critical control algorithms.
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10:40-11:00, Paper WeA06.3 | |
>Finite-Gain L1 Interval Impulsive Observer Design under Denial-Of-Service Attacks |
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Tagne Mogue, Ruth Line | Univ. Orleans |
Courtial, Estelle | Laboratory PRISME, University of Orleans |
Becis-Aubry, Yasmina | Univ. of Orléans |
Rabehi, Djahid | University of Orléans |
Meslem, Nacim | GIPSA-LAB, CNRS |
Ramdani, Nacim | University of Orléans |
Keywords: Estimation, Hybrid systems
Abstract: The design of a robust observer under denial-of-service attacks is addressed for linear time invariant systems in the bounded-error framework. The cyber-attacks occur between the output of the sensors localized on the physical plant and the cyber part embedding the observer. The data required by the observer are thus available at sporadic measurement time instants. In this setting, an interval impulsive observer is synthesized. The stability analysis of the dynamics of the state estimation error is done leveraging finite-gain L1 stability theory for hybrid systems. The observer L1 gain is computed by combining interval analysis and the resolution of algebraic inequalities that greatly reduces the synthesis complexity when compared to the state-of-the-art approaches that usually rely on solving many bilinear matrix inequalities. A numerical example illustrates the approach and the performance of the designed robust observer.
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11:00-11:20, Paper WeA06.4 | |
>Modeling and State Estimation for Lithium Sulfur Batteries As a Piecewise Affine System |
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Goujard, Guillaume | UC Berkeley |
Dangwal, Chitra | University of California Berkeley |
Gill, Preet | University of California Berkeley |
Kato, Dylan | University of California, Berkeley |
Moura, Scott | University of California, Berkeley |
Keywords: Estimation, Hybrid systems, Machine learning
Abstract: Lithium-sulfur (Li-S) is a promising battery chem- istry for applications demanding high energy densities, such as electrified aircraft and heavy-duty trucks, among others. A critical challenge in modeling the Li-S chemistry lies in the use of differential algebraic (DAE) equations for representing the electrochemical dynamics. Due to their constrained and stiff nature, these equations are not conducive to real-time state estimation. In this study, we propose a novel approach to constrained state estimation for Li-S batteries by integrating a piecewise affine (PWA) model into a moving horizon estimation (MHE) framework. We begin by deriving the PWA model using a linear tree algorithm based on data obtained from simulations of a calibrated DAE model. We further leverage the unique structural advantages of the proposed PWA model to formulate a real-time state estimation algorithm grounded in a mixed-integer quadratic program. Overall, our initial findings, based on a single constant current trajectory, demonstrate that our approach offers an accurate and computationally efficient method for modeling and state estimation of Li-S batteries. The coupled PWA-MHE framework effectively captures the dynamics of the DAE system, even in the presence of high observational noise (20mV).
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11:20-11:40, Paper WeA06.5 | |
>Regularization for Distributionally Robust State Estimation and Prediction |
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Brouillon, Jean-Sébastien | EPFL |
Dörfler, Florian | Swiss Federal Institute of Technology (ETH) Zurich |
Ferrari-Trecate, Giancarlo | Ecole Polytechnique Fédérale De Lausanne |
Keywords: Estimation, Filtering, Time-varying systems
Abstract: The increasing availability of sensing techniques provides a great opportunity for engineers to design state estimation methods, which are optimal for the system under observation and the observed noise patterns. However, these patterns often do not fulfill the assumptions of existing methods. We provide a direct method using samples of the noise to create a moving horizon observer for linear time-varying and nonlinear systems, which is optimal under the empirical noise distribution. Moreover, we show how to enhance the observer with distributional robustness properties in order to handle unmodeled components in the noise profile, as well as different noise realizations. We prove that, even though the design of distributionally robust estimators is a complex minmax problem over an infinite-dimensional space, it can be transformed into a regularized linear program using a system level synthesis approach. Numerical experiments with the Van der Pol oscillator show the benefits of not only using empirical samples of the noise to design the state estimator, but also of adding distributional robustness. We show that our method can significantly outperform state-of-the-art approaches under challenging noise distributions, including multi-modal and deterministic components.
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11:40-12:00, Paper WeA06.6 | |
>A Peaking Free Time-Varying High-Gain Observer with Reduced Sensitivity to Measurement Noise |
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Mousavi, Seyed Mohammadmoein | Queen's University |
Guay, Martin | Queens University |
Keywords: Observers for nonlinear systems, Nonlinear output feedback, Filtering
Abstract: This study is concerned with observer design for a class of Lipschitz nonlinear systems. A high-gain observer with a straightforward structure is proposed. As opposed to the well-known high gain observers, dynamic gains obtained are used to reduce the effect of peaking. In addition, the injection term of the observer is passed through a linear filter to reduce its sensitivity to noise. It is shown that the suggested observer is peaking free with respect to the initial conditions, while achieving the input to state stability with respect to measurement noise, as a HGO. The analysis of the steady-state response also shows that the proposed observer performs better in the presence of high-frequency noise. The simulation results compare the performance of the proposed method with some existing observers.
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WeA07 |
Simpor Junior 4813 |
Game Theory I |
Regular Session |
Chair: Hayakawa, Tomohisa | Tokyo Institute of Technology |
Co-Chair: Riess, Hans | Duke University |
|
10:00-10:20, Paper WeA07.1 | |
>Stability and Stabilization of Nash Equilibrium for Noncooperative Systems with Vector-Valued Payoff Functions |
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Guo, Zehui | Tokyo Institute of Technology |
Hayakawa, Tomohisa | Tokyo Institute of Technology |
Yan, Yuyue | Tokyo Institute of Technology |
Keywords: Game theory, Agents-based systems, Linear systems
Abstract: A zero-sum tax/subsidy approach and a necessary condition for stabilizing unstable Nash equilibria in pseudo-gradient-based noncooperative dynamical systems with vector-valued payoff functions are proposed. Specifically, we first present a necessary and sufficient condition for the Nash equilibrium of the noncooperative game with vector-valued payoff functions to be bounded. Then we give a sufficient condition for such Nash equilibrium to be stable. After that, we develop a framework where a system manager constructs a zero-sum tax/subsidy incentive structure by collecting taxes from one agent and giving the same amount of subsidy to the other agent to make the incentivized Nash equilibrium stable and bounded, which can make the trajectories converge to the interior of original Nash equilibrium set. Finally, we present a numerical example to illustrate the utility of the zero-sum tax/subsidy approach.
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10:20-10:40, Paper WeA07.2 | |
>A Nash Equilibrium Solution for Periodic Double Auctions |
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Manvi, Bharat | Tata Consultancy Services |
Subramanian, Easwar | Senior Scientist, TCS Research, Tata Consultancy Services, India |
Keywords: Game theory, Agents-based systems, Markov processes
Abstract: We consider a periodic double auction (PDA) setting where buyers of the auction have multiple (but finite)opportunities to procure multiple but fixed units of a commodity. The goal of each buyer participating in such auctions is to reduce their cost of procurement by planning their purchase across multiple rounds of the PDA. Formulating such optimal bidding strategies in a multi-agent periodic double auction setting is a challenging problem as such strategies involve planning across current and future auctions. In this work, we consider one such setup wherein the composite supply curve is known to all buyers. Specifically, for the complete information setting, we model the PDA as a Markov game and derive Markov perfect Nash equilibrium (MPNE) solution to devise an optimal bidding strategy for the case when each buyer is allowed to make one bid per round of the PDA. Thereafter, the efficacy of the Nash policies obtained is demonstrated with numerical experiments.
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10:40-11:00, Paper WeA07.3 | |
>The Cost of Informing Decision-Makers in Multi-Agent Maximum Coverage Problems with Random Resource Values |
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Ferguson, Bryce L. | University of California, Santa Barbara |
Paccagnan, Dario | Imperial College London |
Marden, Jason R. | University of California, Santa Barbara |
Keywords: Game theory, Agents-based systems, Uncertain systems
Abstract: The emergent behavior of a distributed system is conditioned by the information available to the local decision makers. Therefore, one may expect that providing decision makers with more information will improve system performance; in this work, we find that this is not necessarily the case. In multi-agent maximum coverage problems, we find that even when agents’ objectives are aligned with the global welfare, informing agents about the realization of the resource’s random values can reduce equilibrium performance by a factor of 1/2. This affirms an important aspect of designing distributed systems: information need be shared carefully. We further this understanding by providing lower and upper bounds on the ratio of system welfare when information is (fully or partially) revealed and when it is not, termed the value-of-informing. We then identify a trade-off that emerges when optimizing the performance of the best-case and worst-case equilibrium.
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11:00-11:20, Paper WeA07.4 | |
>Max-Plus Synchronization in Decentralized Trading Systems |
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Riess, Hans | Duke University |
Munger, Michael | Duke University |
Zavlanos, Michael M. | Duke University |
Keywords: Game theory, Algebraic/geometric methods, Discrete event systems
Abstract: We introduce a decentralized mechanism for pricing and exchanging alternatives constrained by transaction costs. We characterize the time-invariant solutions of a heat equation involving a (weighted) Tarski Laplacian operator, defined for max-plus matrix-weighted graphs, as approximate equilibria of the trading system. We study algebraic properties of the solution sets as well as convergence behavior of the dynamical system. We apply these tools to the "economic problem"' of allocating scarce resources among competing uses. Our theory suggests differences in competitive equilibrium, bargaining, or cost-benefit analysis, depending on the context, are largely due to differences in the way that transaction costs are incorporated into the decision-making process. We present numerical simulations of the synchronization algorithm (RRAggU), demonstrating our theoretical findings.
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11:20-11:40, Paper WeA07.5 | |
>Almost-Bayesian Quadratic Persuasion with a Scalar Prior |
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Massicot, Olivier | UIUC |
Langbort, Cedric | Univ of Illinois, Urbana-Champaign |
Keywords: Game theory, Communication networks, Uncertain systems
Abstract: In this article, we consider a problem of strategic communication between a sender (Alice) and a receiver (Bob) akin to the now-traditional model of Bayesian Persuasion intro- duced by Kamenica & Gentzkow, with the crucial difference that Bob is not assumed Bayesian. In lieu of the Bayesian assumption, Alice assumes that Bob behaves “almost like” a Bayesian agent, in some sense, without resorting to any specific model. Under this assumption, we study Alice’s strategy when both utilities are quadratic and the prior is scalar. We show that, contrary to the Bayesian case, Alice’s optimal response may be more subtle than revealing “all or nothing.” More precisely, Alice reveals the state of the world when it lies outside a specific interval, and nothing otherwise. This interval increases (and the amount of information shared decreases) as Bob further departs from Bayesianity, much to his detriment.
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11:40-12:00, Paper WeA07.6 | |
>Collaboration As a Mechanism for More Robust Strategic Classification |
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Jin, Kun | University of Michigan, Ann Arbor |
Huang, Ziyuan | University of Michigan |
Liu, Mingyan | University of Michigan |
Keywords: Game theory, Control of networks, Learning
Abstract: A conventional strategic classification problem takes on a Stackelberg form: a decision maker commits to a decision rule (e.g., in the form of a binary classifier) and agents best respond to the published decision rule by deciding on an effort level so as to maximize their chance of getting a favorable decision less the cost of the effort. This problem becomes significantly more complex when we allow agents access to two types of effort: honest (improvement actions) and dishonest (or cheating/gaming). While the former improves an agent's underlying unobservable states (e.g., certain types of qualification), the latter merely improves an agent's outward observable feature, serving as input to the classifier. Under the natural assumption that honest effort is more costly than cheating, prior work has shown that the decision maker has limited ability to mitigate cheating by simply adjusting the decision rule. In this paper, we consider a collaboration mechanism, which the decision maker establishes at a cost and offers to the agents together with the decision rule. In this case, an agent best responds by choosing not only its effort but also whether to participate in the mechanism and if so, with which other agents it wishes to form a connection or collaboration relation. While agents outside the mechanism remain independent of each other, those inside the mechanism are connected to a group of collaborators and enjoy positive externality in the form of a boost in their observable features and consequently enhanced probability of a favorable decision outcome. We show how the collaboration mechanism can induce agents to participate and take improvement actions over gaming and how it can benefit both sides. We also discuss the social values of the system, including social welfare, social qualification status, and the mechanism surplus.
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WeA08 |
Simpor Junior 4812 |
Optimal Control I |
Regular Session |
Chair: Cassandras, Christos G. | Boston University |
Co-Chair: Tanaka, Takashi | University of Texas at Austin |
|
10:00-10:20, Paper WeA08.1 | |
>Safe Q-Learning for Continuous-Time Linear Systems |
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Bandyopadhyay, Soutrik | Indian Institute of Technology Delhi |
Bhasin, Shubhendu | Indian Institute of Technology Delhi |
Keywords: Optimal control, Adaptive control, Constrained control
Abstract: Q-learning is a promising method for solving optimal control problems for uncertain systems without the explicit need for system identification. However, approaches for continuous-time Q-learning have limited provable safety guarantees, which restrict their applicability to real-time safety-critical systems. This paper proposes a safe Q-learning algorithm for partially unknown linear time-invariant systems to solve the linear quadratic regulator problem with user-defined state constraints. We frame the safe Q-learning problem as a constrained optimal control problem using reciprocal control barrier functions and show that such an extension provides a safety-assured control policy. To the best of our knowledge, Q-learning for continuous-time systems with state constraints has not yet been reported in the literature.
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10:20-10:40, Paper WeA08.2 | |
>A Bilevel Optimization Scheme for Persistent Monitoring |
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Hall, Jonas | Boston University |
Beaver, Logan E. | Boston University |
Cassandras, Christos G. | Boston University |
Andersson, Sean B. | Boston University |
Keywords: Optimal control, Autonomous systems, Optimization
Abstract: In this paper we study an infinite-horizon persistent monitoring problem in a two-dimensional mission space containing a finite number of statically placed targets, at each of which we assume a constant rate of uncertainty accumulation. Equipped with a sensor of finite range, the agent is capable of reducing the uncertainty of nearby targets. We derive a steady-state minimum time periodic trajectory over which each of the target uncertainties is driven down to zero during each visit. A hierarchical decomposition leads to purely local optimal control problems, coupled via boundary conditions. We optimize both the local trajectory segments as well as the boundary conditions in an on-line bilevel optimization scheme.
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|
10:40-11:00, Paper WeA08.3 | |
>Navigation with Shadow Prices to Optimize Multi Commodity Flow Rates |
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Boero, Ignacio | Univerisidad De La Republica |
Spasojevic, Igor | MIT |
del Castillo, Mariana | Facultad De Ingeniería, Universidad De La República |
Pappas, George J. | University of Pennsylvania |
Kumar, Vijay | University of Pennsylvania |
Ribeiro, Alejandro | University of Pennsylvania |
Keywords: Optimal control, Communication networks, Autonomous systems
Abstract: We propose a method for providing communication network infrastructure in autonomous multi-agent teams. In particular, we consider a set of communication agents that are placed alongside regular agents from the system. In order to find the optimal positions to place such agents, we define a flexible performance function that adapts to network requirements for different systems. We provide an algorithm based on shadow prices of a related convex optimization problem in order to arrive at a local maximum. We run the algorithm for three different performance functions associated to three practical scenarios, in which we show both the performance of the algorithm and the flexibility for different network requirements.
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11:00-11:20, Paper WeA08.4 | |
>Separable Approximations of Optimal Value Functions under a Decaying Sensitivity Assumption |
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Sperl, Mario | University of Bayreuth |
Saluzzi, Luca | Imperial College London |
Gruene, Lars | University of Bayreuth |
Kalise, Dante | Imperial College London |
Keywords: Optimal control, Computational methods
Abstract: An efficient approach for the construction of separable approximations of optimal value functions from interconnected optimal control problems is presented. The approach is based on assuming decaying sensitivities between subsystems, enabling a curse-of-dimensionality free approximation, for instance by deep neural networks.
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11:20-11:40, Paper WeA08.5 | |
>Economic Model Predictive Control of Water Distribution Systems with Solar Energy and Batteries |
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Zheng, Xiangyi | The University of Melbourne |
Wang, Ye | The University of Melbourne |
Weyer, Erik | Univ. of Melbourne |
Manzie, Chris | The University of Melbourne |
Keywords: Optimal control, Control applications, Smart grid
Abstract: Pumping in water distribution systems (WDSs) consumes a significant amount of power from the grid and may incur large electricity cost. WDSs with solar panels and batteries can greatly reduce the electricity cost by displacing the use of grid-based electricity with solar or stored energy, while also utilising water storage elements to allow selective pumping. A novel economic model predictive control (EMPC) scheme is proposed in this paper to facilitate optimal operation of pumps, batteries and solar panels in the WDSs. The proposed EMPC controller seeks to minimize the energy cost for water pumping while keeping the water levels in tanks and the battery state of charge within restricted limits. The EMPC is applied to an EPANET model of the Richmond Pruned Network, a Doyle Fuller Newman model of a lithium-ion battery, and simulated output from solar panels to to determine the efficacy of the proposed scheme.
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11:40-12:00, Paper WeA08.6 | |
>Simulator-Driven Deceptive Control Via Path Integral Approach |
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Patil, Apurva | The University of Texas at Austin |
Karabag, Mustafa O. | The University of Texas at Austin |
Tanaka, Takashi | University of Texas at Austin |
Topcu, Ufuk | The University of Texas at Austin |
Keywords: Optimal control, Cyber-Physical Security, Autonomous systems
Abstract: We consider a setting where a supervisor delegates an agent to perform a certain control task, while the agent is incentivized to deviate from the given policy to achieve its own goal. In this work, we synthesize the optimal deceptive policies for an agent who attempts to hide its deviations from the supervisor's policy. We study the deception problem in the continuous-state discrete-time stochastic dynamics setting and, using motivations from hypothesis testing theory, formulate a Kullback-Leibler control problem for the synthesis of deceptive policies. This problem can be solved using backward dynamic programming in principle, which suffers from the curse of dimensionality. However, under the assumption of deterministic state dynamics, we show that the optimal deceptive actions can be generated using path integral control. This allows the agent to numerically compute the deceptive actions via Monte Carlo simulations. Since Monte Carlo simulations can be efficiently parallelized, our approach allows the agent to generate deceptive control actions online. We show that the proposed simulation-driven control approach asymptotically converges to the optimal control distribution.
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|
WeA10 |
Roselle Junior 4713 |
Machine Learning I |
Regular Session |
Chair: Mahony, Robert | Australian National University, |
Co-Chair: Pappas, George J. | University of Pennsylvania |
|
10:00-10:20, Paper WeA10.1 | |
>Reprojection Methods for Koopman-Based Modelling and Prediction |
|
van Goor, Pieter | Australian National University |
Mahony, Robert | Australian National University, |
Schaller, Manuel | Technische Universität Ilmenau |
Worthmann, Karl | Technische Universität Ilmenau |
Keywords: Machine learning, Algebraic/geometric methods, Predictive control for nonlinear systems
Abstract: Extended Dynamic Mode Decomposition (eDMD) is a powerful tool to generate data-driven surrogate models for the prediction and control of nonlinear dynamical systems in the Koopman framework. In eDMD a compression of the lifted system dynamics on the space spanned by finitely many observables is computed, in which the original space is embedded as a low-dimensional manifold. While this manifold is invariant for the infinite-dimensional Koopman operator, this invariance is typically not preserved for its eDMD-based approximation. Hence, an additional (re-)projection step is often tacitly incorporated to improve the prediction capability. We propose a novel framework for consistent reprojectors respecting the underlying manifold structure. Further, we present a new geometric reprojector based on maximum-likelihood arguments, which significantly enhances the approximation accuracy and preserves known finite-data error bounds.
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|
10:20-10:40, Paper WeA10.2 | |
>Robust Meta-Learning of Vehicle Yaw Rate Dynamics Via Conditional Neural Processes |
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Ullrich, Lars | Chair of Automatic Control, Friedrich-Alexander-Universität Erla |
Völz, Andreas | Friedrich-Alexander-University Erlangen-Nürnberg |
Graichen, Knut | University Erlangen-Nürnberg (FAU) |
Keywords: Machine learning, Autonomous vehicles, Data driven control
Abstract: Trajectory planners of autonomous vehicles usually rely on physical models to predict the vehicle behavior. However, despite their suitability, physical models have some shortcomings. On the one hand, simple models suffer from larger model errors and more restrictive assumptions. On the other hand, complex models are computationally more demanding and depend on environmental and operational parameters. In each case, the drawbacks can be associated to a certain degree to the physical modeling of the yaw rate dynamics. Therefore, this paper investigates the yaw rate prediction based on conditional neural processes (CNP), a data-driven meta-learning approach, to simultaneously achieve low errors, adequate complexity and robustness to varying parameters. Thus, physical models can be enhanced in a targeted manner to provide accurate and computationally efficient predictions to enable safe planning in autonomous vehicles. High fidelity simulations for a variety of driving scenarios and different types of cars show that CNP makes it possible to employ and transfer knowledge about the yaw rate based on current driving dynamics in a human-like manner, yielding robustness against changing environmental and operational conditions.
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|
10:40-11:00, Paper WeA10.3 | |
>Combinatorial Optimization Approach to Client Scheduling for Federated Learning |
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Omori, Tomohito | Kyoto University |
Kashima, Kenji | Kyoto University |
Keywords: Machine learning, Control over communications, Optimization algorithms
Abstract: For machine learning in situations where data is scattered and cannot be aggregated, federated learning, in which aggregators and agents send and receive model parameters, is one of the most promising methods. The scheduling problem of deciding which agents to communicate with has been studied in various ways, but it is not easy to solve due to its combinatorial optimization nature. In this letter, we attempt to solve this scheduling problem using combinatorial optimization theory. Specifically, we propose an efficient exact solution method based on dynamic programming and a greedy method whose superiority is confirmed by numerical examples. We also discuss the applicability of the proposed methods to a more realistic federated learning setting.
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|
11:00-11:20, Paper WeA10.4 | |
>Robust Safe Reinforcement Learning under Adversarial Disturbances |
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Li, Zeyang | Tsinghua University |
Hu, Chuxiong | Tsinghua University |
Li, Shengbo Eben | Tsinghua University |
Cheng, Jia | Tsinghua University |
Wang, Yunan | Tsinghua University |
Keywords: Machine learning, Data driven control, Constrained control
Abstract: Safety is a primary concern when applying reinforcement learning to real-world control tasks, especially in the presence of external disturbances. However, existing safe reinforcement learning algorithms rarely account for external disturbances, limiting their applicability and robustness in practice. To address this challenge, this paper proposes a robust safe reinforcement learning framework that tackles worst-case disturbances. First, this paper presents a policy iteration scheme to solve for the robust invariant set, i.e., a subset of the safe set, where persistent safety is only possible for states within. The key idea is to establish a two-player zero-sum game by leveraging the safety value function in Hamilton-Jacobi reachability analysis, in which the protagonist (i.e., control inputs) aims to maintain safety and the adversary (i.e., external disturbances) tries to break down safety. This paper proves that the proposed policy iteration algorithm converges monotonically to the maximal robust invariant set. Second, this paper integrates the proposed policy iteration scheme into a constrained reinforcement learning algorithm that simultaneously synthesizes the robust invariant set and uses it for constrained policy optimization. This algorithm tackles both optimality and safety, i.e., learning a policy that attains high rewards while maintaining safety under worst-case disturbances. Experiments on classic control tasks show that the proposed method achieves zero constraint violation with learned worst-case adversarial disturbances, while other baseline algorithms violate the safety constraints substantially. Our proposed method also attains comparable performance as the baselines even in the absence of the adversary.
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11:20-11:40, Paper WeA10.5 | |
>Uncertainty Quantification for Learning-Based MPC Using Weighted Conformal Prediction |
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Chee, Kong Yao | University of Pennsylvania |
Hsieh, M. Ani | University of Pennsylvania |
Pappas, George J. | University of Pennsylvania |
Keywords: Machine learning, Identification for control, Predictive control for nonlinear systems
Abstract: Nonlinear model predictive control (MPC) is an established control framework that not only provides a systematic way to handle state and input constraints, but also offers the flexibility to incorporate data-driven models. With the proliferation of machine learning techniques, there is an uptrend in the development of learning-based MPC, with neural networks (NN) being an important cornerstone. Although it has been shown that NNs are expressive enough to model the dynamics of complex systems and produce accurate state predictions, these predictions often do not include uncertainty estimates or have practical finite sample guarantees. In contrast to existing work that either requires the data samples to be exchangeable or relies on properties of the underlying data distribution, we propose an approach that utilizes weighted conformal prediction to alleviate these assumptions and to synthesize provably valid, finite-sample uncertainty estimates for data-driven dynamics models, in a distribution-free manner. These uncertainty estimates are generated online and incorporated into a novel uncertainty-aware learning-based MPC framework. Through a case study with a cartpole system controlled by a state-of-the-art learning-based MPC framework, we demonstrate that our approach not only provides well-calibrated uncertainty estimates, but also enhances the closed-loop performance of the system.
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11:40-12:00, Paper WeA10.6 | |
>Federated TD Learning Over Finite-Rate Erasure Channels: Linear Speedup under Markovian Sampling |
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Dal Fabbro, Nicolò | Università Degli Studi Di Padova |
Mitra, Aritra | University of Pennsylvania |
Pappas, George J. | University of Pennsylvania |
Keywords: Machine learning, Large-scale systems, Communication networks
Abstract: Federated learning (FL) has recently gained much attention due to its effectiveness in speeding up supervised learning tasks under communication and privacy constraints. However, whether similar speedups can be established for reinforcement learning remains much less understood theoretically. Towards this direction, we study a federated policy evaluation problem where agents communicate via a central aggregator to expedite the evaluation of a common policy. To capture typical communication constraints in FL, we consider finite capacity up-link channels that can drop packets based on a Bernoulli erasure model. Given this setting, we propose and analyze QFedTD - a quantized federated temporal difference learning algorithm with linear function approximation. Our main technical contribution is to provide a finite-sample analysis of QFedTD that (i) highlights the effect of quantization and erasures on the convergence rate; and (ii) establishes a linear speedup w.r.t. the number of agents under Markovian sampling. Notably, while different quantization mechanisms and packet drop models have been extensively studied in the FL, distributed optimization, and networked control systems literature, our work is the first to provide a non-asymptotic analysis of their effects in multi-agent and federated reinforcement learning.
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WeA12 |
Roselle Junior 4711 |
Cooperative Control I |
Regular Session |
Chair: Shao, Jinliang | University of Electronic Science and Technology of China, Chengdu |
Co-Chair: He, Jianping | Shanghai Jiao Tong University |
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10:00-10:20, Paper WeA12.1 | |
>Simultaneous Synchronization and Topology Identification of Complex Dynamical Networks |
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Restrepo, Esteban | CNRS, INRIA Rennes – Bretagne Atlantique |
Wang, Nana | Royal Institute of Technology (KTH) |
Dimarogonas, Dimos V. | KTH Royal Institute of Technology |
Keywords: Cooperative control, Adaptive control, Identification
Abstract: We propose a new method for simultaneous synchronization and topology identification of a complex dynamical network that relies on the edge-agreement framework and on adaptive-control approaches by design of an auxiliary network. Our method guarantees the identification of the unknown topology and it guarantees that once the topology is identified the complex network achieves synchronization. Under our identification algorithm we are able to provide stability results for the estimation errors in the form of uniform semiglobal practical asymptotic stability. Finally, we demonstrate the effectiveness of our approach with an illustrating example.
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10:20-10:40, Paper WeA12.2 | |
>Topology-Preserving Second-Order Consensus: A Strategic Compensation Approach |
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Wang, Zitong | Shanghai Jiao Tong University |
Li, Yushan | Shanghai Jiao Tong University |
Duan, Xiaoming | Shanghai Jiao Tong University |
He, Jianping | Shanghai Jiao Tong University |
Keywords: Cooperative control, Agents-based systems, Cyber-Physical Security
Abstract: The interaction topology plays a significant role in the collaboration of multi-agent systems. How to preserve the topology against inference attacks has become an imperative task for security concerns. In this paper, we propose a distributed topology-preserving algorithm for second-order multiagent systems by adding noisy inputs. The major novelty is that we develop a strategic compensation approach to overcome the noise accumulation issue in the second-order dynamic process while ensuring the exact second-order consensus. Specifically, we design two distributed compensation strategies that make the topology more invulnerable against inference attacks. Furthermore, we derive the relationship between the inference error and the number of observations by taking the ordinary least squares estimator as a benchmark. Extensive simulations are conducted to verify the topology-preserving performance of the proposed algorithm.
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10:40-11:00, Paper WeA12.3 | |
>An Adaptive Distributed Observer for a Class of Discrete-Time Uncertain Linear Systems Over Acyclic Digraphs |
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Liu, Tao | Southern University of Science and Technology |
Huang, Jie | The Chinese University of Hong Kong |
Keywords: Cooperative control, Adaptive systems, Uncertain systems
Abstract: This paper proposes an adaptive distributed observer for a class of discrete-time uncertain linear leader systems. The leader system is assumed to be neutrally stable with unknown parameters in the system matrix. Such a leader system can produce multi-tone sinusoidal signals with unknown frequencies, magnitudes, and phases. Under the assumption that the digraph of the communication network is a spanning tree with the leader system as the root, the proposed adaptive distributed observer is shown to be capable of estimating over the communication network not only the leader's state, but also the unknown parameters of the leader's system matrix.
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11:00-11:20, Paper WeA12.4 | |
>Mutualistic Interactions in Heterogeneous Multi-Agent Systems |
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Nguyen, Alexander A. | University of California, Irvine |
Jabbari, Faryar | Univ. of California at Irvine |
Egerstedt, Magnus | University of California, Irvine |
Keywords: Cooperative control, Agents-based systems, Autonomous robots
Abstract: This paper presents a collaboration strategy that enables heterogeneous agents, i.e., different capabilities and dynamics, to accomplish tasks by working together. The collaboration between multiple agents is inspired by the ecological concept known as a mutualism, an interaction between two or more species that benefits everyone involved. A collaborative act is made possible through the composition of barrier functions, which allows the heterogeneous agents to work together safely. Moreover, a measure of collaborative potential is established to assess the merit of agents interacting with each other. Furthermore, the collaboration framework is provided for a general multi-agent setting. Finally, the collaboration framework's efficacy is demonstrated in two case studies that necessitate collaboration between the heterogeneous agents to complete their respective tasks.
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11:20-11:40, Paper WeA12.5 | |
>Bipartite Flocking Control for Multi-Agent Systems with Switching Topologies and Time Delays under Coopetition Interactions |
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Ma, Zhuangzhuang | University of Electronic Science and Technology of China |
Li, Bowen | University of Electronic Science and Technology of China |
Shao, Jinliang | University of Electronic Science and Technology of China, Chengd |
Cheng, Yuhua | University of Electronic Science and Technology of China |
Zheng, Wei Xing | Western Sydney University |
Keywords: Cooperative control, Agents-based systems, Communication networks
Abstract: This paper investigates the bipartite flocking behavior of multi-agent systems with coopetition interactions, where communications between agents are described by signed digraphs. The scenario with switching topologies due to the movement of agents, and time delays caused by the limited data transmission capability, is considered comprehensively. Nonlinear weight functions are designed to describe the relationship between the communication distance of agents and the coopetition degree in real biological networks. A distributed update rule based on the neighbors' information and the designed weight functions is proposed. By the aid of the graph theory and sub-stochastic matrix properties, the effectiveness of the proposed update rule is proved theoretically, and the algebraic conditions for achieving the bipartite flocking behavior are obtained. Finally, the theoretical results are verified by numerical simulations.
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11:40-12:00, Paper WeA12.6 | |
>Finite-Time Topology Identification for Complex Dynamical Networks |
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Wang, Nana | Royal Institute of Technology (KTH) |
Dimarogonas, Dimos V. | KTH Royal Institute of Technology |
Keywords: Cooperative control, Adaptive control, Identification for control
Abstract: This paper presents a finite-time topology identification method for complex dynamical networks. This method prevents the difficulty of verifying linear independence conditions and ensures the success of accurate topology identification. The topology identification scheme first renders the error dynamics between the networks and reference signals zero in finite time, and afterward, the topology is estimated by building an auxiliary network. The identification of topology is achieved once a relaxed excitation condition holds. The excitation condition is guaranteed by the proposed tracking control scheme. A finite-time topology identification and synchronization scheme for complex systems is further proposed where synchronization is realized by removing the exciting signals after the identification of the topology. At last, the simulation results verify the feasibility of the proposed method.
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WeA13 |
Roselle Junior 4613 |
Identification in Networked Systems |
Invited Session |
Chair: Hendrickx, Julien M. | UCLouvain |
Co-Chair: Van den Hof, Paul M.J. | Eindhoven University of Technology |
Organizer: Hendrickx, Julien M. | UCLouvain |
Organizer: Van den Hof, Paul M.J. | Eindhoven University of Technology |
Organizer: Vizuete, Renato | UCLouvain |
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10:00-10:20, Paper WeA13.1 | |
>Local Identification in Dynamic Networks Using a Multi-Step Least Squares Method (I) |
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Fonken, Stefanie J.M. | Eindhoven University of Technology |
Ramaswamy, Karthik R. | Eindhoven University of Technology |
Van den Hof, Paul M.J. | Eindhoven University of Technology |
Keywords: Closed-loop identification, Large-scale systems, Networked control systems
Abstract: For identification of a single module in a linear dynamic network with correlated disturbances different methods are available in a prediction error setting. While indirect methods fully rely on the presence of a sufficient number of external excitation signals for achieving data-informativity, the local direct method with a MIMO predictor model can exploit also non-measured disturbance signals for data-informativity. However, a simple two-node example shows that this local direct method can also be conservative in terms of the number of external excitation signals that is required. Inspired by a recently introduced multi-step method for full network identification, we present a multi-step least squares method for single module identification. In a first indirect step a model is estimated that is used to reconstruct the innovation on a set of output signals, which in a second step is used to directly estimate the module dynamics with a MISO predictor model. The resulting path based conditions for data-informativity show that the multi-step method requires a smaller number of excitation signals for data-informativity than the local direct method.
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10:20-10:40, Paper WeA13.2 | |
>Connecting Graphical Notions of Separation and Statistical Notions of Independence for Topology Reconstruction (I) |
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Materassi, Donatello | University of Minnesota |
Keywords: Network analysis and control, Stochastic systems, Identification
Abstract: Over the last decade, there has been a significant increase in interest for techniques that can infer the connectivity structure of a network of dynamic systems. This article examines a flexible class of network systems and reviews various methods for reconstructing their underlying graph. However, these techniques typically only guarantee consistent reconstruction if additional assumptions on the model are made, such as the network topology being a tree, the dynamics being strictly causal, or the absence of directed loops in the network. The central theme of the article is to reinterpret these methodologies under a unified framework where a graphical notion of separation between nodes of the underlying graph corresponds to a probabilistic notion of separation among associated stochastic processes. This duality property enables the creation of algorithms for reconstructing the network topology. The article also endeavors to connect the considered class of networks with other semantically similar network models.
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10:40-11:00, Paper WeA13.3 | |
>Nonlinear Network Identifiability: The Static Case (I) |
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Vizuete, Renato | UCLouvain |
Hendrickx, Julien M. | UCLouvain |
Keywords: Network analysis and control, Identification
Abstract: We analyze the problem of network identifiability with nonlinear functions associated with the edges. We consider a static model for the output of each node and by assuming a perfect identification of the function associated with the measurement of a node, we provide conditions for the identifiability of the edges in a specific class of functions. First, we analyze the identifiability conditions in the class of all nonlinear functions and show that even for a path graph, it is necessary to measure all the nodes except by the source. Then, we consider analytic functions satisfying f(0)=0 and we provide conditions for the identifiability of paths and trees. Finally, by restricting the problem to a smaller class of functions where none of the functions is linear, we derive conditions for the identifiability of directed acyclic graphs. Some examples are presented to illustrate the results.
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11:00-11:20, Paper WeA13.4 | |
>Boolean Internal Structure Reconstruction from Collapsed Small-Scale Networks (I) |
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Teng, Basi | University of Cambridge |
Zhao, Yuxuan | Huazhong University of Science and Technology |
Yuan, Ye | Huazhong University of Science and Technology |
Goncalves, Jorge | University of Luxembourg |
Keywords: Boolean control networks and logic networks, Identification, Large-scale systems
Abstract: Dynamic network reconstruction aims to infer network structure from input-output data. Dynamical structure functions (DSFs) have been introduced to represent structural information between observable nodes of linear time-invariant systems. However, reconstructing large-scale DSFs can be difficult since most existing methods do not scale. Instead of inferring large DSFs directly, an alternative approach is to reconstruct many small-scale DSFs that are easier to infer. Given a sparsity constraint on the network, this paper proposes a necessary and sufficient condition for perfect reconstruction of the Boolean network using collapsed small-scale networks. For sparse networks, such as gene regulatory networks, this method can significantly reduce time and computational costs of Boolean network inference for most links in the network, especially when using parallel computing.
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11:20-11:40, Paper WeA13.5 | |
>Optimal PMU Placement for Voltage Estimation in Partially Known Power Networks (I) |
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Mishra, Aditya | University of California, San Diego |
de Callafon, Raymond A. | Univ. of California, San Diego |
Keywords: Estimation, Power systems, Optimization
Abstract: Observability of all bus voltages in a power network enables overall monitoring and fault detection of power flow. Information on this voltage state is often a combination of voltage, current measurements obtained by Phasor Measurement Units (PMUs) and state estimation techniques that use admittance information of the connections between nodes within the power network. Voltage state estimation is a challenge for a power network in which limited PMUs need to be combined with partially know network admittance information. The challenge lies in choosing locations of PMUs such that full voltage state reconstruction is possible, despite the lack of full knowledge on network admittance information. This paper proposes a methodology of placing PMUs across a network with incomplete network admittance information that guarantees complete observability of the voltage states. The methodology separates network nodes in distinct nodal sets based on voltage, current and admittance information. Permutations of the sets are uses to establish the minimum number of PMUs required for full voltage state observability for a power network with partially known admittance information. Subsequently, an additional optimal placement can be used to further minimize the variance of the estimated voltage states. The proposed PMU placement approach is tested on a modified IEEE-14 bus with incomplete network admittance information.
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11:40-12:00, Paper WeA13.6 | |
>Latent Dynamic Networked System Identification with High-Dimensional Networked Data (I) |
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Yu, Jiaxin | CityU of Hong Kong |
Mo, Yanfang | City University of Hong Kong |
Qin, S. Joe | Lingnan University |
Keywords: Identification, Networked control systems, Statistical learning
Abstract: Networked dynamic systems are ubiquitous in various domains such as industrial processes, social networks, and biological systems. These systems produce high-dimensional data that reflect the complex interactions among the network nodes with rich sensor measurements. In this paper, we propose a novel algorithm for latent dynamic networked system identification that leverages the network structure and performs dimension reduction for each node via dynamic latent variables (DLV). The algorithm assumes that the DLVs of each node have an auto-regressive model with exogenous input and interactions from other nodes. The DLVs of each node are extracted to capture the most predictable latent variables in the high dimensional data, while the residual factors are not predictable. The advantage of the proposed framework is demonstrated on an industrial process network for system identification and dynamic data analytics.
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WeA14 |
Roselle Junior 4612 |
Modeling, Analysis, and Control of Complex Systems |
Invited Session |
Chair: Ye, Mengbin | Curtin University |
Co-Chair: Cao, Ming | University of Groningen |
Organizer: Ye, Mengbin | Centre for Optimisation and Decision Science, Curtin University |
Organizer: Zino, Lorenzo | Politecnico Di Torino |
Organizer: Cao, Ming | University of Groningen |
Organizer: Leonard, Naomi Ehrich | Princeton University |
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10:00-10:20, Paper WeA14.1 | |
>Species Coexistence and Extinction Resulting from Higher-Order Lokta-Volterra Two-Faction Competition (I) |
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Cui, Shaoxuan | University of Groningen |
Zhao, Qi | Qingdao University of Science and Technology |
Jardón-Kojakhmetov, Hildeberto | University of Groningen |
Cao, Ming | University of Groningen |
Keywords: Biological systems, Stability of nonlinear systems, Agents-based systems
Abstract: It is known that the effect of species' density on species' growth is non-additive in real ecological systems. This challenges the conventional Lokta-Volterra model, where the interactions are always pairwise and their effects are additive. To address this challenge, we introduce HOIs (Higher-Order Interactions) and are able to capture, for example, the indirect effect of one species on a second one correlating to a third species. Towards this end, we propose a purely cooperative higher-order Lokta-Volterra model and a higher-order Lokta-Volterra two-faction competition model. By utilizing the theory of monotone systems, we provide stability conditions for both models. The stability analysis further shows that small HOIs usually promote the coexistence of all species, while the extinction of some species is usually caused by a huge difference among the higher-order competitive terms. Finally, illustrative numerical examples are provided to highlight our contributions.
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10:20-10:40, Paper WeA14.2 | |
>Population Games with Replicator Dynamics under Event-Triggered Payoff Provider and a Demand Response Application |
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Martinez-Piazuelo, Juan | Universitat Politècnica De Catalunya |
Ananduta, Wicak | Flemish Institute for Technological Research (VITO) |
Ocampo-Martinez, Carlos | Universitat Politècnica De Catalunya (UPC) |
Grammatico, Sergio | Delft University of Technology |
Quijano, Nicanor | Universidad De Los Andes |
Keywords: Game theory, Hybrid systems, Optimization
Abstract: We consider a large population of decision makers that choose their evolutionary strategies based on simple pairwise imitation rules. We describe such a dynamic process by the replicator dynamics. Differently from the available literature, where the payoffs signals are assumed to be updated continuously, we consider a more realistic scenario where they are updated occasionally. Our main technical contribution is to devise two event-triggered communication schemes with asymptotic convergence guarantees to a Nash equilibrium. Finally, we show how our proposed approach is applicable as an efficient distributed demand response mechanism.
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10:40-11:00, Paper WeA14.3 | |
>Structural Properties of Optimal Risk-Aware Controllers for Spatially Invariant Systems |
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Arbelaiz, Juncal | Princeton University |
Bamieh, Bassam | Univ. of California at Santa Barbara |
Leonard, Naomi Ehrich | Princeton University |
Keywords: Control of networks, Distributed control, Optimal control
Abstract: We analyze the optimal Linear Exponential Quadratic Gaussian (LEQG) control synthesis of a spatially distributed system with a shift invariance in its spatial coordinate, perturbed by additive white Gaussian noise. We refer to such a system as spatially invariant. The LEQG framework accounts for the risk attitude of the controller in its synthesis by appropriate selection of the value of a free parameter, providing the possibility to continuously tune the degree of risk awareness of the controller. We prove important structural properties of the optimal LEQG control problem for spatially invariant systems, namely that: (i) the optimal LEQG control gain is spatially invariant itself; (ii) the LEQG control synthesis problem is equivalent to a family of decoupled LEQG optimization problems of smaller dimension; and (iii) under some further assumptions, the optimal LEQG control gain is spatially localized. Through a case study, we illustrate how the risk attitude of the controller tunes the degree of spatial localization of the optimal control gain. We argue that the proven structural properties can be leveraged to reduce the computational complexity of obtaining the optimal LEQG control gain in large-scale systems and to design distributed risk-aware controller implementations.
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11:00-11:20, Paper WeA14.4 | |
>On Adaptive-Gain Control of Replicator Dynamics in Population Games (I) |
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Zino, Lorenzo | Politecnico Di Torino |
Ye, Mengbin | Centre for Optimisation and Decision Science, Curtin University |
Rizzo, Alessandro | Politecnico Di Torino |
Calafiore, Giuseppe C. | Politecnico Di Torino |
Keywords: Game theory, Nonlinear systems, Adaptive control
Abstract: Controlling evolutionary game-theoretic dynamics is a problem of paramount importance for the systems and control community, with several applications spanning from social science to engineering. Here, we study a population of individuals who play a generic 2-action matrix game, and whose actions evolve according to a replicator equation - a nonlinear ordinary differential equation that captures salient features of the collective behavior of the population. Our objective is to steer such a population to a specified equilibrium that represents a desired collective behavior - e.g., to promote cooperation in the prisoner's dilemma. To this aim, we devise an adaptive-gain controller, which regulates the system dynamics by adaptively changing the entries of the payoff matrix of the game. The adaptive-gain controller is tailored according to distinctive features of the game, and conditions to guarantee global convergence to the desired equilibrium are established.
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11:20-11:40, Paper WeA14.5 | |
>Propagation of Stubborn Opinions on Signed Graphs (I) |
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Razaq, Muhammad Ahsan | Linkoping University |
Altafini, Claudio | Linkoping University |
Keywords: Network analysis and control, Agents-based systems, Communication networks
Abstract: This paper addresses the problem of propagation of opinions in a Signed Friedkin-Johnsen (SFJ) model, i.e., an opinion dynamics model in which the agents are stubborn and the interaction graph is signed. We provide sufficient conditions for the stability of the SFJ model and for convergence to consensus of a concatenation of such SFJ models.
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11:40-12:00, Paper WeA14.6 | |
>Nash-Equilibrium Seeking Algorithm for Power Allocation Games on Networks of International Relations (I) |
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Zhang, Chuanzhe | Peking University |
Li, Yuke | Peking University |
Mei, Wenjun | Peking University |
Keywords: Game theory, Network analysis and control, Optimization algorithms
Abstract: In the field of international security, understanding the strategic interactions between countries within a networked context is crucial. Our previous research has introduced a “games-on-signed graphs” framework to analyze these interactions. While the framework is intended to be basic and general, there is much left to be explored, particularly in capturing the complexity of strategic scenarios in international relations. Our paper aims to fill this gap in two key ways. First, we modify the existing preference axioms to allow for a more nuanced understanding of how countries pursue self-survival, defense of allies, and offense toward adversaries. Second, we introduce a novel algorithm that proves the existence of a pure strategy Nash equilibrium for these revised games. To validate our model, we employ historical data from the year 1940 as the game input and predict countries’ survivability. Our contributions thus extend the real-world applicability of the original framework, offering a more comprehensive view of strategic interactions in a networked security environment.
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WeA16 |
Peony Junior 4512 |
Computational Techniques for Automation in Energy Systems |
Invited Session |
Chair: Guo, Yi | ETH Zürich |
Co-Chair: Jiang, Yuning | EPFL |
Organizer: Guo, Yi | ETH Zürich |
Organizer: Jiang, Yuning | EPFL |
Organizer: Mallada, Enrique | Johns Hopkins University |
Organizer: Jones, Colin N. | EPFL |
Organizer: Hug, Gabriela | ETH Zurich |
Organizer: Lygeros, John | ETH Zurich |
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10:00-10:20, Paper WeA16.1 | |
>MIMO Grid Impedance Identification of Three-Phase Power Systems: Parametric vs. Nonparametric Approaches (I) |
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Häberle, Verena | ETH Zurich |
Huang, Linbin | ETH Zurich |
He, Xiuqiang | ETH Zurich |
Prieto-Araujo, Eduardo | CITCEA-UPC |
Smith, Roy S. | ETH Zurich |
Dörfler, Florian | Swiss Federal Institute of Technology (ETH) Zurich |
Keywords: Power systems, Power electronics, Identification
Abstract: A fast and accurate grid impedance measurement of three-phase power systems is crucial for online assessment of power system stability and adaptive control of grid-connected converters. Existing grid impedance measurement approaches typically rely on pointwise sinusoidal injections or sequential wideband perturbations to identify a nonparametric grid impedance curve via fast Fourier computations in the frequency domain. This is not only time-consuming, but also inaccurate during time-varying grid conditions, while on top of that, the identified nonparametric model cannot be immediately used for stability analysis or control design. To tackle these problems, we propose to use parametric system identification techniques (e.g., prediction error or subspace methods) to obtain a parametric impedance model directly from time-domain current and voltage data. Our approach relies on injecting wideband excitation signals in the converter's controller and allows to accurately identify the grid impedance in closed loop within one injection and measurement cycle. Even though the underlying parametric system identification techniques are well-studied in general, their utilization in a grid impedance identification setup poses specific challenges, is vastly underexplored, and has not gained adequate attention in urgent and timely power systems applications. To this end, we demonstrate in numerical experiments how the proposed parametric approach can accomplish a significant improvement compared to prevalent nonparametric methods.
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10:20-10:40, Paper WeA16.2 | |
>Tractable Identification of Electric Distribution Networks (I) |
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Stanojev, Ognjen | ETH Zürich |
Werner, Lucien | California Institute of Technology |
Low, Steven | California Institute of Technology |
Hug, Gabriela | ETH Zurich |
Keywords: Power systems, Smart grid, Network analysis and control
Abstract: The identification of distribution network topology and parameters is a critical problem that lays the foundation for improving network efficiency, enhancing reliability, and increasing its capacity to host distributed energy resources. Network identification problems often involve estimating a large number of parameters based on highly correlated measurements, resulting in an ill-conditioned and computationally demanding estimation process. We address these challenges by proposing two admittance matrix estimation methods. In the first method, we use the eigendecomposition of the admittance matrix to generalize the notion of stationarity to electrical signals and demonstrate how the stationarity property can be used to facilitate a maximum a posteriori estimation procedure. We relax the stationarity assumption in the second proposed method by employing Linear Minimum Mean Square Error (LMMSE) estimation. Since LMMSE estimation is often ill-conditioned, we introduce an approximate well-conditioned solution. Our quantitative results demonstrate the improvement in computational efficiency compared to the state-of-the-art methods while preserving the estimation accuracy.
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10:40-11:00, Paper WeA16.3 | |
>Safe Zeroth-Order Optimization Using Linear Programs (I) |
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Guo, Baiwei | EPF Lausanne |
Wang, Yang | Delft University of Technology |
Jiang, Yuning | EPFL |
Kamgarpour, Maryam | EPFL |
Ferrari-Trecate, Giancarlo | Ecole Polytechnique Fédérale De Lausanne |
Keywords: Optimization, Power systems, Data driven control
Abstract: To solve unmodeled optimization problems with hard constraints, this paper proposes a novel zeroth-order approach called Safe Zeroth-order Optimization using Linear Programs (SZO-LP). The SZO-LP method solves a linear program in each iteration to find a descent direction, followed by a step length determination. We prove that, under mild conditions, the iterates of SZO-LP have an accumulation point that is also the primal of a KKT pair. We then apply SZO-LP to solve an Optimal Power Flow (OPF) problem on the IEEE 30-bus system. The results demonstrate that SZO-LP requires less computation time and samples compared to state-of-the-art approaches.
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11:00-11:20, Paper WeA16.4 | |
>Battery Optimization for Power Systems: Feasibility and Optimality (I) |
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Elsaadany, Mazen | University of Vermont |
Almassalkhi, Mads | University of Vermont |
Keywords: Optimization, Modeling, Power systems
Abstract: The deployment of battery energy storage systems (BESS) is necessary to integrate terawatts of renewable generation while supporting grid resilience and reliability efforts. Optimizing battery dispatch requires predictive battery models that accurately characterize the battery state of charge (SOC) to ensure that the battery operates within the energy and power limits and avoids unexpected saturation effects. Furthermore, most BESS are unable to simultaneously charge and discharge, which begets an additional, non-convex complementary constraint. This paper presents and compares recently developed predictive battery models that side-step the non-convexity while providing supporting analysis on modeling error and optimal parameter selection. Specifically, insights for four different predictive BESS formulations are presented, including non-linear, mixed-integer, linear convex relaxation, and linear robust formulations. Additionally, two two-stage approaches are also considered. Analysis is conducted on optimal parameter selection for two of the methods, as well, as providing a new and improved SOC error bound on the relaxed formulation and the role of sustainability constraints on the robust formulation. Through the lens of relevant BESS use-cases, the paper discusses optimality and feasibility guarantees between the different models and provides extensive simulation-based analysis.
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11:20-11:40, Paper WeA16.5 | |
>Leveraging Predictions in Power System Frequency Control: An Adaptive Approach (I) |
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Cui, Wenqi | University of Washington |
Shi, Guanya | Carnegie Mellon University |
Shi, Yuanyuan | University of California San Diego |
Zhang, Baosen | University of Washington |
Keywords: Power systems, Learning
Abstract: Ensuring the frequency stability of electric grids with increasing renewable resources is a key problem in power system operations. In recent years, a number of advanced controllers have been designed to optimize frequency control. These controllers, however, almost always assume that the net load in the system remains constant over a sufficiently long time. Given the intermittent and uncertain nature of renewable resources, it is becoming important to explicitly consider net load that is time-varying. This paper proposes an adaptive approach to frequency control in power systems with significant time-varying net load. We leverage the advances in short-term load forecasting, where the net load in the system can be accurately predicted using weather and other features. We integrate these predictions into the design of adaptive controllers, which can be seamlessly combined with most existing controllers including conventional droop control and emerging neural network-based controllers. We prove that the overall control architecture achieves frequency restoration decentralizedly. Case studies verify that the proposed method improves both transient and frequency-restoration performances compared to existing approaches.
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11:40-12:00, Paper WeA16.6 | |
>Fast Constraint Screening for Multi-Interval Unit Commitment (I) |
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He, Xuan | Hong Kong University of Science and Technology (Guangzhou) |
Tian, Jiayu | Sun Yat-Sen University |
Zhang, Yufan | University of California, San Diego |
Wen, Honglin | Shanghai Jiaotong University |
Chen, Yize | Hong Kong University of Science and Technology |
Keywords: Power systems, Power generation, Machine learning
Abstract: Power systems Unit Commitment (UC) problem determines the generator commitment schedule and dispatch decisions for power networks based on forecasted electricity demand. However, with the increasing penetration of renewables and stochastic demand behaviors, it becomes challenging to solve the large-scale, multi-interval UC problem in an efficient manner. The main objective of this paper is to propose a fast and reliable scheme to eliminate a set of redundant or inactive physical constraints in the high-dimensional, multi-interval, mixed-integer UC problem, while the reduced problem is equivalent to the original full problem in terms of commitment decisions. Our key insights lie on pre-screening the constraints based on the load distribution and considering the physical feasibility regions of multi-interval UC problem. For the multi-step UC formulation, we overcome screening conservativeness by utilizing the multi-step ramping relationships, and can reliably screen out more constraints compared to current practice. Extensive simulations on both specific load samples and load regions validate the proposed technique can screen out more than 80% constraints while preserving the feasibility of multi-interval UC problem.
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WeA17 |
Peony Junior 4511 |
Data-Driven Control I |
Regular Session |
Chair: Padoan, Alberto | ETH Zürich |
Co-Chair: Dörfler, Florian | Swiss Federal Institute of Technology (ETH) Zurich |
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10:00-10:20, Paper WeA17.1 | |
>Informativity for Identification for 2D State-Representable Autonomous Systems, with Applications to Data-Driven Simulation |
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Rapisarda, Paolo | Univ. of Southampton |
Pal, Debasattam | Indian Institute of Technology Bombay |
Keywords: Data driven control, Autonomous systems, Behavioural systems
Abstract: We define persistency of excitation and informativity for system identification for the class of 2D state- representable autonomous systems. We characterize informativity for system identification in terms of properties of a matrix constructed from the restrictions of a system trajectory on successive consecutive lines. We state a procedure to compute arbitrary trajectories from a "sufficiently rich" one.
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10:20-10:40, Paper WeA17.2 | |
>Direct Data-Driven Computation of Polytopic Robust Control Invariant Sets and State-Feedback Controllers |
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Mejari, Manas | University of Applied Sciences and Arts of Southern Switzerland |
Gupta, Ankit | Zenseact AB |
Keywords: Data driven control, Constrained control, Robust control
Abstract: This paper presents a direct data-driven approach for computing robust control invariant (RCI) sets and their associated state-feedback control laws for linear time-invariant systems affected by bounded disturbances. The proposed method utilizes a single state-input trajectory generated from the system, to compute a polytopic RCI set with a desired complexity and an invariance-inducing feedback controller, without the need to identify a model of the system. The problem is formulated in terms of a set of sufficient linear matrix inequality conditions that are then combined in a semi-definite program to maximize the volume of the RCI set while respecting the state and input constraints. We demonstrate through a numerical case study that the proposed data-driven approach can generate RCI sets that are of comparable size to those obtained by a model-based method in which exact knowledge of the system matrices is assumed.
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10:40-11:00, Paper WeA17.3 | |
>Data-Driven Representations of Conical, Convex, and Affine Behaviors |
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Padoan, Alberto | ETH Zürich |
Dörfler, Florian | Swiss Federal Institute of Technology (ETH) Zurich |
Lygeros, John | ETH Zurich |
Keywords: Data driven control, Behavioural systems, Identification
Abstract: The paper studies conical, convex, and affine models in the framework of behavioral systems theory. We investigate basic properties of such behaviors and address the problem of constructing models from measured data. We prove that closed, shift-invariant, conical, convex, and affine models have the intersection property, thereby enabling the definition of most powerful unfalsified models based on infinite-horizon measurements. We then provide necessary and sufficient conditions for representing conical, convex, and affine finite-horizon behaviors using raw data matrices, expressing persistence of excitation requirements in terms of non-negative rank conditions. The applicability of our results is demonstrated by a numerical example arising in population ecology.
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11:00-11:20, Paper WeA17.4 | |
>On the Sample Complexity of the Linear Quadratic Gaussian Regulator |
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Al Makdah, Abed AlRahman | University of California Riverside |
Pasqualetti, Fabio | University of California, Riverside |
Keywords: Data driven control, Learning, Optimal control
Abstract: In this paper we provide direct data-driven expressions for the Linear Quadratic Regulator (LQR), the Kalman filter, and the Linear Quadratic Gaussian (LQG) controller using a finite dataset of noisy input, state, and output trajectories. We show that our data-driven expressions are consistent, since they converge as the number of experimental trajectories increases, we characterize their convergence rate, and quantify their error as a function of the system and data properties. These results complement the body of literature on data-driven control and finite-sample analysis, and provide new ways to solve canonical control and estimation problems that do not assume, nor require the estimation of, a model of the system and noise and do not rely on solving implicit equations.
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11:20-11:40, Paper WeA17.5 | |
>Combining Q-Learning and Deterministic Policy Gradient for Learning-Based MPC |
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Seel, Katrine | NTNU |
Gros, Sebastien | NTNU |
Gravdahl, Jan Tommy | Norwegian Univ. of Science & Tech |
Keywords: Data driven control, Learning, Optimization
Abstract: This paper considers adjusting a fully parametrized model predictive control (MPC) scheme to approximate the optimal policy for a system as accurately as possible. By adopting MPC as a function approximator in reinforcement learning (RL), the MPC parameters can be adjusted using Q-learning or policy gradient methods. However, each method has its own specific shortcomings when used alone. Indeed, Q-learning does not exploit information about the policy gradient and therefore may fail to capture the optimal policy, while policy gradient methods miss any cost function corrections not affecting the policy directly. The former is a general problem, whereas the latter is an issue when dealing with economic problems specifically. Moreover, it is notoriously difficult to perform second-order steps in the context of policy gradient methods while it is straightforward in the context of Q-learning. This calls for an organic combination of these learning algorithms, in order to fully exploit the MPC parameterization as well as speed up convergence in learning.
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11:40-12:00, Paper WeA17.6 | |
>Data-Driven Eigenstructure Assignment for Sparse Feedback Design |
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Celi, Federico | University of California, Riverside |
Baggio, Giacomo | University of Padova, Italy |
Pasqualetti, Fabio | University of California, Riverside |
Keywords: Data driven control, Linear systems, Stability of linear systems
Abstract: This paper presents a novel approach for solving the pole placement and eigenstructure assignment problems through data-driven methods. By using open-loop data alone, the paper shows that it is possible to characterize the allowable eigenvector subspaces, as well as the set of feedback gains that solve the pole placement problem. Additionally, the paper proposes a closed-form expression for the feedback gain that solves the eigenstructure assignment problem. Finally, the paper discusses a series of optimization problems aimed at finding sparse feedback gains for the pole placement problem.
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WeA18 |
Peony Junior 4412 |
Nonlinear Systems I |
Regular Session |
Chair: Isidori, Alberto | Universita Di Roma |
Co-Chair: Kaldmäe, Arvo | Tallinn University of Technology |
|
10:00-10:20, Paper WeA18.1 | |
>Synthesizing Stable Reduced-Order Visuomotor Policies for Nonlinear Systems Via Sums-Of-Squares Optimization |
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Chou, Glen | MIT |
Tedrake, Russ | MIT |
Keywords: Nonlinear output feedback, Robotics, Vision-based control
Abstract: We present a method for synthesizing dynamic, reduced-order output-feedback polynomial control policies for control-affine nonlinear systems which guarantees runtime stability to a goal state, when using visual observations and a learned perception module in the feedback control loop. We leverage Lyapunov analysis to formulate the problem of synthesizing such policies. This problem is nonconvex in the policy parameters and the Lyapunov function that is used to prove the stability of the policy. To solve this problem approximately, we propose two approaches: the first solves a sequence of sum-of-squares optimization problems to iteratively improve a policy which is provably-stable by construction, while the second directly performs gradient-based optimization on the parameters of the polynomial policy, and its closed-loop stability is verified a posteriori. We extend our approach to provide stability guarantees in the presence of observation noise, which realistically arises due to errors in the learned perception module. We evaluate our approach on several underactuated nonlinear systems, including pendula and quadrotors, showing that our guarantees translate to empirical stability when controlling these systems from images, while baseline approaches can fail to reliably stabilize the system.
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10:20-10:40, Paper WeA18.2 | |
>Feasibility Detection for Nested Codesign of Hypersonic Vehicles |
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van der Heide, Chris | University of Melbourne |
Cudmore, Peter | University of Melbourne |
Jahn, Ingo | The University of Queensland |
Bone, Viv | The University of Melbourne |
Dower, Peter M. | University of Melbourne |
Manzie, Chris | The University of Melbourne |
Keywords: Nonlinear systems, Aerospace
Abstract: Controllability and feasaiblity measures are used to determine whether a given system can achieve its specified objective. However, for nonlinear systems with space constraints, the controllable and feasible sets may be highly sensitive to minor perturbations in the system's constraints, initial states and parameters. This becomes particularly important in codesign of hypersonic vehicles, where functions governing the dynamics must be estimated from expensive computational fluid dynamics simulations, and poor initialization can lead to significant wasted resources. By relaxation of the constraints and introduction of a surrogate cost, we provide a method for detection and quantification of which constraints are violating feasibility. To demonstrate the method in a concrete example, we apply the technique to simulation of hypersonic vehicle trajectories.
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10:40-11:00, Paper WeA18.3 | |
>Further Results on the Structure of Normal Forms of Input-Affine Nonlinear MIMO Systems |
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Isidori, Alberto | Universita Di Roma |
Keywords: Nonlinear systems, Algebraic/geometric methods
Abstract: In a recent paper it has been shown that the existence, for a MIMO nonlinear system, of normal forms with a special structure that proves to be useful in the design of feedback laws is implied by an assumption introduced a long time ago by Hirschorn in his work on systems invertibility. In this paper, we provide an alternative viewpoint and prove that a necessary and sufficient condition for the existence of such kind of normal forms can be identified in a special feature of the so-called maximal controlled invariant distribution algorithm.
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11:00-11:20, Paper WeA18.4 | |
>Relations between Modules Associated to Input-Output Nonlinear Equations with Delays and Their Realizations |
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Bartosiewicz, Zbigniew | Bialystok University of Technology |
Kaldmäe, Arvo | Tallinn University of Technology |
Kotta, Ülle | Tallinn University of Technology |
Wyrwas, Malgorzata | Bialystok University of Technology |
Keywords: Nonlinear systems, Algebraic/geometric methods
Abstract: The relations between a control system with delays given by a nonlinear input-output equation and its realization are addressed. The algebraic formalism based on rings of polynomials over the rings associated with the considered systems and modules of differential one-forms is used to show the relations between submodules corresponding to the input-output equation and its realization.
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11:20-11:40, Paper WeA18.5 | |
>Controlled Density Transport Using Perron Frobenius Generators |
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Buzhardt, Jake | Clemson University |
Tallapragada, Phanindra | Clemson University |
Keywords: Nonlinear systems, Fluid flow systems, Data driven control
Abstract: We consider the problem of the transport of a density of states from an initial state distribution to a desired final state distribution through a dynamical system with actuation. In particular, we consider the case where the control signal is a function of time, but not space; that is, the same actuation is applied at every point in the state space. This is motivated by several problems in fluid mechanics, such as mixing and manipulation of a collection of particles by a global control input such as a uniform magnetic field, as well as by more general control problems where a density function describes an uncertainty distribution or a distribution of agents in a multi-agent system. We formulate this problem using the generators of the Perron-Frobenius operator associated with the drift and control vector fields of the system. By considering finite-dimensional approximations of these operators, the density transport problem can be expressed as a control problem for a bilinear system in a high-dimensional, lifted state. With this system, we frame the density control problem as a problem of driving moments of the density function to the moments of a desired density function, where the moments of the density can be expressed as an output which is linear in the lifted state. This output tracking problem for the lifted bilinear system is then solved using differential dynamic programming, an iterative trajectory optimization scheme.
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11:40-12:00, Paper WeA18.6 | |
>Convergence Rates for Approximations of Deterministic Koopman Operators Via Inverse Problems |
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Powell, Nathan | EPFL |
Bouland, Ali | Virginia Tech |
Burns, John A | Virginia Tech |
Kurdila, Andrew J. | Virginia Tech |
Keywords: Nonlinear systems, Estimation, Statistical learning
Abstract: This paper derives rates of convergence of approximations of the deterministic Koopman operator using a framework based on estimating solutions of inverse problems. By restricting the domain of the Koopman operator, simple sufficient conditions are derived that ensure that the resulting Koopman operator is compact when acting on a suitable reproducing kernel Hilbert space (RKHS). Approximations of the Koopman operator, or its inverse, are derived in terms of Galerkin approximations of solutions to an associated inverse problem which depends on noisy data. The resulting bounds on accuracy of approximations to the Koopman operator then take a classical form: we obtain explicit representations of the contributions of the approximation error and the generalization error in terms of the reduced dimension and noise level. As the reduced dimension of the approximations increases, the approximation error decreases, while the generalization error increases. The generalization error increases with an increase in the noise level. In the case of a discrete evolution over a smooth, compact, connected, Riemannian manifold, we show that these two contributions to the error can be bounded in terms of the fill distance of centers of approximation and samples in the manifold
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WeA19 |
Peony Junior 4411 |
Linear Systems I |
Regular Session |
Chair: Iannelli, Andrea | University of Stuttgart |
Co-Chair: Bianchin, Gianluca | University of Louvain |
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10:00-10:20, Paper WeA19.1 | |
>Condition for Sensitivity Unidentifiability of Linear Systems with Affinely Parameter-Dependent Coefficient Matrices |
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Yamakawa, Masafumi | Nagoya University |
Asai, Toru | Nagoya University |
Ariizumi, Ryo | Nagoya University |
Azuma, Shun-ichi | Kyoto University |
Keywords: Linear systems, Estimation, Identification
Abstract: In this paper, we analyze "sensitivity identifiability" of initial states and parameters in affinely parametrized linear systems. If the true parameter is sensitivity unidentifiable (non-SI), optimization-based estimation algorithms may face computational problems. Thus, it is important to detect whether the parameter is non-SI a priori. To this aim, we address a problem to find the condition that the parameter is non-SI for any initial state and input. Then, we obtain a sufficient condition for the problem. The condition is given by algebraic equations and is expected to be the foundation of structural conditions. We show systems that satisfy the condition and are observable and controllable.
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10:20-10:40, Paper WeA19.2 | |
>A Data-Driven Approach to System Invertibility and Input Reconstruction |
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Mishra, Vikas Kumar | Technische Universitat Kaiserlautern |
Iannelli, Andrea | University of Stuttgart |
Bajcinca, Naim | University of Kaiserslautern |
Keywords: Linear systems, Estimation
Abstract: We consider the problems of system invertibility and input reconstruction for linear time-invariant (LTI) systems using only measured data. The two problems are connected in the sense that input reconstruction is possible provided that the system is left invertible. To verify the latter property without model knowledge, we leverage behavioral systems theory and develop two data-driven algorithms: one based on input/state/output data and the other based only on input/output data. We then consider the problem of input reconstruction for both noise-free and noisy data settings. In the case of noisy data, a statistical approach is leveraged to formulate the problem as a maximum likelihood estimation (MLE) problem. The proposed approaches are finally illustrated with numerical examples that show: exact input reconstruction in the noise-free setting; and the better performance of the MLE-based approach compared to the standard least-norm solution.
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10:40-11:00, Paper WeA19.3 | |
>Non-Overshooting Tracking Controllers Based on Combinatorial Polynomials |
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Taghavian, Hamed | KTH Royal Institute of Technology |
Johansson, Mikael | KTH - Royal Institute of Technology |
Keywords: Linear systems
Abstract: This paper presents a technique for designing two-parameter compensators that stabilize a plant and provide offset-free tracking of set-points without overshooting or undershooting. We first represent the impulse response of linear systems using combinatorial polynomials, based on which a new set of conditions is derived for the system to be externally positive. This result is then used in control synthesis to achieve monotonic tracking. In contrast to the methods available in the literature, the proposed technique always gives a solution whenever the problem is feasible, can yield as small a settling time as desired, and provides the freedom to choose the closed-loop poles arbitrarily inside the unit circle, all obtained by low-degree controllers.
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11:00-11:20, Paper WeA19.4 | |
>Data-Driven Exact Pole Placement for Linear Systems |
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Bianchin, Gianluca | University of Louvain |
Keywords: Linear systems, Identification for control, Stability of linear systems
Abstract: The exact pole placement problem concerns computing a static feedback law for a linear dynamical system that will assign its poles at a set of pre-specified locations. This is a classic problem in feedback control and numerous methodologies have been proposed in the literature for cases where a model of the system to control is available. In this paper, we study the problem of computing feedback laws for pole placement (and, more generally, eigenstructure assignment) directly from experimental data. Interestingly, we show that the closed-loop poles can be placed exactly at arbitrary locations without relying on any model description but by using only finite-length trajectories generated by the open-loop system. In turn, these findings imply that classical control goals, such as feedback stabilization or meeting transient transient performance specifications, can be achieved directly from data without first identifying a system model. Numerical experiments demonstrate the benefits of the data-driven pole-placement approach compared to its model-based counterpart.
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11:20-11:40, Paper WeA19.5 | |
>Phase of Multivariable Systems: A Revisit Via mathcal{H}_2^T-Dissipativity |
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Wang, Dan | KTH Royal Institute of Technology |
Chen, Wei | Peking University |
Johansson, Karl H. | KTH Royal Institute of Technology |
Keywords: Linear systems
Abstract: A new notion of phase of multi-input multi-output (MIMO) systems was recently defined and studied, leading to new understandings in various fronts including a formulation of small phase theorem, a performance criterion named mathcal{H}_{infty} phase sector, and a sectored real lemma, etc. In this paper, we define a new notion of mathcal{H}_2^T-dissipativity and show the connection between the phase of a multivariable linear time-invariant (LTI) system and the mathcal{H}_2^T-dissipativity. The mathcal{H}_2^T-dissipativity, roughly speaking, is dissipativity restricted to the time-domain mathcal{H}_2 space which consists of mathcal{L}_2 signals with only positive frequency components. In addition, by exploiting the newly defined mathcal{H}_2^T-dissipativity, we also study the phase of a feedback system and provide a physical interpretation of the sectored real lemma.
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11:40-12:00, Paper WeA19.6 | |
>Markov Chain Monte Carlo for Gaussian: A Linear Control Perspective |
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Yuan, Bo | Georgia Institute of Technology |
Fan, Jiaojiao | Georgia Institute of Technology |
Wang, Yuqing | Georgia Institute of Technology |
Tao, Molei | Georgia Institute of Technology |
Chen, Yongxin | Georgia Institute of Technology |
Keywords: Linear systems, Lyapunov methods, Filtering
Abstract: Drawing samples from a given target probability distribution is a fundamental task in many science and engineering applications. A commonly used method for sampling is the Markov chain Monte Carlo (MCMC) which simulates a Markov chain whose stationary distribution coincides with the target one. In this work, we study the convergence and complexity of MCMC algorithms from a dynamic system point of view. We focus on the special cases with Gaussian target distributions and provide a Lyapunov perspective to them using tools from linear control theory. In particular, we systematically analyze two popular MCMC algorithms: Langevin Monte Carlo (LMC) and kinetic Langevin Monte Carlo (KLMC). By applying Lyapunov theory we derive tight complexity bounds to these algorithms. Our analysis also highlights subtle differences between sampling and optimization that could inform the more challenging task to sample from general distributions. Overall, our findings offer valuable insights for improving MCMC algorithms.
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WeA21 |
Orchid Junior 4311 |
Constrained Control I |
Regular Session |
Chair: Panagou, Dimitra | University of Michigan, Ann Arbor |
Co-Chair: You, Keyou | Tsinghua University |
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10:00-10:20, Paper WeA21.1 | |
>Enhancements on a Saturated Control for Stabilizing a Quadcopter: Adaptive and Robustness Analysis in the Flat Output Space |
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Do, Huu-Thinh | Grenoble Institute of Technology (Grenoble INP) |
Blanchini, Franco | Univ. Degli Studi Di Udine |
Prodan, Ionela | Grenoble Institute of Technology (Grenoble INP) - Esisar |
Keywords: Constrained control, Adaptive control, Feedback linearization
Abstract: This paper extends our previous study on an explicit saturated control for a quadcopter, which ensures both constraint satisfaction and stability thanks to the linear representation of the system in the flat output space. The novelty here resides in the adaptivity of the controller’s gain to enhance the system’s performance without exciting its parasitic dynamics and avoid lavishing the input actuation with excessively high gain parameters. Moreover, we provide a thorough robustness analysis of the proposed controller when additive disturbances are affecting the system behavior. Finally, simulation and experimental tests validate the performances of the proposed controller.
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10:20-10:40, Paper WeA21.2 | |
>Adaptive Safe Backstepping for Collaborative Levitation Control of Maglev Trains with Unknown Mass |
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Zhang, Tianbo | Tsinghua University |
Li, Xingchen | Tsinghua University |
Zhang, TiYao | Beijing Jiaotong University |
You, Keyou | Tsinghua University |
Keywords: Constrained control, Adaptive control
Abstract: Maglev trains are levitated by magnetic forces to maintain a desired air gap between guideways and magnets. Although every two magnets are mechanically coupled via a levitation bogie, the existing controllers are usually designed only for each individual magnet, which may result in unstable air gaps or levitation failures. Differently, this paper proposes an adaptive safe backstepping scheme to collaboratively control two magnets of the same bogie. In particular, safety constraints are introduced to adaptive backstepping control via quadratic programs, which ensures the air gap within a permissible range and significantly reduces overshoots. Finally, simulation results validate the effectiveness of the proposed collaborative controller.
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10:40-11:00, Paper WeA21.3 | |
>Adaptation for Validation of Consolidated Control Barrier Functions |
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Black, Mitchell | Toyota Motor North America |
Panagou, Dimitra | University of Michigan, Ann Arbor |
Keywords: Constrained control, Autonomous robots, Nonlinear systems
Abstract: We develop a novel adaptation-based technique for safe control design in the presence of multiple state constraints. Specifically, we introduce an approach for synthesizing any number of candidate control barrier functions (CBFs), each encoding a different state constraint, into one consolidated CBF (C-CBF) candidate. We then propose a parameter adaptation law for the weights of the C-CBF's constituent functions such that its controllable dynamics are non-vanishing. We prove that the adaptation law certifies the consolidated CBF candidate as valid for a class of nonlinear, control-affine, multi-agent systems, which permits its use in a quadratic program based control law. We highlight the success of our approach in simulation on a multi-robot goal-reaching problem in a warehouse environment, and further demonstrate its efficacy via a laboratory study with an AION ground rover operating amongst other vehicles behaving both aggressively and conservatively.
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11:00-11:20, Paper WeA21.4 | |
>Anti-Windup Coordination Strategy Around a Fair Equilibrium in Resource Sharing Networks |
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Agner, Felix | Lund University |
Kergus, Pauline | CNRS |
Rantzer, Anders | Lund University |
Tarbouriech, Sophie | LAAS-CNRS |
Zaccarian, Luca | LAAS-CNRS |
Keywords: Constrained control, Energy systems, Distributed control
Abstract: We coordinate interconnected agents where the control input of each agent is limited by the control input of others. In that sense, the systems have to share a limited resource over a network. Such problems can arise in different areas and it is here motivated by a district heating example. When the shared resource is insufficient for the combined need of all systems, the resource will have to be shared in an optimal fashion. In this scenario, we want the systems to automatically converge to an optimal equilibrium. The contribution of this paper is the proposal of a control architecture where each separate system is controlled by a local PI controller. The controllers are then coordinated through a global rank-one anti- windup signal. It is shown that the equilibrium of the proposed closed-loop system minimizes the infinity-norm of stationary state deviations. A proof of linear-domain passivity is given, and a numerical example highlights the benefits of the proposed method with respect to the state-of-the-art.
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11:20-11:40, Paper WeA21.5 | |
>Safety-Critical Control for Systems with Impulsive Actuators and Dwell Time Constraints |
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Breeden, Joseph | University of Michigan, Ann Arbor |
Panagou, Dimitra | University of Michigan, Ann Arbor |
Keywords: Constrained control, Hybrid systems, Aerospace
Abstract: This paper presents extensions of control barrier function (CBF) and control Lyapunov function (CLF) theory to systems wherein all actuators cause impulsive changes to the state trajectory, and can only be used again after a minimum dwell time has elapsed. These rules define a hybrid system, wherein the controller must at each control cycle choose whether to remain on the current state flow or to jump to a new trajectory. We first derive a sufficient condition to render a specified set forward invariant using extensions of CBF theory. We then derive related conditions to ensure asymptotic stability in such systems, and apply both conditions online in an optimization-based control law with aperiodic impulses. We simulate both results on a spacecraft docking problem with multiple obstacles.
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11:40-12:00, Paper WeA21.6 | |
>On the Relationship between Control Barrier Functions and Projected Dynamical Systems |
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Delimpaltadakis, Giannis | Eindhoven University of Technology |
Heemels, W.P.M.H. | Eindhoven University of Technology |
Keywords: Constrained control, Hybrid systems, Stability of nonlinear systems
Abstract: In this paper, we study the relationship between systems controlled via Control Barrier Function (CBF) approaches and a class of discontinuous dynamical systems, called Projected Dynamical Systems (PDSs). In particular, under appropriate assumptions, we show that the vector field of CBF-controlled systems is a Krasovskii-like perturbation of the set-valued map of a differential inclusion, that abstracts PDSs. This result provides a novel perspective to analyze and design CBF-based controllers. Specifically, we show how, in certain cases, it can be employed for designing CBF-based controllers that, while imposing safety, preserve asymptotic stability and do not introduce undesired equilibria or limit cycles. Finally, we briefly discuss about how it enables continuous implementations of certain projection-based controllers, that are gaining increasing popularity.
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WeA22 |
Orchid Junior 4212 |
Stochastic Optimal Control I |
Regular Session |
Chair: Bhatnagar, Shalabh | Indian Institute of Science |
Co-Chair: Chakravorty, Suman | Texas A&M University |
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10:00-10:20, Paper WeA22.1 | |
>Convex Q Learning in a Stochastic Environment |
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Lu, Fan | University of Florida |
Meyn, Sean P. | Univ. of Florida |
Keywords: Stochastic optimal control, Adaptive control, Machine learning
Abstract: The paper introduces the first formulation of convex Q-learning for Markov decision processes with function approximation. The algorithms and theory rest on a relaxation of a dual of Manne's celebrated linear programming characterization of optimal control. The main contributions firstly concern properties of the relaxation, described as a deterministic convex program: we identify conditions for a bounded solution, a significant connection between the solution to the new convex program, and the solution to standard Q-learning with linear function approximation. The second set of contributions concern algorithm design and analysis: (i) A direct model-free method for approximating the convex program for Q-learning shares properties with its ideal. In particular, a bounded solution is ensured subject to a simple property of the basis functions; (ii) The proposed algorithms are convergent and new techniques are introduced to obtain the rate of convergence in a mean-square sense; (iii) The approach can be generalized to a range of performance criteria, and it is found that variance can be reduced by considering ``relative'' dynamic programming equations; (iv) The theory is illustrated with an application to a classical inventory control problem.
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10:20-10:40, Paper WeA22.2 | |
>Signalling of Information Via Coding in a Series Network of Unstable Stochastic Dynamical Control Systems |
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Charalambous, Charalambos D. | University of Cyprus |
Kourtellaris, Christos | University of Cyprus |
Tzortzis, Ioannis | University of Cyprus |
Keywords: Stochastic optimal control, Control over communications, Networked control systems
Abstract: We address the asymptotic problem of signalling information from one controller to another controller, in a series network, consisting of control system 1 (CS-1) and control system 2 (CS-2), as shown in the Figure, first analyzed in [1] for finite-horizon. Controller 2 of CS-2 has access to feedback information from its output, while controller 1 of CS-1 does not have access to feedback information from its output. Under suitable detectability and stabilizability conditions of matrix algebraic Riccati equations (AREs), it is shown that, if the rate of generating information by CS-1 is below the asymptotic control-coding (CC) capacity of CS-2, then we can synthesize, i) a controller-encoder for CS-2 that simultaneously controls the CS-2 and encodes the state of the CS-1, and operates at the CC capacity of CS-2, ii) a decoder for CS-2 that is optimal with respect to a mean-square error (MSE) criterion, and iii) a controller for CS-1, which acts on the decoder output, and it is optimal with respect to the pay-off of CS-1. Compared to [1], this paper includes bounds to MSE and Error probability of communicating digital messages.
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10:40-11:00, Paper WeA22.3 | |
>Learning to Control under Uncertainty with Data-Based Iterative Linear Quadratic Regulator |
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Wang, Ran | Texas A&M University |
Goyal, Raman | Texas A&M University |
Chakravorty, Suman | Texas A&M University |
Keywords: Stochastic optimal control, Iterative learning control, Nonlinear output feedback
Abstract: This paper studies the learning-to-control problem under process and sensing uncertainties for dynamical systems. In our previous work, we developed a data-based generalization of the iterative linear quadratic regulator (iLQR) to design closed-loop feedback control for high-dimensional dynamical systems with partial state observation. This method required perfect simulation rollouts which are not realistic in real applications. In this work, we briefly introduce this method and explore its efficacy under process and sensing uncertainties. We prove that in the fully observed case where the system dynamics are corrupted with noise but the measurements are perfect, it still converges to the global minimum. However, in the partially observed case where both process and measurement noise exist in the system, this method converges to a biased ``optimum". Thus multiple rollouts need to be averaged to retrieve the true optimum. The analysis is verified in two nonlinear robotic examples simulated in the above cases.
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11:00-11:20, Paper WeA22.4 | |
>Stochastic Nonlinear Control Via Finite-Dimensional Spectral Dynamic Embedding |
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Ren, Tongzheng | University of Texas, Austin |
Ren, Zhaolin | Harvard University |
Li, Na | Harvard University |
Dai, Bo | Google Brain & Georgia Tech |
Keywords: Stochastic optimal control, Iterative learning control, Optimal control
Abstract: Optimal control is notoriously difficult for stochastic nonlinear systems. Ren et.al. 2022 introduced Spectral Dynamics Embedding for developing reinforcement learning methods for controlling an unknown system. It uses an infinite-dimensional feature to linearly represent the state-value function and exploits finite-dimensional truncation approximation for practical implementation. However, the finite-dimensional approximation properties in control have not been investigated even when the model is known. In this paper, we provide a tractable stochastic nonlinear control algorithm that exploits the nonlinear dynamics upon the finite-dimensional feature approximation, Spectral Dynamics Embedding Control (SDEC), with an in-depth theoretical analysis to characterize the approximation error induced by the finite-dimension truncation and statistical error induced by finite-sample approximation in both policy evaluation and policy optimization. We also empirically test the algorithm and compare the performance with Koopman-based methods and iLQR methods on the pendulum swingup problem.
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11:20-11:40, Paper WeA22.5 | |
>Large-Population Optimal Control with Mixed Agents: The Multi-Scale Analysis and Decentralized Control |
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Huang, Minyi | Carleton University |
Nguyen, Son | University of Puerto Rico, Rio Piedras |
Keywords: Stochastic optimal control, Large-scale systems, Decentralized control
Abstract: We consider a large-population optimal control problem involving a major agent and a large number of minor agents. By starting with a centralized optimal control problem, we employ a re-scaling method to derive decentralized control laws. This re-scaling method is further used to obtain a tight upper bound of O(1/N) for the performance loss resulting from decentralized control. This improves upon known results of O(1/sqrt{N}) in the literature for similar models.
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11:40-12:00, Paper WeA22.6 | |
>Actor-Critic or Critic-Actor? a Tale of Two Time Scales |
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Bhatnagar, Shalabh | Indian Institute of Science |
Borkar, Vivek S. | Indian Institute of Technology |
Guin, Soumyajit | Indian Institute of Science, Bengaluru |
Keywords: Stochastic optimal control, Machine learning, Iterative learning control
Abstract: We revisit the standard formulation of tabular actor-critic algorithm as a two time-scale stochastic approximation with value function computed on a faster time-scale and policy computed on a slower time-scale. This emulates policy iteration. We begin by observing that reversal of the time scales will in fact emulate value iteration and is a legitimate algorithm. We provide a proof of convergence and compare the two empirically with and without function approximation (with both linear and nonlinear function approximators) and observe that our proposed critic-actor algorithm performs on par with actor-critic in terms of both accuracy and computational effort.
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WeA23 |
Orchid Junior 4211 |
Cyber-Physical Security I |
Regular Session |
Chair: Chen, Tongwen | University of Alberta |
Co-Chair: Ishii, Hideaki | Tokyo Institute of Technology |
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10:00-10:20, Paper WeA23.1 | |
>Model Extraction Attacks against Reinforcement Learning Based Controllers |
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Sajid, Momina | University of California, Irvine |
Shen, Yanning | UCI |
Shoukry, Yasser | University of California, Irvine |
Keywords: Cyber-Physical Security, Attack Detection, Machine learning
Abstract: We introduce the problem of model-extraction attacks in cyber-physical systems in which an attacker attempts to estimate (or extract) the feedback controller of the system. Extracting (or estimating) the controller provides an unmatched edge to attackers since it allows them to predict the future control actions of the system and plan their attack accordingly. Hence, it is important to understand the ability of the attackers to perform such an attack. In this paper, we focus on the setting when a Deep Neural Network (DNN) controller is trained using Reinforcement Learning (RL) algorithms and is used to control a stochastic system. We play the role of the attacker that aims to estimate such an unknown DNN controller, and we propose a two-phase algorithm. In the first phase, also called the offline phase, the attacker uses side-channel information about the RL-reward function and the system dynamics to identify a set of candidate estimates of the unknown DNN. In the second phase, also called the online phase, the attacker observes the behavior of the unknown DNN and uses these observations to shortlist the set of final policy estimates. We provide theoretical analysis of the error between the unknown DNN and the estimated one. We also provide numerical results showing the effectiveness of the proposed algorithm.
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10:20-10:40, Paper WeA23.2 | |
>Physical Backdoor Trigger Activation of Autonomous Vehicle Using Reachability Analysis |
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Li, Wenqing | New York University Abu Dhabi |
Wang, Yue | New York University |
Shafique, Muhammad | New York University Abu Dhabi |
Jabari, Saif | New York University Abu Dhabi |
Keywords: Cyber-Physical Security, Autonomous vehicles, Traffic control
Abstract: Recent studies reveal that Autonomous Vehicles (AVs) can be manipulated by hidden backdoors, causing them to perform harmful actions when activated by physical triggers. However, it is still unclear how these triggers can be activated while adhering to traffic principles. Understanding this vulnerability in a dynamic traffic environment is crucial. This work addresses this gap by presenting physical trigger activation as a reachability problem of controlled dynamic system. Our technique identifies security-critical areas in traffic systems where trigger conditions for accidents can be reached, and provides intended trajectories for how those conditions can be reached. Testing on typical traffic scenarios showed the system can be successfully driven to trigger conditions with near 100% activation rate. Our method benefits from identifying AV vulnerability and enabling effective safety strategies.
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10:40-11:00, Paper WeA23.3 | |
>Stealthy Linear Deception Attacks against Kalman Filtering with Partially Secured Measurements |
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Zhou, Jing | University of Alberta |
Chen, Tongwen | University of Alberta |
Keywords: Cyber-Physical Security, Computer/Network Security, Estimation
Abstract: In this paper, we investigate an optimal strategy for malicious agents to compromise remote state estimators where only a portion of the transmitted packets are secured. First, the analysis of the performance evolution and stealthiness properties of innovation-based linear attacks that can compromise unsafe transmission channels is provided. An optimal attack policy is then derived by numerically solving an optimization problem step by step. Different from the scenario where all links are vulnerable to cyber-attacks, the existence of secured channels poses a tighter stealthiness constraint and thus can significantly reduce the worst-case attack impact. Additionally, it is shown that the well-studied flipping-sign-attack in existing work cannot remain stealthy. Finally, a numerical example and comparative studies are included to verify the effectiveness of the proposed method.
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11:00-11:20, Paper WeA23.4 | |
>Consensus Resiliency of Stochastic Observation Via Ring Lattices of Sensors Facing Byzantine Attacks |
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Peng, Haotian | Shanghai Jiao Tong University |
Li, Yuke | Peking University |
Jin, Li | Shanghai Jiao Tong University |
Keywords: Cyber-Physical Security, Game theory, Fault tolerant systems
Abstract: We consider the observation of a random, binary environment state via a set of sensing nodes connected through a ring lattice. Each node obtains a correct observation with a positive probability and broadcasts its observation to its neighbors. A system operator selects a consensus threshold for the number of consistent observations, and a consensus is reached when any node has accumulated sufficient consistent observations. A Byzantine attacker can manipulate a certain number of nodes to broadcast misleading information, and thus prohibit a correct consensus. We formulate this problem as a zero-sum game and analyze the equilibria. We show that the attacker has a dominant strategy for selecting the nodes to manipulate and the information to broadcast/block. We show that, unless the attacker's budget is abundant, the system operator can select an optimal consensus threshold to balance between the chance of a correct consensus and the risk of a wrong consensus. We also use the equilibrium structure to characterize the network resiliency, i.e., the minimal number of Byzantine nodes that would eliminate the chance of a correct consensus, given the size and connectivity of the ring lattice. The results are relevant for hardware surveillance, infrastructure inspection, disaster response, etc.
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11:20-11:40, Paper WeA23.5 | |
>Optimal Linear Attack in Cyber-Physical Systems with Periodical Detection |
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Qi, Jia | Shanghai Jiao Tong University |
Fang, Chongrong | Shanghai Jiao Tong University |
He, Jianping | Shanghai Jiao Tong University |
Keywords: Cyber-Physical Security, Networked control systems, Kalman filtering
Abstract: Security issues are of significant importance for cyber-physical systems (CPS), where the attack design is a major concern. Most related studies on attack design implicitly consider that the control period and detection period are the same. However, the two periods could be different in practical systems with remote detection such as SCADA systems, which could lead to new vulnerabilities for attackers. In this paper, we consider the design of innovation-based linear attack strategies for CPS when the control period and detection period are inconsistent. Specifically, we propose an attack framework that consists of attack strategies for detection and non-detection instants under the period discrepancy. On this basis, we design the optimal stealthy innovation-based linear attack strategies for state estimation and LQG control to maximize the estimation error or control cost, respectively. Simulations are given to demonstrate the effectiveness of the proposed attack strategies.
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11:40-12:00, Paper WeA23.6 | |
>Effects of Quantization on Zero-Dynamics Attacks to Closed-Loop Sampled-Data Control Systems |
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Kang, Xile | Tokyo Institute of Technology |
Ishii, Hideaki | Tokyo Institute of Technology |
Keywords: Cyber-Physical Security, Networked control systems, Sampled-data control
Abstract: This paper focuses on cyber-security issues of networked control systems in closed-loop forms from the perspective of quantized sampled-data systems. As sampling can introduce non-minimum phase zeros in discretized systems, we consider zero dynamics attacks, which is a class of false data injection attacks. Quantization of control inputs disables such attacks to be made exactly, resulting in certain errors in the system output. Specifically, we characterize a trade-off relation between attack performance and stealthiness, and then show that the attacker can reduce the output error with a modified approach by considering the quantization error of the attack signal. We provide a numerical example to demonstrate the effectiveness of the proposed approaches.
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WeA24 |
Orchid Main 4201AB |
Event-Triggered and Self-Triggered Control I |
Invited Session |
Chair: Morarescu, Irinel-Constantin | CRAN, CNRS, Université De Lorraine |
Co-Chair: Nesic, Dragan | University of Melbourne |
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 WeA24.1 | |
>Event-Triggered Robust Stabilization by Using Fast-Varying Square Wave Dithers (I) |
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Zhang, Jin | Shanghai University |
Zhang, Zhihao | Shanghai University |
Fridman, Emilia | Tel-Aviv Univ |
Keywords: Stability of linear systems, Robust control
Abstract: This paper is concerned with event-triggered robust static output-feedback stabilization of the second-order linear uncertain systems by a fast-varying square wave with high gain. Recently, a constructive time-delay approach for designing such a fast-varying output-feedback controller was suggested by using continuous measurements. In the present paper, we employ an event-trigger (ET) based on switching approach that determines the measurement transmission instants for this design. For the resulting switching system, we construct appropriate coordinate transformations that cancel the high gains and apply the time-delay approach to periodic averaging of the system in new coordinates. By employing appropriate Lyapunov functionals, we derive linear matrix inequalities (LMIs) for finding an efficient upper bound on the square wave frequency that guarantees the stability of the original systems. Numerical examples illustrate the efficiency of the method.
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10:20-10:40, Paper WeA24.2 | |
>Output-Based Event-Holding Control in Presence of Measurement Noise (I) |
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Scheres, Koen | Eindhoven University of Technology |
Postoyan, Romain | CNRS, CRAN, Université De Lorraine |
Nesic, Dragan | University of Melbourne |
Heemels, W.P.M.H. | Eindhoven University of Technology |
Keywords: Hybrid systems, Networked control systems, Control over communications
Abstract: We present rules to stabilize the origin of a networked system, where data exchanges between the plant and the controller only occur when an output-dependent inequality has been satisfied for a given amount of time. This strategy, called Event-Holding Control (EHC), differs from time-regularized event-triggered control (ETC) techniques, which generate transmissions as soon as a triggering condition is verified and the time elapsed since the last transmission is larger than a given bound. Indeed, the clock involved in EHC is not running continuously after each transmission instant, but only when a criterion is verified. We propose an output-based design of these triggering mechanisms that are robust to additive measurement noise and ensure an input-to-state stability (ISS) property. This EHC scheme naturally has a positive lower bound on the transmission interval. Additionally, we show via an example that, in presence of measurement noise, Zeno-like behavior, where events are generated near the minimum inter-event time consistently, may occur when the system is close to the attractor. We introduce space-regularization to mitigate this issue, resulting in an input-to-state practical stability (ISpS) property rather than ISS.
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10:40-11:00, Paper WeA24.3 | |
>Forward Invariance-Based Hybrid Control Using Uncertified Controllers (I) |
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Wintz, Paul K. | University of California, Santa Cruz |
Sanfelice, Ricardo G. | University of California at Santa Cruz |
Keywords: Supervisory control, Hybrid systems, Fault accomodation
Abstract: For a constrained nonlinear control system, an automated supervisor is proposed that determines switching between a barrier function–certified controller and an uncertified controller. The switching strategy allows for properties of the uncertified controller to be exploited while preserving the forward invariance that is guaranteed by the barrier function for the certified controller. Tunable threshold functions determine regions of the state space where the supervisor switches between controllers. Conditions are given to prevent chattering by establishing a positive minimum time between switches. An example illustrates achieving forward invariance despite using an uncertified MPC controller with delayed computations.
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11:00-11:20, Paper WeA24.4 | |
>Intermittent Safety Filters for Event-Triggered Safety Maneuvers with Application to Satellite Orbit Transfers (I) |
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Ong, Pio | California Institute of Technology |
Ames, Aaron D. | California Institute of Technology |
Keywords: Discrete event systems, Hybrid systems, Nonlinear systems
Abstract: In balancing safety with the nominal control objectives, e.g., stabilization, it is desirable to reduce the time period when safety filters are in effect. Inspired by traditional spacecraft maneuvers, and with the ultimate goal of reducing the duration when safety is of concern, this paper proposes an event-triggered control framework with switching state-based triggers. Our first trigger in the scheme monitors safety constraints encoded by barrier functions, and thereby ensures safety without the need to alter the nominal controller---and when the boundary of the safety constraint is approached, the controller drives the system to the region where control actions are not needed. The second trigger condition determines if the safety constraint has improved enough for the success of the first trigger. We begin by motivating this framework for impulsive control systems, e.g., a satellite orbiting an asteroid. We then expand the approach to more general nonlinear system through the use of safety filtered controllers. Simulation results demonstrating satellite orbital maneuvers illustrate the utility of the proposed event-triggered framework.
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11:20-11:40, Paper WeA24.5 | |
>Event-Triggered Sensor Scheduling for Remote State Estimation with Error-Detecting Code |
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Zhong, Yuxing | The Hong Kong University of Science and Technology |
Tang, Jiawei | Hong Kong University of Science and Technology |
Yang, Nachuan | Hong Kong University of Science and Technology |
Shi, Dawei | Beijing Institute of Technology |
Shi, Ling | Hong Kong University of Science and Technology |
Keywords: Discrete event systems, Kalman filtering, Networked control systems
Abstract: This paper addresses the problem of remote state estimation subject to packet dropouts, focusing on the use of an event-triggered sensor scheduler to conserve communication resources. However, packet dropouts introduce significant challenges, as the remote estimator cannot distinguish between packet loss caused by poor channel conditions and packet loss due to the event trigger. To overcome this issue, we propose a novel formulation that incorporates error-detecting codes. We prove that the Gaussian property, commonly assumed in the literature, does not hold in this setup, and instead, the system state follows an extended Gaussian mixture model (GMM). We present an exact minimum mean-squared error (MMSE) estimator and an approximate estimator, which significantly reduces algorithm complexity without sacrificing performance. Our simulation results show that the approximate estimator achieves nearly the same performance as the exact estimator while requiring much less computation time. Moreover, the proposed event trigger outperforms existing schedulers in terms of estimation accuracy.
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11:40-12:00, Paper WeA24.6 | |
>Event-Triggered Transmission Policies for Nonlinear Control Systems Over Erasure Channels |
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Satheeskumar Varma, Vineeth | CNRS |
Postoyan, Romain | CNRS, CRAN, Université De Lorraine |
Quevedo, Daniel E. | Queensland University of Technology |
Morarescu, Irinel-Constantin | CRAN, CNRS, Université De Lorraine |
Keywords: Networked control systems, Stochastic systems
Abstract: We investigate the scenario where a controller communicates with a nonlinear plant via a wireless erasure channel. We present an event-based control strategy to stabilize the plant while sporadically using the unreliable wireless network. In particular, control packets may be lost at any time with a certain probability. Consequently, stability is ensured in a stochastic sense. We then compare the proposed event-based policy with a baseline policy that transmits according to the age of information, i.e., the time elapsed since the last successful reception. For any given baseline policy, we show how to design an event-based policy that ensures the same guaranteed control performance while leading, on average, to a strictly smaller channel utilization. Numerical simulations suggest that the achieved channel utilization may in fact be significantly smaller.
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WeA25 |
Lotus Junior 4DE |
Contraction Theory for Analysis, Synchronization and Regulation I |
Invited Session |
Chair: Astolfi, Daniele | Cnrs - Lagepp |
Co-Chair: Bullo, Francesco | Univ of California at Santa Barbara |
Organizer: Astolfi, Daniele | Cnrs - Lagepp |
Organizer: Bullo, Francesco | Univ of California at Santa Barbara |
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10:00-10:20, Paper WeA25.1 | |
>Euclidean Contractivity of Neural Networks with Symmetric Weights |
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Centorrino, Veronica | Scuola Superiore Meridionale |
Gokhale, Anand | University of California, Santa Barbara |
Davydov, Alexander | University of California, Santa Barbara |
Russo, Giovanni | University of Salerno |
Bullo, Francesco | Univ of California at Santa Barbara |
Keywords: Stability of nonlinear systems, Neural networks, Optimization
Abstract: This paper investigates stability conditions of continuous-time Hopfield and firing-rate neural networks by leveraging contraction theory. First, we present a number of useful general algebraic results on matrix polytopes and products of symmetric matrices. Then, we give sufficient conditions for strong and weak Euclidean contractivity, i.e., contractivity with respect to the ell_2 norm, of both models with symmetric weights and (possibly) non-smooth activation functions. Our contraction analysis leads to contraction rates which are log-optimal in almost all symmetric synaptic matrices. Finally, we use our results to propose a firing-rate neural network model to solve a quadratic optimization problem with box constraints.
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10:20-10:40, Paper WeA25.2 | |
>Parametrization of Linear Controllers for P-Dominance |
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Kawano, Yu | Hiroshima University |
Sato, Yusuke | Hiroshima University |
Wada, Nobutaka | Hiroshima University |
Keywords: Stability of nonlinear systems, Variational methods, LMIs
Abstract: Recently, the concept of p-dominance has been proposed as a unified framework to study rich behaviors of nonlinear systems. In this paper, we consider finding a set of linear dynamic output feedback controllers rendering the closed-loop systems p-dominant. We first derive an existence condition. Based on this condition, we then provide a parametrization of controllers. For Lure's systems, the proposed method can be applied only by solving a finite family of linear matrix inequalities, which is illustrated by achieving multi-stabilization and stabilization of a limit cycle.
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10:40-11:00, Paper WeA25.3 | |
>Range-Only Bearing Estimator for Localization and Mapping |
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Marcantoni, Matteo | University of Groningen |
Jayawardhana, Bayu | University of Groningen |
Bunte, Kerstin | University of Groningen |
Keywords: Observers for nonlinear systems, Estimation, Autonomous vehicles
Abstract: Navigation and exploration within unknown environments are typical examples in which simultaneous localization and mapping (SLAM) algorithms are applied. When mobile agents deploy only range sensors without bearing information, the agents must estimate the bearing using the online distance measurement for the localization and mapping purposes. In this paper, we propose a scalable dynamic bearing estimator to obtain the relative bearing of the static landmarks in the local coordinate frame of a moving agent in real-time. Using contraction theory, we provide convergence analysis of the proposed range-only bearing estimator and present upper and lower-bound for the estimator gain. Numerical simulations demonstrate the effectiveness of the proposed method.
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11:00-11:20, Paper WeA25.4 | |
>A Small-Gain Approach to Incremental Input-To-State Stability Analysis of Hybrid Integrator-Gain Systems |
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van den Eijnden, Sebastiaan | Eindhoven University of Technology |
Heertjes, Marcel | Eindhoven University of Technology |
Nijmeijer, Hendrik | Eindhoven University of Technology |
Heemels, W.P.M.H. | Eindhoven University of Technology |
Keywords: Switched systems, Stability of hybrid systems, Hybrid systems
Abstract: Incremental input-to-state stability plays an important role in the analysis of nonlinear systems, as it opens up the possibility for accurate performance characterizations beyond classical approaches. In this paper, we are interested in deriving conditions for incremental stability of a specific class of discontinuous dynamical systems containing a so-called hybrid integrator. Recently, it was shown that hybrid integrators have the potential for overcoming fundamental performance limitations of linear time-invariant control, thereby making them interesting for use in, e.g., high-precision motion control applications. The main contribution of this paper is to show that these hybrid integrators have incremental input-to-state stability properties, and that, under an incremental small-gain condition, the feedback interconnection of a hybrid integrator and a linear time-invariant plant is incrementally input-to-state stable.
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11:20-11:40, Paper WeA25.5 | |
>Nonlinear Singular Switched Systems in Discrete-Time: Solution Theory and Incremental Stability under Restricted Switching Signals (I) |
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Sutrisno, Sutrisno | University of Groningen and Diponegoro Unversity |
Yin, Hao | University of Groningen |
Trenn, Stephan | University of Groningen |
Jayawardhana, Bayu | University of Groningen |
Keywords: Switched systems, Differential-algebraic systems, Stability of nonlinear systems
Abstract: In this article the solvability analysis of discrete-time nonlinear singular switched systems with restricted switching signals is studied. We provide necessary and sufficient conditions for the solvability analysis under fixed switching signals and fixed mode sequences. The so-called surrogate systems (ordinary systems that have the equivalent behavior to the original switched systems) are introduced for solvable switched systems. Incremental stability, which ensures that all solution trajectories converge with each other, is then studied by utilizing these surrogate systems. Sufficient (and necessary) conditions are provided for this stability analysis using single and switched Lyapunov function approaches.
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11:40-12:00, Paper WeA25.6 | |
>Semicontraction and Synchronization of Kuramoto-Sakaguchi Oscillator Networks |
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Delabays, Robin | University of Applied Sciences and Arts of Western Switzerland / |
Bullo, Francesco | Univ of California at Santa Barbara |
Keywords: Stability of nonlinear systems
Abstract: This paper studies the celebrated Kuramoto-Sakaguchi model of coupled oscillators adopting two recent concepts. First, we consider appropriately-defined subsets of the n-torus called winding cells. Second, we analyze the semicontractivity of the model, i.e., the property that the distance between trajectories decreases when measured according to a seminorm. This paper establishes the local semicontractivity of the Kuramoto-Sakaguchi model, which is equivalent to the local contractivity for the reduced model. The reduced model is defined modulo the rotational symmetry. The domains where the system is semicontracting are convex phase-cohesive subsets of winding cells. Our sufficient conditions and estimates of the semicontracting domains are less conservative and more explicit than in previous works. Based on semicontraction on phase-cohesive subsets, we establish the "at most uniqueness" of synchronous states within these domains, thereby characterizing the multistability of this model.
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WeA26 |
Orchid Main 4301AB |
Delay Systems |
Regular Session |
Chair: Sahoo, Soumya Ranjan | Indian Institute of Technology Kanpur |
Co-Chair: Bekiaris-Liberis, Nikolaos | Technical University of Crete |
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10:00-10:20, Paper WeA26.1 | |
>Delay Feedback Active Inference Based on Predicted States for Uncertain Systems with Input Delay |
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Ji, Mingyue | Northwestern Polytechnical University |
Lyu, Yang | Northwestern Polytechnical University |
Pan, Kunpeng | Northwestern Polytechnical University |
Zhang, Xiaoxuan | Northwestern Polytechnical University |
Pan, Quan | Northwestern Polytechnical University |
Li, Yang | Northwestern Polytechnical University |
Zhao, Chunhui | Northwestern Polytechnical University |
Hu, Jinwen | Northwestern Polytechnical University |
Keywords: Delay systems, Agents-based systems, Adaptive control
Abstract: Active inference (AIF) as a comprehensive theory has been proven that it is promising in state estimation and adaptive control of uncertain systems. However, the input delay in the controller was ignored in the normal framework. When taking input delay into consideration in the uncertain system, the optimal estimation state in the normal AIF differs greatly from the real state of the system due to the accumulation of the delay effect. Therefore, delay feedback active inference(D- AIF) is proposed in this paper. Different from normal AIF, a predictive state based on the delay state becomes the expectation of the state of normal AIF. Meanwhile, the expectation of the controller becomes an epitaxial delayed feedback Proportional- Integral (PI) control. The variational free energy (VFE) is extended by adding a quadratic of control consumption, In order to minimize the variational free energy, the model uncertainty and measurement uncertainty are compensated by approximate Gaussian distributions. Surprisingly, the state estimation does not depend on the given target state in D-AIF. When AIF and D-AIF are applied for trajectory tracking of an unmanned aircraft with input delay, it can be seen from the results that delay feedback active inference control (D-AIFC) can accurately estimate the current state and has stronger robustness when dealing with sudden disturbance than active inference control (AIFC).
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10:20-10:40, Paper WeA26.2 | |
>Nonlinear Predictor-Feedback Cooperative Adaptive Cruise Control |
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Bekiaris-Liberis, Nikolaos | Technical University of Crete |
Keywords: Delay systems, Autonomous vehicles, Stability of nonlinear systems
Abstract: We construct a nonlinear predictor-feedback Cooperative Adaptive Cruise Control (CACC) design for homogeneous vehicular platoons subject to actuators delays, which achieves: i) positivity of vehicles' speed and spacing states, ii) mathcal{L}_{infty} string stability of the platoon, iii) stability of each individual vehicular system, and iv) tracking of a constant reference speed (dictated by the leading vehicle) and spacing. The design relies on a nominal, nonlinear control law, which guarantees i)--iv) in the absence of actuator delay, and nonlinear predictor feedback. We consider a second-order, nonlinear vehicle model with input delay. The proofs of the theoretical guarantees i)--iv) rely on derivation of explicit estimates on solutions (both during open-loop and closed-loop operation), capitalizing on the ability of predictor feedback to guarantee complete delay compensation after the dead-time interval has elapsed, and derivation of explicit conditions on initial conditions and parameters of the nominal control law. We also present consistent simulation results.
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10:40-11:00, Paper WeA26.3 | |
>On the Intelligent Proportional Controller Applied to Linear Systems |
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Belhadjoudja, Mohamed Camil | Gipsa Lab / Cnrs |
Maghenem, Mohamed Adlene | Gipsa Lab, CNRS, France |
Witrant, Emmanuel | Université Grenoble Alpes |
Keywords: Delay systems, Data driven control, Linear systems
Abstract: We analyze in this paper the effect of the well-known intelligent proportional controller on the stability of linear control systems. Inspired by the literature on neutral time-delay systems and advanced-type systems, we derive sufficient conditions on the order of the control system, under which, the used controller fails to achieve exponential stability. Furthermore, we obtain conditions, relating the system’s and the control parameters, such that the closed-loop system is either unstable or not exponentially stable. After that, we provide cases where the used controller achieves exponential stability. The obtained results are illustrated on an experimental benchmark that consists of an electronic throttle valve.
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11:00-11:20, Paper WeA26.4 | |
>Synchronization for Linear Networked Systems Subject to Input and Communication Delays |
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De, Souradip | Indian Institute of Technology Kanpur |
Sahoo, Soumya Ranjan | Indian Institute of Technology Kanpur |
Wahi, Pankaj | Indian Institute of Technology |
Keywords: Delay systems, Distributed control, LMIs
Abstract: This paper investigates the synchronization problem for generic linear multi-agent systems with known or unknown heterogeneous input and communication delays. We propose two protocols that consist of consensus-based internal controller states and decentralized controllers. This kind of distributed dynamic control methodology is able to circumvent the interactive nature of two delays by translating the synchronization problem of agents into the stability of a set of delay differential equations. We examine the synchronization problem for two distinct cases, namely, known delays and unknown delays. When the delays are known, the stability criteria are satisfied by the feasibility of an input-delay-dependent linear matrix inequality and a communication-delay-dependent coupling strength bound. The margin on the communication delay is dependent not only on the network topology but also on the system matrix, which does not have any eigenvalues with positive real parts. We also develop a distributed dynamic control protocol that can handle unknown input and communication delays, and the stability criteria are realized by using the feasibility of a linear matrix inequality and a positive coupling strength. Synchronization is guaranteed even if the unknown communication delays are arbitrarily large but bounded and the upper bound on the heterogeneous input delays is known. The proposed control methodology guarantees that inaccurate measurements of the actual states of a particular agent will not lead to an irretrievable failure of the mission.
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11:20-11:40, Paper WeA26.5 | |
>Some Remarks on LQ Mean-Field Games for Stochastic Input Delay Systems |
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Mukaidani, Hiroaki | Hiroshima University |
Irie, Shunpei | Hiroshima University |
Xu, Hua | Univ. of Tsukuba |
Zhuang, Weihua | University of Waterloo |
Keywords: Delay systems, Mean field games, Stochastic optimal control
Abstract: In this study, we consider linear-quadratic (LQ) mean-field social control problems for a class of stochastic systems with ordinary control input and delay control input. We define a stabilization problem via a memoryless static output feedback (SOF) strategy and then solve the problem of minimizing the upper bound of the cost function using guaranteed cost control theory. It is found that the minimization of the upper bound of the cost function cannot be attained if only a delay control input exists. Futhermore, it is proved that it is impossible to implement a mean-field SOF strategy to solve the minimization problem, and the input matrix must have the same dimension as the state matrix. To solve this minimiztion problem, the necessary conditions for the sub-optimality are established via stochastic cross-coupled matrix equations (SCCMEs) using the Karush-Kuhn-Tucker condition and the state feedback strategy. Finally, the performance and usefulness of the proposed strategy are investigated using an order-reduced scheme based on the direct method.
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11:40-12:00, Paper WeA26.6 | |
>On Stability of Second-Order Nonlinear Time-Delay Systems without Damping |
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Aleksandrov, Alexander | St. Petersburg State University |
Efimov, Denis | Inria |
Fridman, Emilia | Tel-Aviv Univ |
Keywords: Delay systems, Nonlinear systems, Stability of nonlinear systems
Abstract: For a second-order system with time delays and power nonlinearity of the degree higher than one, which does not contain a velocity-proportional damping term, the conditions of local asymptotic stability of the zero solution are proposed. The result is based on application of the Lyapunov-Razumikhin approach, and it is illustrated by simulations. Our local stability conditions for nonlinear systems are less restrictive than stability conditions of the corresponding linear models.
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WeB01 |
Orchid Main 4202-4306 |
Statistical Learning Theory for Identification and Control |
Tutorial Session |
Chair: Ziemann, Ingvar | University of Pennsylvania |
Co-Chair: Tsiamis, Anastasios | ETH Zurich |
Organizer: Jedra, Yassir | KTH |
Organizer: Matni, Nikolai | University of Pennsylvania |
Organizer: Pappas, George J. | University of Pennsylvania |
Organizer: Tsiamis, Anastasios | ETH Zurich |
Organizer: Ziemann, Ingvar | University of Pennsylvania |
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13:30-13:50, Paper WeB01.1 | |
>Introduction and Roadmap (I) |
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Ziemann, Ingvar | University of Pennsylvania |
Tsiamis, Anastasios | ETH Zurich |
Keywords: Statistical learning, Identification, Estimation
Abstract: Machine learning methods are being integrated at an ever-increasing rate into domains that have traditionally been within the purview of controls. There is a wide range of examples, including perception-based control, agile robotics, and autonomous driving and racing. As exciting as these developments may be, they have been most pronounced on the experimental and empirical sides. To deploy these systems safely, stably, and robustly into the real world, we argue that a principled and integrated theoretical understanding of a) fundamental limitations and b) statistical optimality is needed. In the past few years, a host of new techniques have been introduced to our field. Existing results in this area are relatively inaccessible to a typical first- or second-year graduate student in control theory, as they require sophisticated mathematical tools not typically included in a control theorist’s training (e.g., high-dimensional statistics and learning theory). In the first talk, we present the scope of our tutorial, which is to introduce recently developed non-asymptotic methods in the theory of (mainly linear) system identification to a wider audience. Our aim is to give simple proofs of the main developments and to highlight and collect the key technical tools to arrive at these results. We present the roadmap of the tutorial, offering a high-level preview of these tools, which lie at the intersection of Non-asymptotic Statistics and Control Theory. We emphasize that existing results for linear systems rely on the non asymptotic analysis of the least squares estimator under time-dependent data.
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13:50-14:10, Paper WeB01.2 | |
>Basic Concentration Inequalities (I) |
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Jedra, Yassir | KTH |
Ziemann, Ingvar | University of Pennsylvania |
Keywords: Statistical learning, Identification
Abstract: In this talk we introduce the basic technical machinery - concentration inequalities- underlying much of modern statistical learning theory. We discuss how the Chernoff trick and notions such as sub-Gaussianity allow for a relatively satisfying non-asymptotic analogue to classical asymptotics. We conclude by introducing a more advanced concentration inequality, the Hanson- Wright inequality, which provides estimate of the deviation of certain random quadratic forms. This inequality will be key in the following talks.
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14:10-14:30, Paper WeB01.3 | |
>The Lower Tail of the Empirical Covariance (I) |
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Ziemann, Ingvar | University of Pennsylvania |
Keywords: Statistical learning, Estimation, Identification
Abstract: In this talk we present a streamlined approach to control the lower spectrum of certain empirical covariance matrices of Causal Linear sub-Gaussian processes. The lower tail of this empirical covariance matrix arises as one of the two key terms in the canonical error decomposition of the least squares estimator. Put differently, this technique allows to quantify persistency of excitation in a non-asymptotic fashion for host of interesting processes, including for instance linear dynamical systems. The proof technique we present here is novel to the literature and only uses the Hanson-Wright Inequality and basic covering arguments.
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14:30-14:50, Paper WeB01.4 | |
>Self-Normalized Martingales (I) |
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Lee, Bruce | University of Pennsylvania |
Keywords: Statistical learning, Estimation, Identification
Abstract: In this talk, we present a brief overview of the theory of self-normalized processes as used in the analysis of least squares over causally dependent data. The self-normalized martingale arises as one of two key terms in the decomposition of the least squares parameter estimation error. We first review the relevant definitions and assumptions required to derive a (almost) time-scale invariant bound on this self-normalized martingale term. We then provide an interpretation of the result, along with a roadmap for how it is applied in the analysis of system identification. We conclude by sketching a proof for the result by employing an approach known as pseudo-maximization.
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14:50-15:10, Paper WeB01.5 | |
>Non-Asymptotic Linear System Identification (I) |
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Tsiamis, Anastasios | ETH Zurich |
Keywords: Statistical learning, Identification, Estimation
Abstract: In this talk, we analyze well-known linear system identification algorithms that rely on the least squares algorithm. First, we focus on the identification of autoregressive systems with exogenous inputs, also known as ARX systems. By utilizing the tools presented in previous talks and contained in our tutorial paper, we establish a non-asymptotic, high-probability bound on the performance of the least-squares estimator. The bound describes how the system identification accuracy changes with the number of samples, the required confidence, and system-theoretic properties such as system size/dimension and signal-to-noise ratio. We also establish non-asymptotic persistency of excitation, that is, excitation of all the modes of the system with high probability, which is crucial for system identification. Next, we analyze the system identification of Markov parameters of statespace systems by reducing the problem to (approximate) ARX identification, which is a fundamental step for many subspace identification algorithms.
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15:10-15:30, Paper WeB01.6 | |
>Beyond Linear System Identification (I) |
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Ziemann, Ingvar | University of Pennsylvania |
Keywords: Statistical learning, Identification, Estimation
Abstract: In this talk we outline some recent advances beyond the linear setting, focusing on finite hypothesis classes for simplicity. We illustrate how the two key concepts—persistency of excitation and control of a random walk-type quantity—for proving learning rates with the square loss function generalize to the nonlinear setting. In the nonlinear setting, the lower uniform estimate can be seen as a generalized notion of persistency of excitation, whereas a variational perspective of the empirical least squares error allows for a development very much in parallel to the self-normalized theory discussed in the fourth talk.
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WeB02 |
Melati Main 4001AB-4102 |
Learning-Based Control II: Safety and Robustness |
Invited Session |
Chair: Zeilinger, Melanie N. | ETH Zurich |
Co-Chair: Rantzer, Anders | Lund University |
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 WeB02.1 | |
>A Computationally Lightweight Safe Learning Algorithm (I) |
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Baumann, Dominik | Aalto University |
Kowalczyk, Krzysztof | Wroclaw University of Science and Technology |
Tiels, Koen | Eindhoven University of Technology |
Wachel, Pawel | Wroclaw University of Science and Technology, Poland |
Keywords: Statistical learning, Machine learning, Learning
Abstract: Safety is an essential asset when learning control policies for physical systems, as violating safety constraints during training can lead to expensive hardware damage. In response to this need, the field of safe learning has emerged with algorithms that can provide probabilistic safety guarantees without knowledge of the underlying system dynamics. Those algorithms often rely on Gaussian process inference. Unfortunately, Gaussian process inference scales cubically with the number of data points, limiting applicability to high-dimensional and embedded systems. In this paper, we propose a safe learning algorithm that provides probabilistic safety guarantees but leverages the Nadaraya-Watson estimator instead of Gaussian processes. For the Nadaraya-Watson estimator, we can reach logarithmic scaling with the number of data points. We provide theoretical guarantees for the estimates, embed them into a safe learning algorithm, and show numerical experiments on a simulated seven-degrees-of-freedom robot manipulator.
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13:50-14:10, Paper WeB02.2 | |
>Learning Over Contracting and Lipschitz Closed-Loops for Partially-Observed Nonlinear Systems (I) |
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Barbara, Nicholas H. | The University of Sydney |
Wang, Ruigang | The University of Sydney |
Manchester, Ian R. | University of Sydney |
Keywords: Learning, Nonlinear output feedback, Robust control
Abstract: This paper presents a policy parameterization for learning-based control on nonlinear, partially-observed dynamical systems. The parameterization is based on a nonlinear version of the Youla parameterization and the recently proposed Recurrent Equilibrium Network (REN) class of models. We prove that the resulting Youla-REN parameterization automatically satisfies stability (contraction) and user-tunable robustness (Lipschitz) conditions on the closed-loop system. This means it can be used for safe learning-based control with no additional constraints or projections required to enforce stability or robustness. We test the new policy class in simulation on two reinforcement learning tasks: 1) magnetic suspension, and 2) inverting a rotary-arm pendulum. We find that the Youla-REN performs similarly to existing learning-based and optimal control methods while also ensuring stability and exhibiting improved robustness to adversarial disturbances.
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14:10-14:30, Paper WeB02.3 | |
>An Online Learning Analysis of Minimax Adaptive Control (I) |
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Renganathan, Venkatraman | Lund University |
Iannelli, Andrea | University of Stuttgart |
Rantzer, Anders | Lund University |
Keywords: Robust adaptive control, Adaptive control, Robust control
Abstract: We present an online learning analysis of minimax adaptive control for the case where the uncertainty includes a finite set of linear dynamical systems. Precisely, for each system inside the uncertainty set, we define the model-based regret by comparing the state and input trajectories from the minimax adaptive controller against that of an optimal controller in hindsight that knows the true dynamics. We then define the total regret as the worst case model-based regret with respect to all models in the considered uncertainty set. We study how the total regret accumulates over time and its effect on the adaptation mechanism employed by the controller. Moreover, we investigate the effect of the disturbance on the growth of the regret over time and draw connections between robustness of the controller and the associated regret rate.
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14:30-14:50, Paper WeB02.4 | |
>Risk-Sensitive Inhibitory Control for Safe Reinforcement Learning (I) |
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Lederer, Armin | Technical University of Munich |
Noorani, Erfaun | University of Maryland College Park |
Baras, John S. | University of Maryland |
Hirche, Sandra | Technische Universität München |
Keywords: Machine learning, Learning, Uncertain systems
Abstract: Humans have the ability to deviate from their natural behavior when necessary, which is a cognitive process called response inhibition. Similar approaches have independently received increasing attention in recent years for ensuring the safety of control. Realized using control barrier functions or predictive safety filters, these approaches can effectively ensure the satisfaction of state constraints through an online adaptation of nominal control laws, e.g., obtained through reinforcement learning. While the focus of these realizations of inhibitory control has been on risk-neutral formulations, human studies have shown a tight link between response inhibition and risk attitude. Inspired by this insight, we propose a flexible, risk-sensitive method for inhibitory control. Our method is based on a risk-aware condition for value functions, which guarantees the satisfaction of state constraints. We propose a method for learning these value functions using common techniques from reinforcement learning and derive sufficient conditions for its success. By enforcing the derived safety conditions online using the learned value function, risk-sensitive inhibitory control is effectively achieved. The effectiveness of the developed control scheme is demonstrated in simulations.
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14:50-15:10, Paper WeB02.5 | |
>Learning Safety Filters for Unknown Discrete-Time Linear Systems |
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Farokhi, Farhad | The University of Melbourne |
Leong, Alex S. | DST Group |
Zamani, Mohammad | University of Melbourne |
Shames, Iman | Australian National University |
Keywords: Networked control systems, Linear systems, Stochastic systems
Abstract: A learning-based safety filter is developed for discrete-time linear time-invariant systems with unknown models subject to Gaussian noises with unknown covariance. Safety is characterized using polytopic constraints on the states and control inputs. The empirically learned model and process noise covariance with their confidence bounds are used to construct a robust optimization problem for minimally modifying nominal control actions to ensure safety with high probability. The optimization problem relies on tightening the original safety constraints. The magnitude of the tightening is larger at the beginning since there is little information to construct reliable models, but shrinks with time as more data becomes available.
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15:10-15:30, Paper WeB02.6 | |
>Data-Driven Synthesis of Safety Controllers for Partially-Observable Systems with Unknown Models (I) |
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Jahanshahi, Niloofar | Ludwig Maximilian University of Munich |
Zamani, Majid | University of Colorado Boulder |
Keywords: Optimization
Abstract: This paper is concerned with the formal synthesis of safety controllers for partially-observable discrete-time control systems with unknown mathematical models. Given a state estimator with unknown dynamics but a known upper bound on the estimation error, we propose a data-driven approach to compute controllers that render the partially-observable systems with unknown dynamics safe. Our proposed method is based on the construction of control barrier certificates, where we first formulate the barrier-based safety problem as a robust program (RP). The proposed RP is not tractable since the unknown model of the estimator appears in one of its constraints. To tackle this issue, we collect a set of data from the black-box system and its estimator and replace the original RP with a scenario program (SP). Due to the existence of a max-min constraint in the SP, we construct an analogous scenario program, denoted by SP^alpha, in which the max-min constraint is replaced with a single inequality constraint. The control barrier certificates together with their corresponding controllers can then be computed by solving SP^alpha via the collected data. By connecting the feasible solutions of SP^alpha and SP, the safety of the partially-observable system equipped with the synthesized controller can be guaranteed with 100% confidence. We show the effectiveness of our results by synthesizing a safety controller for a partially-observable Van der Pol oscillator with unknown dynamics.
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WeB03 |
Melati Junior 4010A-4111 |
Learning Algorithms for Optimization and Applications |
Invited Session |
Chair: Li, Xiuxian | Tongji University |
Co-Chair: Yi, Xinlei | Massachusetts Institute of Technology |
Organizer: Li, Xiuxian | Tongji University |
Organizer: Yi, Xinlei | Massachusetts Institute of Technology |
Organizer: Yang, Tao | Northeastern University |
Organizer: Xie, Lihua | Nanyang Tech. Univ |
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13:30-13:50, Paper WeB03.1 | |
>Variance-Reduced Shuffling Gradient Descent with Momentum for Finite-Sum Minimization |
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Jiang, Xia | Beijing Institute of Technology |
Zeng, Xianlin | Beijing Institute Fo Technology |
Xie, Lihua | Nanyang Tech. Univ |
Sun, Jian | Beijing Institute of Technology |
Keywords: Optimization, Numerical algorithms
Abstract: Finite-sum minimization is a fundamental optimization problem in signal processing and machine learning. This paper proposes a variance-reduced shuffling gradient descent with Nesterov’s momentum for smooth convex finite-sum optimization. We integrate an explicit variance reduction into the shuffling gradient descent to deal with the variance introduced by shuffling gradients. The proposed algorithm with a unified shuffling scheme converges at a rate of O(1/T), where T is the number of epochs. The convergence rate independent of gradient variance is better than most existing shuffling gradient algorithms for convex optimization. Finally, numerical simulations demonstrate the convergence performance of the proposed algorithm.
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13:50-14:10, Paper WeB03.2 | |
>Quantized Distributed Online Projection-Free Convex Optimization |
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Zhang, Wentao | Nanjing University of Science and Technology |
Shi, Yang | University of Victoria |
Zhang, Baoyong | Nanjing University of Science and Technology |
Lu, Kaihong | Shandong University of Science and Technology |
Yuan, Deming | Nanjing University of Science and Technology |
Keywords: Network analysis and control, Optimization algorithms, Cooperative control
Abstract: This paper considers online distributed convex constrained optimization over a time-varying multi-agent network. Agents in this network cooperate to minimize the global objective function through information exchange with their neighbors and local computation. Since the capacity or bandwidth of communication channels often is limited, a random quantizer is introduced to reduce the transmission bits. Through incorporating this quantizer, we develop a quantized distributed online projection-free optimization algorithm, which can achieve the saving of communication resources and computational costs. The dynamic regret bound mathcal{O}( max{T^{1-gamma}, T^{gamma}(1+H_T) } +D_T) of the proposed algorithm is rigorously established, which depends on the total time T, function variation H_T, gradient variation D_T, and the parameter 0
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14:10-14:30, Paper WeB03.3 | |
>A Game Theoretic Approach for Safe and Distributed Control of Unmanned Aerial Vehicles (I) |
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Andre do Nascimento, Allan | University of Oxford |
Papachristodoulou, Antonis | University of Oxford |
Margellos, Kostas | University of Oxford |
Keywords: Optimization algorithms, Game theory, Predictive control for linear systems
Abstract: This paper presents a distributed methodology to produce collision-free control laws for an Unmanned Aerial Vehicles (UAVs) fleet. We use a game theoretic framework, where UAVs accommodate for individual and fleet goals, while respecting safety requirements. The method combines Control Barrier Functions (CBFs) and a primal-dual algorithm for Nash equilibrium (NE) seeking in generalized games. Feedback is introduced by Model Predictive Control (MPC) and we analyze its stability properties. The combination of these tools allows for a distributed, collision-free pointwise equilibrium solution, despite the agents’ coupling, due to common target tracking and the collision avoidance constraints. Our algorithmic results are supported theoretically and its efficacy is demonstrated via extensive numerical simulations.
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14:30-14:50, Paper WeB03.4 | |
>Linear Last-Iterate Convergence for Continuous Games with Coupled Inequality Constraints (I) |
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Meng, Min | Tongji University |
Li, Xiuxian | Tongji University |
Keywords: Game theory
Abstract: In this paper, the generalized Nash equilibrium (GNE) seeking problem for continuous games with coupled affine inequality constraints is investigated in a partial-decision information scenario, where each player can only access its neighbors' information through local communication although its cost function possibly depends on all other players' strategies. To this end, a novel decentralized primal-dual algorithm based on consensus and dual diffusion methods is devised for seeking the variational GNE of the studied games. This paper also provides theoretical analysis to show that the designed algorithm converges linearly for the last-iterate, which, to our best knowledge, is the first to propose a linearly convergent GNE seeking algorithm under coupled affine inequality constraints. Finally, a numerical example is presented to demonstrate the efficiency of the obtained theoretical results.
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14:50-15:10, Paper WeB03.5 | |
>Delay-Agnostic Asynchronous Distributed Optimization (I) |
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Wu, Xuyang | KTH Royal Institute of Technology |
Liu, Changxin | KTH Royal Institute of Technology |
Magnusson, Sindri | Stockholm University |
Johansson, Mikael | KTH - Royal Institute of Technology |
Keywords: Optimization algorithms, Optimization
Abstract: Existing asynchronous distributed optimization algorithms often use diminishing step-sizes that cause slow practical convergence, or fixed step-sizes that depend on an assumed upper bound of delays. Not only is such a delay bound hard to obtain in advance, but it is also large and therefore results in unnecessarily slow convergence. This paper develops asynchronous versions of two distributed algorithms, DGD and DGD-ATC, for solving consensus optimization problems over undirected networks. In contrast to alternatives, our algorithms can converge to the fixed point set of their synchronous counterparts using step-sizes that are independent of the delays. We establish convergence guarantees under both partial and total asynchrony. The practical performance of our algorithms is demonstrated by numerical experiments.
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15:10-15:30, Paper WeB03.6 | |
>PIQP: A Proximal Interior-Point Quadratic Programming Solver (I) |
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Schwan, Roland | EPFL |
Jiang, Yuning | EPFL |
Kuhn, Daniel | EPFL |
Jones, Colin N. | EPFL |
Keywords: Numerical algorithms, Computational methods, Optimization algorithms
Abstract: This paper presents PIQP, a high-performance toolkit for solving generic sparse quadratic programs (QP). Combining an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM), the algorithm can handle ill-conditioned convex QP problems without the need for linear independence of the constraints. The open-source implementation is written in C++ with interfaces to C, Python, Matlab, and R leveraging the Eigen3 library. The method uses a pivoting-free factorization routine and allocation-free updates of the problem data, making the solver suitable for embedded applications. The solver is evaluated on the Maros-Mészáros problem set and optimal control problems, demonstrating state-of-the-art performance for both small and large-scale problems, outperforming commercial and open-source solvers.
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WeB04 |
Simpor Junior 4913 |
Connected Automated Traffic Systems |
Invited Session |
Chair: Yu, Huan | The Hong Kong University of Science and Technology(Guangzhou) |
Co-Chair: Molnar, Tamas G. | California Institute of Technology |
Organizer: Yu, Huan | The Hong Kong University of Science and Technology(Guangzhou) |
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13:30-13:50, Paper WeB04.1 | |
>Safety-Critical Traffic Control for Mixed Autonomy Systems with Input Delay and Disturbances (I) |
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Zhao, Chenguang | The Hong Kong University of Science and Technology |
Yu, Huan | The Hong Kong University of Science and Technology(Guangzhou) |
Keywords: Traffic control, Delay systems, Lyapunov methods
Abstract: While the connected automated vehicle (CAV) has been applied in vehicle-based traffic control that aims to stabilize a string of car-following human-driven vehicles (HV), the safety impact of a CAV controller on the overall traffic flow system is still an open question. In this paper, we propose a Robust Safety-critical Traffic Control (RSTC) design to impart safety for the mixed autonomy traffic system, in which the speed disturbance from a leading HV and input delay of the stabilizing CAV controller are considered. We employ Control Barrier Function (CBF) to impose safety constraints on a nominal CAV control input that achieves string stability. The key challenge lies in incorporating effect of the input delay and external disturbances into the CBF constraints. The predicted speed and spacing gap in the robust CBF design is obtained using a delay-compensating state predictor. The forward invariance of the safe set is proved given the derivative of speed disturbance, i.e., acceleration of the leading vehicle, is bounded. The safety improvement of RSTC over the nominal controller is then validated via numerical simulation.
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13:50-14:10, Paper WeB04.2 | |
>Observer-Based Output Feedback Stabilization for Stop-And-Go Waves of Vehicle Traffic Flow (I) |
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Luan, Haoran | Beijing University of Technology |
Zhan, Jingyuan | Beijing University of Technology |
Li, Xiaoli | Beijing University of Technology |
Zhang, Liguo | Beijing University of Technology |
Keywords: Distributed parameter systems, Backstepping, Traffic control
Abstract: This paper designs an observer–based output feedback controller for traffic flow with stop–and–go waves and disturbances in order to dissipate traffic congestion. The macroscopic traffic flow dynamics in the congestion regime is described by the linearized Aw–Rascle–Zhang (ARZ) traffic flow model over a time–varying moving spatial domain, and according to the Rankine–Hugoniot condition and the characteristic velocities of the ARZ model, a novel propagation model of the stop–and–go waves is proposed. To stabilize the traffic state and the stop–and–go waves, and to suppress traffic disturbances, an observer–based output feedback controller is designed by using the PDE backstepping method. The controller utilizes the estimated state of an observer, which is constructed based on boundary measurements only. The exponential stability of the closed–loop system in the H1 norm is proved by the Lyapunov analysis. Finally, the effectiveness of the controller for stabilizing the traffic state with stop-and-go waves and disturbances is verified by numerical simulations.
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14:10-14:30, Paper WeB04.3 | |
>On the Safety of Connected Cruise Control: Analysis and Synthesis with Control Barrier Functions (I) |
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Molnar, Tamas G. | California Institute of Technology |
Orosz, Gabor | University of Michigan |
Ames, Aaron D. | California Institute of Technology |
Keywords: Autonomous vehicles, Constrained control, Traffic control
Abstract: Connected automated vehicles have shown great potential to improve the efficiency of transportation systems in terms of passenger comfort, fuel economy, stability of driving behavior and mitigation of traffic congestions. Yet, to deploy these vehicles and leverage their benefits, the underlying algorithms must ensure their safe operation. In this paper, we address the safety of connected cruise control strategies for longitudinal car following using control barrier function (CBF) theory. In particular, we consider various safety measures such as minimum distance, time headway and time to conflict, and provide a formal analysis of these measures through the lens of CBFs. Additionally, motivated by how stability charts facilitate stable controller design, we derive safety charts for existing connected cruise controllers to identify safe choices of controller parameters. Finally, we combine the analysis of safety measures and the corresponding stability charts to synthesize safety-critical connected cruise controllers using CBFs. We verify our theoretical results by numerical simulations.
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14:30-14:50, Paper WeB04.4 | |
>Learning Optimal Robust Control of Connected Vehicles in Mixed Traffic Flow (I) |
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Li, Jie | Tsinghua University |
Wang, Jiawei | Tsinghua University |
Li, Shengbo Eben | Tsinghua University |
Li, Keqiang | Tsinghua University, Beijing, China |
Keywords: Traffic control, Robust control, Autonomous vehicles
Abstract: Connected and automated vehicles (CAVs) technologies promise to attenuate undesired traffic disturbances. However, in mixed traffic where human-driven vehicles (HDVs) also exist, the nonlinear human-driving behavior has brought critical challenges for effective CAV control. This paper employs the policy iteration method to learn the optimal robust controller for nonlinear mixed traffic systems. Precisely, we consider the H_{infty} control framework and formulate it as a zero-sum game, the equivalent condition for whose solution is converted into a Hamilton–Jacobi inequality with a Hamiltonian constraint. Then, a policy iteration algorithm is designed to generate stabilizing controllers with desired attenuation performance. Based on the updated robust controller, the attenuation level is further optimized in sum of squares program by leveraging the gap of the Hamiltonian constraint. Simulation studies verify that the obtained controller enables the CAVs to dampen traffic perturbations and smooth traffic flow.
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14:50-15:10, Paper WeB04.5 | |
>How Does Driver Non-Compliance Destroy Traffic Routing Control? (I) |
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Tang, Yu | New York University |
Jin, Li | Shanghai Jiao Tong University |
Ozbay, Kaan | New York University |
Keywords: Transportation networks, Traffic control
Abstract: Routing control is one of important traffic man- agement strategies against urban congestion. However, it could be compromised by heterogeneous driver non-compliance with routing instructions. In this article, we model the compliance in a stochastic manner and investigate its impacts on routing control. We consider traffic routing for two parallel links. Particularly, we consider two scenarios: one ignores congestion spillback while the other one considers it. We formulate the problem as a Markov chain, given random drivers’ adherence. Then, we propose the stability and instability conditions to reveal when the routing is able or unable to stabilize the traffic. We show that for links without congestion spillback there exists a necessary and sufficient stability criterion. For links admiting congestion propagation, we present one stability condition and one instability condition. These stability conditions allow us to quantify the impacts of driver non-compliance on the two-link network in terms of throughput. Finally, we illustrate the results with a set of numerical examples.
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15:10-15:30, Paper WeB04.6 | |
>Uncertainty-Aware Grounded Action Transformation towards Sim-To-Real Transfer for Traffic Signal Control (I) |
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Da, Longchao | New Jersey Institute of Technology |
Mei, Hao | New Jersey Institue of Technology |
Sharma, Romir | West Windsor-Plainsboro High School South |
Wei, Hua | Arizona State University |
Keywords: Adaptive control, Traffic control, Intelligent systems
Abstract: Traffic signal control (TSC) is a complex and important task that affects the daily lives of millions of people. Reinforcement Learning (RL) has shown promising results in optimizing traffic signal control, but current RL-based TSC methods are mainly trained in simulation and suffer from the performance gap between simulation and the real world. In this paper, we propose a simulation-to-real-world (sim-to-real) transfer approach called UGAT, which transfers a learned policy trained from a simulated environment to a real-world environment by dynamically transforming actions in the simulation with uncertainty to mitigate the domain gap of transition dynamics. We evaluate our method on a simulated traffic environment and show that it significantly improves the performance of the transferred RL policy in the real world.
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WeB05 |
Simpor Junior 4912 |
Distributed Optimization and Learning for Networked Systems |
Invited Session |
Chair: Yang, Tao | Northeastern University |
Co-Chair: Uribe, Cesar A. | Rice University |
Organizer: Yang, Tao | Northeastern University |
Organizer: Uribe, Cesar A. | Rice University |
Organizer: Lu, Jie | ShanghaiTech University |
Organizer: Nedich, Angelia | Arizona State University |
Organizer: Hong, Yiguang | Tongji University |
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13:30-13:50, Paper WeB05.1 | |
>A Robust Dynamic Average Consensus Algorithm That Ensures Both Differential Privacy and Accurate Convergence (I) |
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Wang, Yongqiang | Clemson University |
Keywords: Control Systems Privacy, Cooperative control, Decentralized control
Abstract: We propose a new dynamic average consensus algorithm that is robust to information-sharing noise arising from differential-privacy design. Not only is dynamic average consensus widely used in cooperative control and distributed tracking, it is also a fundamental building block in numerous distributed computation algorithms such as multi-agent optimization and distributed Nash equilibrium seeking. We propose a new dynamic average consensus algorithm that is robust to persistent and independent information-sharing noise added for the purpose of differential-privacy protection. In fact, the algorithm can ensure both provable convergence to the exact average reference signal and rigorous ϵ-differential privacy (even when the number of iterations tends to infinity), which, to our knowledge, has not been achieved before in average consensus algorithms. Given that channel noise in communication can be viewed as a special case of differential-privacy noise, the algorithm can also be used to counteract communication imperfections. Numerical simulation results confirm the effectiveness of the proposed approach.
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13:50-14:10, Paper WeB05.2 | |
>Distributed Optimization on Directed Graphs Based on Inexact ADMM with Partial Participation (I) |
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Yi, Dingran | University of Science and Technology of China |
Freris, Nikolaos M. | University of Science and Technology of China |
Keywords: Optimization, Optimization algorithms
Abstract: We consider the problem of minimizing the sum of cost functions pertaining to agents over a network whose topology is captured by a directed graph (i.e., asymmetric communication). We cast the problem into the ADMM setting, via a consensus constraint, for which both primal subproblems are solved inexactly. In specific, the computationally demanding local minimization step is replaced by a single gradient step, while the averaging step is approximated in a distributed fashion. Furthermore, partial participation is allowed in the implementation of the algorithm. Under standard assumptions on strong convexity and Lipschitz continuous gradients, we establish linear convergence and characterize the rate in terms of the connectivity of the graph and the conditioning of the problem. Our line of analysis provides a sharper convergence rate compared to Push-DIGing. Numerical experiments corroborate the merits of the proposed solution in terms of superior rate as well as computation and communication savings over baselines.
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14:10-14:30, Paper WeB05.3 | |
>Convergence Analysis of the Best Response Algorithm for Time-Varying Games (I) |
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Wang, Zifan | KTH Royal Institute of Technology |
Shen, Yi | Duke University |
Zavlanos, Michael M. | Duke University |
Johansson, Karl H. | KTH Royal Institute of Technology |
Keywords: Optimization, Game theory
Abstract: This paper studies a class of strongly monotone games involving non-cooperative agents that optimize their own time-varying cost functions. We assume that the agents can observe other agents' historical actions and choose actions that best respond to other agents' previous actions; we call this a best response scheme. We start by analyzing the convergence rate of this best response scheme for standard time-invariant games. Specifically, we provide a sufficient condition on the strong monotonicity parameter of the time-invariant games under which the proposed best response algorithm achieves exponential convergence to the static Nash equilibrium. We further illustrate that this best response algorithm may oscillate when the proposed sufficient condition fails to hold, which indicates that this condition is tight. Next, we analyze this best response algorithm for time-varying games where the cost functions of each agent change over time. Under similar conditions as for time-invariant games, we show that the proposed best response algorithm stays asymptotically close to the evolving equilibrium. We do so by analyzing both the equilibrium tracking error and the dynamic regret. Numerical experiments on economic market problems are presented to validate our analysis.
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14:30-14:50, Paper WeB05.4 | |
>Distributed Nonsmooth Optimization with Different Local Constraints Via Exact Penalty (I) |
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Liu, Shuyu | Tongji University |
Liang, Shu | Tongji University |
Hong, Yiguang | Chinese Academy of Sciences |
Keywords: Optimization algorithms, Optimization, Lyapunov methods
Abstract: In this paper, we study a distributed optimization problem, where decision variables of agents need to satisfy different local constraints and the consensus constraint to minimize the sum of local cost functions. We propose a novel method to remove all these constraints by employing the exact penalty so that the derived equivalent unconstrained problem can be directly solved by subgradient descent type differential inclusions. The algorithm achieves O(1/t) rate of convergence when the cost functions are convex. Moreover, it achieves exponential convergence when the cost functions are strongly convex. Our method needs no dual variable to deal with the constraints so that computation and communication resources are saved in comparison with primal-dual methods. In addition, the method overcomes a divergence problem arising from an existing exponentially convergent distributed algorithm based on the exact penalty when the local constraints are different.
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14:50-15:10, Paper WeB05.5 | |
>Resilient Federated Learning under Byzantine Attack in Distributed Nonconvex Optimization with 2-F Redundancy (I) |
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Dutta, Amit | Virginia Polytechnic Institute and State University |
Doan, Thinh T. | Virginia Tech |
Reed, Jeffrey | Virginia Tech |
Keywords: Optimization, Distributed control, Fault tolerant systems
Abstract: We study the problem of Byzantine fault tolerance in a distributed optimization setting, where there is a group of N agents communicating with a trusted centralized coordinator. Among these agents, there is a subset of f agents that may not follow a prescribed algorithm and may share arbitrarily incorrect information with the coordinator. The goal is to find the optimizer of the aggregate cost functions of the honest agents. We will be interested in studying the local gradient descent method, also known as federated learning, to solve this problem. However, this method often returns an approximate value of the underlying optimal solution in the Byzantine setting. Recent work showed that by incorporating the so-called comparative elimination (CE) filter at the coordinator, one can provably mitigate the detrimental impact of Byzantine agents and precisely compute the true optimizer in the convex setting. The focus of the present work is to provide theoretical results to show the convergence of local gradient methods with the CE filter in a nonconvex setting. We will also provide a number of numerical simulations to support our theoretical results.
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15:10-15:30, Paper WeB05.6 | |
>Distributed Online Optimization with Coupled Inequality Constraints Over Unbalanced Directed Networks (I) |
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Wang, Dandan | ShanghaiTech University |
Zhu, Daokuan | ShanghaiTech University |
Sou, Kin Cheong | National Sun Yat-Sen University |
Lu, Jie | ShanghaiTech University |
Keywords: Optimization algorithms, Optimization, Networked control systems
Abstract: This paper studies a distributed online convex optimization problem, where agents in an unbalanced network cooperatively minimize the sum of their time-varying local cost functions subject to a coupled inequality constraint. To solve this problem, we propose a distributed dual subgradient tracking algorithm, called DUST, which attempts to optimize a dual objective by means of tracking the primal constraint violations and integrating dual subgradient and push-sum techniques. Different from most existing works, we allow the underlying network to be unbalanced with a column stochastic mixing matrix. We show that DUST achieves sublinear dynamic regret and constraint violations, provided that the accumulated variation of the optimal sequence grows sublinearly. If the standard Slater’s condition is additionally imposed, DUST acquires a smaller constraint violation bound than the alternative existing methods applicable to unbalanced networks. Simulations on a plug-in electric vehicle charging problem demonstrate the superior convergence of DUST.
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WeB06 |
Simpor Junior 4911 |
Estimation II |
Regular Session |
Chair: Dong, Daoyi | University of New South Wales |
Co-Chair: Chen, Hua | Southern University of Science and Technology |
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13:30-13:50, Paper WeB06.1 | |
>A Unified Approach to Optimally Solving Sensor Scheduling and Sensor Selection Problems in Kalman Filtering |
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Dutta, Shamak | University of Waterloo |
Wilde, Nils | TU Delft |
Smith, Stephen L. | University of Waterloo |
Keywords: Estimation, Kalman filtering, Optimization
Abstract: We consider a general form of the sensor scheduling problem for state estimation of linear dynamical systems, which involves selecting sensors that minimize the trace of the Kalman filter error covariance (weighted by a positive semidefinite matrix) subject to polyhedral constraints. This general form captures several well-studied problems including sensor placement, sensor scheduling with budget constraints, and Linear Quadratic Gaussian (LQG) control and sensing co-design. We present a mixed integer optimization approach that is derived by exploiting the optimality of the Kalman filter. While existing work has focused on approximate methods to specific problem variants, our work provides a unified approach to computing optimal solutions to the general version of sensor scheduling. In simulation, we show this approach finds optimal solutions for systems with 30 to 50 states in seconds.
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13:50-14:10, Paper WeB06.2 | |
>A General Iterative Extended Kalman Filter Framework for State Estimation on Matrix Lie Groups |
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Liu, Ben | Southern University of Science and Technology |
Chen, Hua | Southern University of Science and Technology |
Zhang, Wei | Southern University of Science and Technology |
Keywords: Estimation, Kalman filtering
Abstract: In this paper, we focus on state estimation prob- lem for nonlinear systems on joint matrix Lie group G and Euclidean space Rn. We propose a general iterative Kalman filter, aiming to integrate the prediction step into the iteration scheme, which is not considered in the conventional iterative extended Kalman filter framework. Such an extra iteration scheme in the prediction step helps improving the accuracy of probability density function propagation through nonlinearities, which can further lead to more accurate estimations of the system states. In addition, the proposed framework unifies the Kalman filter based estimation schemes on studied manifold by adopting the perspective from Gaussian Bayesian inference. The improvement of the proposed framework is illustrated by the ES-GIKF algorithm that is instantiated from the proposed framework in a numerical simulation.
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14:10-14:30, Paper WeB06.3 | |
>Data Informativity for Lyapunov Equations |
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Banno, Ikumi | Nagoya University |
Azuma, Shun-ichi | Kyoto University |
Ariizumi, Ryo | Tokyo University of Agriculture and Technology |
Asai, Toru | Nagoya University |
Imura, Jun-ichi | Tokyo Institute of Technology |
Keywords: Estimation, Linear systems, Computational methods
Abstract: Recently, the novel framework for data-driven analysis and control, called data informativity, was proposed. This notion represents whether the given data contain sufficient information to solve a problem or not. However, data informativity for solving a Lyapunov equation has never been addressed before. This letter characterizes the data informativity for the Lyapunov equations in the form of AP + PA^T = -Q, where A and Q are square matrices and P is an unknown matrix. First, we clarify the relationship between the unique solution to the Lyapunov equation and the controllable subspace of a system. Second, based on this result, we provide a necessary and sufficient condition for the data informativity, which is characterized by the possibility of a certain matrix decomposition of Q, called the data-basis decomposition. Finally, we present a direct data-driven method for solving the Lyapunov equation based on our data informativity condition. This method has a potential to compute the solution even if the data do not contain sufficient information to identify the system.
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14:30-14:50, Paper WeB06.4 | |
>Minimax Two-Stage Gradient Boosting for Parameter Estimation |
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Lakshminarayanan, Braghadeesh | KTH Royal Institute of Technology |
Rojas, Cristian R. | KTH Royal Institute of Technology |
Keywords: Estimation, Machine learning, Identification
Abstract: Parameter estimation is an important sub-field in statistics and system identification. Various methods for parameter estimation have been proposed in the literature, among which the Two-Stage (TS) approach is particularly promising, due to its ease of implementation and reliable estimates. Among the different statistical frameworks used to derive TS estimators, the min-max framework is attractive due to its mild dependence on prior knowledge about the parameters to be estimated. However, the existing implementation of the minimax TS approach has currently limited applicability, due to its heavy computational load. In this paper, we overcome this difficulty by using a gradient boosting machine (GBM) in the second stage of TS approach. We call the resulting algorithm the Two-Stage Gradient Boosting Machine (TSGBM) estimator. Finally, we test our proposed TSGBM estimator on several numerical examples including models of dynamical systems.
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14:50-15:10, Paper WeB06.5 | |
>Estimation of Quantum Channels Using Neural Networks |
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Ma, Hailan | University of New South Wales |
Sun, Zhenhong | UNSW |
Xiao, Shuixin | Australian National University |
Dong, Daoyi | Australian National University |
Petersen, Ian R. | Australian National University |
Keywords: Estimation, Machine learning
Abstract: Quantum process tomography is an essential task for characterizing the dynamics of quantum systems and achieving precise quantum control. In this work, we propose a machine learning-based quantum process tomography method to reconstruct the Choi matrices of quantum channels from the measurements of the output states. Numerical results demonstrate that the proposed method exhibits a significant potential to achieve accurate reconstruction of different quantum channels.
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15:10-15:30, Paper WeB06.6 | |
>Log-Sparse Hawkes Network Identification |
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Solo, Victor | University of New South Wales |
Rong, Xinhui | University of New South Wales |
Seneviratne, Akila | The University of New South Wales |
Keywords: Estimation, Model Validation, Identification
Abstract: Point process networks are emerging in wide range of applications, such as finance and social media. Such history dependent data are often modeled by the multivariate Hawkes processes. In this paper, we propose a log-sparsity penalized least squares (log-LS) estimation for the Hawkes intensity to capture the network dynamics, while eliminating the inactive nodes. We develop a new continuous-time log-LS formulation correcting an error in previous work by finding an underlying true global minimum. We use a cyclic descent + BIC algorithm for efficient optimization. We finally compare various penalties in simulations demonstrating advantages of log-sparsity.
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WeB08 |
Simpor Junior 4812 |
Optimal Control II |
Regular Session |
Chair: Chong, Edwin K. P. | Colorado State University |
Co-Chair: Watson, Jeremy | University of Canterbury |
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13:30-13:50, Paper WeB08.1 | |
>Inverse Optimal Control and Passivity-Based Design for Converter-Based Microgrids |
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Hallinan, Liam | University of Cambridge |
Watson, Jeremy | University of Canterbury |
Lestas, Ioannis | University of Cambridge |
Keywords: Optimal control, Decentralized control, Power systems
Abstract: Passivity-based approaches have been suggested as a solution to the problem of decentralised control design in many multi-agent network control problems due to the plug- and-play functionality they provide. However, it is not clear if these controllers are optimal at a network level due to their inherently local formulation, with designers often relying on heuristics to achieve desired global performance. On the other hand, solving for an optimal controller is not guaranteed to produce a passive system. In this paper, we address these dual problems by using inverse optimal control theory to formulate a set of sufficient local conditions, which when satisfied ensure that the resulting decentralised control policies are the solution to a network optimal control problem, while at the same time satisfying appropriate passivity properties. These conditions are then reformulated into a set of linear matrix inequalities (LMIs) which can be solved to obtain such controllers for linear systems. The proposed approach is demonstrated through a DC microgrid case study. The results substantiate the feasibility and efficacy of the presented method.
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13:50-14:10, Paper WeB08.2 | |
>Penalized Least-Squares Method for LQR Problem of Singular Systems |
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Nosrati, Komeil | Tallinn University of Technology |
Belikov, Juri | Tallinn University of Technology |
Tepljakov, Aleksei | Tallinn University of Technology |
Petlenkov, Eduard | Tallinn University of Technology |
Keywords: Optimal control, Differential-algebraic systems, Linear systems
Abstract: The linear quadratic regulator (LQR) algorithms devised using the Riccati equation possess two key attributes---they are recursive and have easily met conditions of existence. Nevertheless, these features only apply for the transformed structure of the regulated dynamics in singular systems, otherwise their optimal performance will be compromised under violation of constraints in non-singular versions. This technical note presents the LQR problem for a time-varying discrete linear singular system in a direct manner avoiding any transformations. This approach eliminates the requirement of making regularity assumptions for the system. To achieve this, first, we formulate a quadratic cost function for LQR derivation based on a penalized weighted least-squares method. Then, by using Bellman's principle of optimality and performing variable substitutions, we connect the formulation to a constrained and recursive minimization problem. We then proceed with investigating the existence conditions and using dynamic programming in a backward strategy at the finite horizon to derive a recursive regulator algorithm for the original system in a matrix array framework, without degrading its optimal performance. The achieved algorithm has more general features compared to the classical LQR problem for standard systems. This study concludes with numerical evaluation of the algorithm and confirmation of the results.
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14:10-14:30, Paper WeB08.3 | |
>An Improved Greedy Curvature Bound in Finite-Horizon String Optimization with an Application to a Sensor Coverage Problem |
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Van Over, Brandon | Colorado State University |
Li, Bowen | Colorado State University |
Chong, Edwin K. P. | Colorado State University |
Pezeshki, Ali | Colorado State University |
Keywords: Optimal control, Discrete event systems, Optimization
Abstract: We study the optimization problem of choosing strings of finite length to maximize string submodular functions on string matroids, which is a broader class of problems than maximizing set submodular functions on set matroids. We provide a lower bound for the performance of the greedy algorithm in our problem, and then prove that our bound is superior to the greedy curvature bound of Conforti and Cornuéjols. Our bound has lower computational complexity than most previously proposed curvature bounds. Finally, we demonstrate the strength of our result on a sensor coverage problem.
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14:30-14:50, Paper WeB08.4 | |
>Optimal Boundary State Feedback Control by Triangularization of the Counterflow Heat Exchanger Model |
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Kadima Kazaku, Jacques | Université Catholique De Louvain, Université De Lubumbashi |
Dochain, Denis | Univ. Catholique De Louvain |
Keywords: Optimal control, Distributed parameter systems, Process Control
Abstract: In this paper we are interested in the LQ-optimal boundary control of counterflow heat exchanger. The dynamics of this system is described (under some assumptions) by hyperbolic partial differential equations (PDEs) and contains singularities which do not guarantee in some cases the uniqueness of solution of the operator Riccati equation. To address this issue, we first propose a state transformation that involves solving a Riccati differential equation, and that allows to put the system in a lower triangular form. Next, for the reachability analysis, the model has been rewritten as an abstract boundary control system with bounded control and observation operators. Finally, the design of an optimal control law with integral action is considered. The results are illustrated by means of numerical simulations for the set point tracking, and show the interest of the control approach proposed in this paper.
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14:50-15:10, Paper WeB08.5 | |
>Sparse Approximate Hamilton-Jacobi Solutions for Optimal Feedback Control with Terminal Constraints |
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Jain, Amit | Penn State University |
Eapen, Roshan Thomas | Pennsylvania State University |
Singla, Puneet | The Pennsylvania State University |
Keywords: Optimal control
Abstract: A semi-analytic method is proposed to solve a class of optimal control problems while exploiting its underlying Hamiltonian structure. Optimal control problems with a fixed final state at a fixed terminal time are considered. The solution methodology proposed in this work solves the Hamilton-Jacobi equation over a predefined domain of states and co-states. The advantage over traditional methods is that an approximate generating function (analogous to the value function of HJB theory) is obtained as a function of time, which allows for the computation of co-states for any final time and final state specified. Numerical experiments are conducted to demonstrate the efficacy of developed method while considering benchmark problems including spin stabilization.
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15:10-15:30, Paper WeB08.6 | |
>A Model-Free Iteration Algorithm for Markov Jump Linear Systems Based on Gauss-Seidel Method |
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Fan, Wenwu | University of Science and Technology of China |
Xiong, Junlin | University of Science and Technology of China |
Keywords: Optimal control, Linear parameter-varying systems, Machine learning
Abstract: This paper focuses on the linear quadratic regulator problem of discrete-time Markov jump linear systems without knowing the system matrices. A model-free fixed-point iteration algorithm is proposed to learn the optimal state feedback control law without the requirement of an initial admissible control policy. Analogous to the Gauss-Seidel method for linear equations, the model-free algorithm is constantly iterating with the latest information of each mode. It is proved that the algorithm converges monotonically to the optimal solution. In addition, our algorithm is faster than the classical model-based value iteration method. Finally, an example is used to illustrate our results.
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WeB10 |
Roselle Junior 4713 |
Machine Learning II |
Regular Session |
Chair: Amidzadeh, Mohsen | Aalto University |
Co-Chair: Rodrigues, Luis | Concordia University |
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13:30-13:50, Paper WeB10.1 | |
>Stable and Safe Reinforcement Learning Via a Barrier-Lyapunov Actor-Critic Approach |
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Zhao, Liqun | University of Oxford |
Gatsis, Konstantinos | University of Oxford |
Papachristodoulou, Antonis | University of Oxford |
Keywords: Machine learning, Learning, Autonomous robots
Abstract: Reinforcement learning (RL) has demonstrated impressive performance in various areas such as video games and robotics. However, ensuring safety and stability, which are two critical properties from a control perspective, remains a significant challenge when using RL to control real-world systems. In this paper, we first provide definitions of safety and stability for the RL system, and then combine the control barrier function (CBF) and control Lyapunov function (CLF) methods with the actor-critic method in RL to propose a Barrier-Lyapunov Actor-Critic (BLAC) framework which helps maintain the aforementioned safety and stability for the system. In this framework, CBF constraints for safety and CLF constraint for stability are constructed based on the data sampled from the replay buffer, and the augmented Lagrangian method is used to update the parameters of the RL-based controller. Furthermore, an additional backup controller is introduced in case the RL-based controller cannot provide valid control signals when safety and stability constraints cannot be satisfied simultaneously. Simulation results show that this framework yields a controller that can help the system approach the desired state and cause fewer violations of safety constraints compared to baseline algorithms.
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13:50-14:10, Paper WeB10.2 | |
>A Scale-Independent Multi-Objective Reinforcement Learning with Convergence Analysis |
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Amidzadeh, Mohsen | Aalto University |
Keywords: Machine learning, Learning, Iterative learning control
Abstract: Many sequential decision-making problems need optimization of different objectives which possibly conflict with each other. The conventional way to deal with a multi-task problem is to establish a scalar objective function based on a linear combination of different objectives. However, for the case of having conflicting objectives with different scales, this method needs a trial-and-error approach to properly find proper weights for the combination. As such, in most cases, this approach cannot guarantee an optimal Pareto solution. In this paper, we develop a single-agent scale-independent multi-objective reinforcement learning on the basis of the Advantage Actor-Critic (A2C) algorithm. A convergence analysis is then done for the devised multi-objective algorithm providing a convergence-in-mean guarantee. We then perform some experiments over a multi-task problem to evaluate the performance of the proposed algorithm. Simulation results show the superiority of developed multi-objective A2C approach against the single-objective algorithm.
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14:10-14:30, Paper WeB10.3 | |
>KCRL: Krasovskii-Constrained Reinforcement Learning with Guaranteed Stability in Nonlinear Discrete-Time Systems |
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Lale, Sahin | Caltech |
Shi, Yuanyuan | University of California San Diego |
Qu, Guannan | Carnegie Mellon University |
Azizzadenesheli, Kamyar | Purdue University |
Wierman, Adam | California Institute of Technology |
Anandkumar, Animashree | California Institute of Technology |
Keywords: Machine learning, Learning, Stability of nonlinear systems
Abstract: Learning a dynamical system requires stabilizing the unknown dynamics to avoid state blow-ups. However, the standard reinforcement learning (RL) methods lack formal stabilization guarantees, which limits their applicability for the control of real-world dynamical systems. We propose a novel policy optimization method that adopts Krasovskii's family of Lyapunov functions as a stability constraint. We show that solving this stability-constrained optimization problem using a primal-dual approach recovers a stabilizing policy for the underlying system even under modeling error. Combining this method with model learning, we propose a model-based RL framework with formal stability guarantees, Krasovskii-Constrained Reinforcement Learning (KCRL). We theoretically study KCRL with kernel-based feature representation in model learning and provide a sample complexity guarantee to learn a stabilizing controller for the underlying system. Further, we empirically demonstrate the effectiveness of KCRL in learning stabilizing policies in online voltage control of a distributed power system. We show that KCRL stabilizes the system under various real-world solar and electricity demand profiles, whereas standard RL methods often fail to stabilize.
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14:30-14:50, Paper WeB10.4 | |
>Distributionally Robust Behavioral Cloning for Robust Imitation Learning |
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Panaganti, Kishan | Texas A&M University |
Xu, Zaiyan | Texas A&M University |
Kalathil, Dileep | Texas A&M University (TAMU) |
Ghavamzadeh, Mohammad | Adobe Systems Inc |
Keywords: Machine learning, Learning
Abstract: Robust reinforcement learning (RL) aims to learn a policy that can withstand uncertainties in model parameters, which often arise in practical RL applications due to modeling errors in simulators, variations in real-world system dynamics, and adversarial disturbances. This paper introduces the robust imitation learning (IL) problem in a Markov decision process (MDP) framework where an agent learns to mimic an expert demonstrator that can withstand uncertainties in model parameters without additional online environment interactions. The agent is only provided with a dataset of state-action pairs from the expert on a single (nominal) dynamics, without any information about the true rewards from the environment. Behavioral cloning (BC), a supervised learning method, is a powerful algorithm to address the vanilla IL problem. We propose an algorithm for the robust IL problem that utilizes distributionally robust optimization (DRO) with BC. We call the algorithm DR-BC and show its robust performance against parameter uncertainties both in theory and in practice. We also demonstrate the empirical performance of our approach to addressing model perturbations on several MuJoCo continuous control tasks.
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14:50-15:10, Paper WeB10.5 | |
>Learning Stable and Robust Linear Parameter-Varying State-Space Models |
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Verhoek, Chris | Eindhoven University of Technology |
Wang, Ruigang | The University of Sydney |
Tóth, Roland | Eindhoven University of Technology |
Keywords: Machine learning, Linear parameter-varying systems, Stability of linear systems
Abstract: This paper presents two direct parameterizations of stable and robust linear parameter-varying state-space (LPV-SS) models. The model parametrizations guarantee a priori that for all parameter values during training, the allowed models are stable in the contraction sense or have their Lipschitz constant bounded by a user-defined value gamma. Furthermore, since the parametrizations are direct, the models can be trained using unconstrained optimization. The fact that the trained models are of the LPV-SS class makes them useful for, e.g., further convex analysis or controller design. The effectiveness of the approach is demonstrated on an LPV identification problem.
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15:10-15:30, Paper WeB10.6 | |
>System Identification and Control Using Quadratic Neural Networks |
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Rodrigues, Luis | Concordia University |
Givigi, Sidney | Queen's University |
Keywords: Machine learning, LMIs, Nonlinear systems identification
Abstract: This paper proposes convex formulations of system identification and control for nonlinear systems using two layer quadratic neural networks. The results in the paper cast system identification, stability and control design as convex optimization problems, which can be solved efficiently with polynomial-time algorithms. The main advantage of using quadratic neural networks for system identification and control as opposed to other neural networks is the fact that they provide a smooth (quadratic) mapping between the input and the output of the network. This allows one to cast stability and control for quadratic neural network models as a Sum of Squares (SOS) optimization, which is a convex optimization program that can be efficiently solved. Additionally, these networks offer other advantages, such as the fact that the architecture is a by-product of the design and is not determined a-priori, and the training can be done by solving a convex optimization problem so that the global optimum of the weights is achieved. It also appears from the examples in this paper that quadratic networks work extremely well using only a small fraction of the training data.
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WeB11 |
Roselle Junior 4712 |
Agent-Based Systems II |
Regular Session |
Chair: Tayebi, Abdelhamid | Lakehead University |
Co-Chair: Hovakimyan, Naira | University of Illinois at Urbana-Champaign |
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13:30-13:50, Paper WeB11.1 | |
>Convergence of Opinion Dynamics under Social Pressure for General Networks |
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Tang, Jennifer | MIT |
Adler, Aviv | MIT |
Ajorlou, Amir | Massachusetts Institute of Technology |
Jadbabaie, Ali | Massachusetts Institute of Technology |
Keywords: Agents-based systems, Distributed control, Stochastic systems
Abstract: Social pressure is a key factor affecting the evolution of opinions on networks in many types of settings, pushing people to conform to their neighbors’ opinions. To study this, the interacting P ́olya urn model was introduced by Jadbabaie et al. [1], in which each agent has two kinds of opinion: inherent beliefs, which are hidden from the other agents and fixed; and declared opinions, which are randomly sampled at each step from a distribution which depends on the agent’s inherent belief and her neighbors’ past declared opinions (the social pressure component), and which is then communicated to their neighbors. Each agent also has a bias parameter denoting her level of resistance to social pressure. At every step, each agent updates her declared opinion (simultaneously with all other agents) according to her neighbors’ aggregate past declared opinions, her inherent belief, and her bias parameter. We study the asymptotic behavior of this opinion dynamics model and show that agents’ declaration probabilities converge almost surely in the limit using Lyapunov theory and stochastic approximation techniques. We also derive a sufficient condition for the agents to approach consensus on their declared opinions.
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13:50-14:10, Paper WeB11.2 | |
>Continuum Swarm Tracking Control: A Geometric Perspective in Wasserstein Space |
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Emerick, Max | University of California Santa Barbara |
Bamieh, Bassam | Univ. of California at Santa Barbara |
Keywords: Agents-based systems, Distributed parameter systems, Algebraic/geometric methods
Abstract: We consider a setting in which one swarm of agents is to service or track a second swarm, and formulate an optimal control problem which trades off between the competing objectives of servicing and motion costs. We consider the continuum limit where large-scale swarms are modeled in terms of their time-varying densities, and where the Wasserstein distance between two densities captures the servicing cost. We show how this non-linear infinite-dimensional optimal control problem is intimately related to the geometry of Wasserstein space, and provide new results in the case of absolutely continuous densities and constant-in-time references. Specifically, we show that optimal swarm trajectories follow Wasserstein geodesics, while the optimal control tradeoff determines the time-schedule of travel along these geodesics. We briefly describe how this solution provides a basis for a model-predictive control scheme for tracking time-varying and real-time reference trajectories as well.
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14:10-14:30, Paper WeB11.3 | |
>Continuification Control of Large-Scale Multiagent Systems under Limited Sensing and Structural Perturbations |
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Maffettone, Gian Carlo | Scuola Superiore Meridionale |
Porfiri, Maurizio | New York University Tandon School of Engineering |
di Bernardo, Mario | University of Naples Federico II |
Keywords: Agents-based systems, Distributed parameter systems, Large-scale systems
Abstract: We investigate the stability and robustness properties of a continuification-based strategy for the control of large-scale multiagent systems. Within this framework, one transforms the microscopic, agent-level description of the system dynamics into a macroscopic continuum-level, for which a control action can be synthesized to steer the macroscopic dynamics towards a desired distribution. Such an action is ultimately discretized to obtain a set of deployable control inputs for the agents to achieve the goal. The mathematical proof of convergence toward the desired distribution typically relies on the assumptions that no disturbance is present and that each agent possesses global knowledge of all the others' positions. Here, we analytically and numerically address the possibility of relaxing these assumptions for the case of a one-dimensional system of agents moving in a ring. We offer compelling evidence in favor of the use of a continuification-based strategy when agents only possess a finite sensing capability and spatio-temporal perturbations affect the macroscopic dynamics of the ensemble. We also discuss some preliminary results about the benefits of adding an integral action in the macroscopic control solution.
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14:30-14:50, Paper WeB11.4 | |
>Tuning Convergence Rate Via Non-Bayesian Social Learning: A Trade-Off between Internal Belief and External Information |
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Sui, Dongyan | Fudan University |
Guan, Chun | Fudan University |
Gan, Zhongxue | Fudan University |
Lin, Wei | Fudan University |
Leng, Siyang | Fudan University |
Keywords: Agents-based systems, Distributed parameter systems, Networked control systems
Abstract: Social learning strategies have been recently developed for multi-agents to learn progressively an underlying state of nature by information communications and evolutions. Existing works define algorithms mainly by swapping the Bayesian update and belief aggregation steps and/or discovering diverse underlying network structures. Inspired by the diversity of agents when they are exposed to new information, this work designs a non-Bayesian learning strategy, named as Parametric Social Learning, by introducing an agent stubbornness parameter to trade-off the significance between its internal belief and external information. This strategy thus allows for tuning the convergence rate by adjusting the introduced parameter, which is consistent highly with the sociological intuition. Theoretical analyses and numerical examples are provided to illustrate several sociological insights. Our work therefore has appealing potential in practical tasks such as dispersed information aggregation and distributed parameter estimation.
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14:50-15:10, Paper WeB11.5 | |
>Pure Pursuit Strategy Enhanced with Defense Margin under Noisy Measurements for Protective Missions |
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Sung, Minjun | University of Illinois at Urbana-Champaign |
Hiltebrandt-McIntosh, Christophe | University of Illinois at Urbana-Champaign |
Kim, Hunmin | Mercer University |
Hovakimyan, Naira | University of Illinois at Urbana-Champaign |
Keywords: Agents-based systems, Emerging control applications, Uncertain systems
Abstract: This paper investigates the problem of protecting a safe zone against rogue drone intrusion when the defender has noisy observations. The conventional strategies were not sufficient to achieve high mission success rates, prompting the introduction of a concept called defense margin. The proposed strategy improves upon the Pure Pursuit (PP) strategy by incorporating the defense margin strategy, offering better performance compared to using either strategy alone. Simulation results demonstrate the effectiveness of the proposed strategy, resulting in higher mission success rates.
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15:10-15:30, Paper WeB11.6 | |
>Bearing-Based Distributed Pose Estimation for Multi-Agent Networks |
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Boughellaba, Mouaad | Lakehead University |
Tayebi, Abdelhamid | Lakehead University |
Keywords: Agents-based systems, Estimation, Observers for nonlinear systems
Abstract: In this paper, we address the distributed pose estimation problem for multi-agent systems under a directed graph topology, where two agents have access to their respective poses, and the other agents have unknown static positions and time-varying orientations. The proposed estimation scheme consists of two cascaded distributed observers, an almost globally asymptotically stable (AGAS) attitude observer and an input-to-state stable (ISS) position observer, leading to an overall AGAS distributed localization scheme. Numerical simulation results are presented to illustrate the performance of our proposed distributed pose estimation scheme.
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WeB12 |
Roselle Junior 4711 |
Cooperative Control II |
Regular Session |
Chair: Pettersen, Kristin Y. | Norwegian University of Science and Technology (NTNU) |
Co-Chair: Jeeninga, Mark | Politecnico Di Torino |
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13:30-13:50, Paper WeB12.1 | |
>Formation Control for Moving Target Enclosing Via Relative Localization |
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Liu, Xueming | Sun Yat-Sen University |
Liu, Kunda | Sun Yat-Sen University |
Hu, Tianjiang | Sun Yat-Sen University |
Zhang, Qingrui | Sun Yat-Sen University |
Keywords: Cooperative control, Autonomous systems, Control applications
Abstract: In this paper, we investigate the problem of controlling multiple unmanned aerial vehicles (UAVs) to enclose a moving target in a distributed fashion based on a relative distance and self-displacement measurements. A relative localization technique is developed based on the recursive least square estimation (RLSE) technique with a forgetting factor to estimates both the ``UAV-UAV'' and ``UAV-target'' relative positions. The formation enclosing motion is planned using a coupled oscillator model, which generates desired motion for UAVs to distribute evenly on a circle. The coupled-oscillator-based motion can also facilitate the exponential convergence of relative localization due to its persistent excitation nature. Based on the generation strategy of desired formation pattern and relative localization estimates, a cooperative formation tracking control scheme is proposed, which enables the formation geometric center to asymptotically converge to the moving target. The asymptotic convergence performance is analyzed theoretically for both the relative localization technique and the formation control algorithm. Numerical simulations are provided to show the efficiency of the proposed algorithm. Experiments with three quadrotors tracking one target are conducted to evaluate the proposed target enclosing method in real platforms.
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13:50-14:10, Paper WeB12.2 | |
>Bearing-Only Formation Control with Bounded Disturbances in Agents' Local Coordinate Frames |
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Garanayak, Chinmay | Indian Institute of Technology Bombay |
Mukherjee, Dwaipayan | Indian Institute of Technology Bombay |
Keywords: Cooperative control, Autonomous systems, Decentralized control
Abstract: This paper studies formation control using bearing-only measurements for elevation angle rigid configurations in the presence of time-varying bounded disturbances. Elevation angle rigidity-based control laws ensure bearing-only formation control in agents' local frame of reference sans any orientation synchronization or orientation estimation algorithms. However, existing control laws do not account for bounded disturbances in the agents' dynamics. Motivated by this, we design bearing-only control laws for single integrators in agents' frame of reference and prove local finite-time convergence to the desired formation. Then control laws for double integrators are proposed, and local asymptotic stability is proved when agents' accelerations are affected by bounded disturbances. Simulations are provided to validate the claims.
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14:10-14:30, Paper WeB12.3 | |
>Formation Control of Underactuated AUVs Using the Hand Position Concept |
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Lie, Erling S. | Norwegian University of Science and Technology - NTNU |
Matous, Josef | NTNU (Norwegian University of Science and Technology) |
Pettersen, Kristin Y. | Norwegian University of Science and Technology (NTNU) |
Keywords: Cooperative control, Autonomous systems, Stability of nonlinear systems
Abstract: This paper presents an extended null-space-based behavioral algorithm for the formation control of fleets of underactuated autonomous underwater vehicles. The null-space-based controller is developed to work directly with second-order integrator systems, handling their dynamics in task space. The method is applied to the formation-path-following problem of a fleet of underactuated autonomous underwater vehicles. The nonlinear six-degrees-of-freedom model of the vehicle is transformed into a second-order integrator system using the 3D hand position output linearizing controller. The behavioral controller implements a hierarchy of path-following, formation-keeping, and collision-avoidance tasks. The closed-loop system is proven uniformly globally asymptotically stable, and the proposed method is validated through numerical simulations.
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14:30-14:50, Paper WeB12.4 | |
>Decentralized Lateral and Longitudinal Control of Vehicle Platoons with Constant Headway Spacing |
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Wijnbergen, Paul | KTH Royal Institute of Technology |
Jeeninga, Mark | Politecnico Di Torino |
de Haan, Redmer | Eindhoven University of Technology |
Lefeber, Erjen | Eindhoven University of Technology |
Keywords: Cooperative control, Autonomous vehicles, Nonlinear systems
Abstract: The formation of platoons, where groups of vehicles follow each other at close distances, has the potential to increase road capacity. In this paper, a decentralized control approach is presented that extends the well-known constant headway vehicle following approach to the two-dimensional case, i.e., lateral control is included in addition to the longitudinal control. The presented control scheme employs a direct vehicle following approach where each vehicle in the platoon is responsible for following the directly preceding vehicle according to a nonlinear spacing policy. The proposed constant headway spacing policy is motivated by an approximation of a delay-based spacing policy and results in a generalization of the constant headway spacing policy to the two-dimensional case. By input-output linearization, necessary and sufficient conditions for the tracking of the nonlinear spacing policy are obtained, which motivate the synthesis of the lateral and longitudinal controllers of each vehicle in the platoon. By deriving an internal state representation of the follower vehicle and showing input-to-state stability, the internal dynamics for each leader-follower subsystem are shown to be well-behaved in case the leader drives in steady state conditions (i.e., the leader vehicle's trajectory is unexcited). The results are illustrated by a simulation.
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14:50-15:10, Paper WeB12.5 | |
>Finite-Time Control Protocol for Uniform Allocation of Second-Order Agents |
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Zimenko, Konstantin | ITMO University |
Efimov, Denis | Inria |
Polyakov, Andrey | Inria, Univ. Lille |
Ping, Xubin | Xidian University |
Keywords: Cooperative control, Decentralized control, Lyapunov methods
Abstract: The paper addresses the problem of uniform finite-time robust allocations of second-order agents on a straight line. A decentralized homogeneous control protocol is proposed that uses only agent's states and local interactions (distances between two closest neighbors). Sufficient conditions of finite-time (input-to-state) stability are proposed in the form of Linear Matrix Inequalities. The theoretical results are illustrated via numerical simulations.
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15:10-15:30, Paper WeB12.6 | |
>A Novel Point-Based Algorithm for Multi-Agent Control Using the Common Information Approach |
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Tang, Dengwang | University of Southern California |
Nayyar, Ashutosh | University of Southern California |
Jain, Rahul | University of Southern California |
Keywords: Cooperative control, Decentralized control, Stochastic optimal control
Abstract: The Common Information (CI) approach provides a systematic way to transform a multi-agent stochastic control problem to a single-agent partially observed Markov decision problem (POMDP) called the coordinator's POMDP. However, such a POMDP can be hard to solve due to its extraordinarily large action space. We propose a new algorithm for multi-agent stochastic control problems, called coordinator's heuristic search value iteration (CHSVI), that combines the CI approach and point-based POMDP algorithms for large action spaces. We demonstrate the algorithm through optimally solving several benchmark problems.
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WeB13 |
Roselle Junior 4613 |
Control of Networks |
Regular Session |
Chair: Kawano, Yu | Hiroshima University |
Co-Chair: Mousavi, Shima Sadat | ETH Zurich |
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13:30-13:50, Paper WeB13.1 | |
>Bipartite Formation Over Undirected Signed Networks with Collision Avoidance |
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Sekercioglu, Pelin | ONERA, Univ Paris-Saclay |
Sarras, Ioannis | ONERA |
Loria, Antonio | CNRS |
Panteley, Elena | CNRS |
Marzat, Julien | ONERA - the French Aerospace Lab |
Keywords: Control of networks, Constrained control, Lyapunov methods
Abstract: We address the problem of bipartite formation control, with collision avoidance, for double integrators with limited sensing ranges. We assume that the systems are interconnected over an undirected, signed, and structurally balanced network. Then, to ensure that the proximity constraints are satisfied, we design a barrier-Lyapunov-function-based control law that guarantees connectivity maintenance for cooperative agents, and inter-agent collision avoidance for all agents. Relying on the edge-based agreement, we establish asymptotic stability of the bipartite formation control for signed networks. Finally, we illustrate our theoretical results via numerical simulations.
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13:50-14:10, Paper WeB13.2 | |
>Distributed Spatial Filtering by a Two-Hop Consensus-Type Algorithm |
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Izumi, Shinsaku | Kochi University of Technology |
Xin, Xin | Okayama Prefectural University |
Yamasaki, Taiga | Okayama Prefectural University |
Keywords: Control of networks, Distributed control, Sensor networks
Abstract: In this study, we discuss distributed spatial filtering (DSF) on networked systems to obtain signal values with a desired spatial frequency characteristic from those assigned to nodes by a distributed algorithm. We present a two-hop consensus-type algorithm for DSF based on an existing one-hop algorithm. We prove that the range of the filter characteristics the presented algorithm can achieve is broader than that for the existing algorithm by deriving a necessary and sufficient condition for achieving DSF. Simulation results show that our filtering algorithm and a new filter characteristic it provides are effective in distributed anomaly detection by sensor networks.
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14:10-14:30, Paper WeB13.3 | |
>Krasovskii and Shifted Passivity Approaches to Mixed Input/Output Consensus |
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Kawano, Yu | Hiroshima University |
Cucuzzella, Michele | University of Pavia |
Scherpen, Jacquelien M.A. | University of Groningen |
Keywords: Control of networks, Distributed control, Lyapunov methods
Abstract: In this letter, we consider nonlinear network systems under unknown disturbance and address the problem of mixed input/output consensus, i.e., consensus among disjoint sets of input and output nodes. We develop two control schemes based on different notions of passivity: 1) Krasovskii passivity and 2) shifted passivity. Furthermore, we propose an input consensus controller which is applicable to either Krasovskii or shifted passive systems. Finally, we validate the proposed controllers in simulation by achieving current sharing in a heterogeneous DC microgrid and power sharing in an AC power system, which are Krasovskii and shifted passive, respectively.
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14:30-14:50, Paper WeB13.4 | |
>Minimal Control Placement of Turing's Model Using Symmetries |
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Cao, Yuexin | KTH Royal Institute of Technology |
Li, Yibei | Nanyang Technological University |
Liu, Zhixin | Academy of Mathematics and Systems Science, ChineseAcademyof Scie |
Zheng, Lirong | Fudan University |
Hu, Xiaoming | Royal Institute of Technology |
Keywords: Control of networks, Linear systems, Control system architecture
Abstract: In this paper, the minimal control placement problem for the Turing's reaction-diffusion system is investigated. The two-dimensional RD system is discretized into square grids and the nodes in the outermost layer are considered as control candidates. Symmetric control sets are defined naturally using the property of symmetry of the network structure. The minimal control placement problem for the diffusion system is investigated first. The necessary condition is provided based on the idea of symmetric control sets. Then we prove that this condition is also sufficient to ensure controllability when the multiplicity of eigenvalues satisfies certain conditions. We show further that symmetric control sets can be extended and prove that the necessary condition can also be applied to the reaction-diffusion system, i.e., the Turing's model. The sufficient condition is proved to be effective for the reaction-diffusion system under similar circumstances. Our conclusion can also be useful for other multi-agent systems with the same topology. Directions of future study include nonlinear reaction terms and time-varying systems.
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14:50-15:10, Paper WeB13.5 | |
>Influencing Opinions in a Nonlinear Pinning Control Model |
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Ancona, Camilla | Università Di Napoli Federico II |
De Lellis, Pietro | University of Naples Federico II |
Lo Iudice, Francesco | Università Di Napoli Federico II |
Keywords: Control of networks, Network analysis and control, Control applications
Abstract: This letter studies how opinions and subsequent actions of groups of individuals are shaped by opinion leaders, nowadays denoted influencers. We model an influencer as a pinner that exerts a control input on a small subset of individuals, and leverages the interaction network to affect the action of a large fraction of individuals. We provide sufficient conditions so that a given agent takes the same action as the pinner. Based on these conditions, we design a heuristic for the pinned node selection that maximizes the number of nodes taking the action elected by the pinner. The performance of the heuristic is then numerically tested against standard pinning strategies.
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15:10-15:30, Paper WeB13.6 | |
>Bearing-Based Formation Maneuver Control of Leader-Follower Multi-Agent Systems |
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Su, Haifan | Shanghai Jiao Tong University |
Yang, Ziwen | Shanghai Jiao Tong University |
Zhu, Shanying | Shanghai Jiao Tong University |
Chen, Cailian | Shanghai Jiao Tong University |
Keywords: Agents-based systems, Distributed control, Cooperative control
Abstract: In this paper, we study the bearing-based formation maneuver control problem of the leader-follower multi-agent system. The objectives are achieving the rotation, translation, and scaling maneuvers with a transformable formation shape. Unlike existing works where the target formation is defined by displacements, distances, or constant bearings, we propose a novel target formation with time-varying bearings. The feasibility and uniqueness of the target formation are analyzed by extending the properties of bearing rigidity to time-varying cases. Compared to the existing methods where the positions and velocities of all the agents are required, an estimation-based control method is proposed to achieve the target formation using relative bearings and only the leaders’ positions and velocities. Both the estimation error and tracking error converge to zero under the extended properties of bearing rigidity and cascade system theories. A sufficient condition for collision avoidance among the agents is also proposed. A numerical example illustrates the effectiveness of the proposed method.
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WeB14 |
Roselle Junior 4612 |
Identification I |
Regular Session |
Chair: Lee, Jin Gyu | INRIA |
Co-Chair: Moreschini, Alessio | Imperial College London |
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13:30-13:50, Paper WeB14.1 | |
>Parametric Continuous-Time Blind System Identification |
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Elton, Augustus | University of Newcastle |
González, Rodrigo A. | Eindhoven University of Technology |
Welsh, James S. | University of Newcastle |
Rojas, Cristian R. | KTH Royal Institute of Technology |
Fu, Minyue | Southern University of Science and Technology |
Keywords: Identification, Linear systems
Abstract: In this paper, the blind system identification problem for continuous-time systems is considered. A direct continuous-time estimator is proposed by utilising a state-variable-filter least squares approach. In the proposed method, coupled terms between the numerator polynomial of the system and input parameters appear in the parameter vector which are subsequently separated using a rank-1 approximation. An algorithm is then provided for the direct identification of a single-input single-output linear time-invariant continuous-time system which is shown to satisfy the property of correctness under some mild conditions. Monte Carlo simulations demonstrate the performance of the algorithm and verify that a model and input signal can be estimated to a proportion of their true values.
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13:50-14:10, Paper WeB14.2 | |
>An Efficient Implementation for Kernel-Based Regularized System Identification with Periodic Input Signals |
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Shen, Zhuohua | The Chinese University of Hong Kong, Shenzhen |
Xu, Yu | The Chinese University of Hong Kong, Shenzhen |
Andersen, Martin S. | Technical University of Denmark |
Chen, Tianshi | The Chinese University of Hong Kong, Shenzhen, China |
Keywords: Identification, Linear systems, Computational methods
Abstract: Efficient implementation of algorithms for kernel-based regularized system identification is an important issue. The state of art result is based on semiseparable kernels and a class of commonly used test input signals in system identification and automatic control, and with such input signals, the output kernel is semiseparable and exploring this structure gives rise to very efficient implementation. In this paper, we consider instead the periodic input signals, which is another class of commonly used test input signals. Unfortunately, with periodic input signals, the output kernel is NOT semiseparable. Nevertheless, it can be shown that the output kernel matrix is hierarchically semiseparable. Moreover, it is possible to develop efficient implementation of algorithms by exploring the hierarchically semiseparable structure of the output kernel matrix and the periodic structure of the regression matrix. The efficiency of the proposed implementation of algorithms is demonstrated by Monte Carlo simulations.
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14:10-14:30, Paper WeB14.3 | |
>Realization from Moments: The Linear Case |
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Lee, Jin Gyu | INRIA |
Astolfi, Alessandro | Imperial College & Univ. of Rome |
Keywords: Identification, Model/Controller reduction, Linear systems
Abstract: By exploiting the time-domain notion of moments we recover a time-domain counterpart of the fact that a certain number of steady-state responses is sufficient to realize a linear system. This may pave the way to a realization theory for nonlinear systems based on their steady-state responses.
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14:30-14:50, Paper WeB14.4 | |
>Kernel-Based Continuous-Time System Identification: A Parametric Approximation |
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Scandella, Matteo | Imperial College London |
Moreschini, Alessio | Imperial College London |
Parisini, Thomas | Imperial College & Univ. of Trieste |
Keywords: Identification, Linear systems, Statistical learning
Abstract: In this paper, we discuss the non-parametric estimate problem using kernel-based LTI system identification techniques by constructing a Loewner-based interpolant of the estimated model. Through this framework, we have been able to retrieve a finite-dimensional approximation of the infinite-dimensional estimate obtained using the classical kernel-based methodologies. The employment of the Loewner framework constitutes an enhancement of recent results which propose to use a Padé approximant to obtain a rational transfer function from an irrational transfer function corresponding to the identified impulse response. The enhancement has been illustrated for the identification of the Rao-Garnier benchmark.
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14:50-15:10, Paper WeB14.5 | |
>Towards Scalable Kernel-Based Regularized System Identification |
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Chen, Lujing | Technical University of Denmark |
Chen, Tianshi | The Chinese University of Hong Kong, Shenzhen, China |
Detha, Utkarsh | MOSEK ApS |
Andersen, Martin S. | Technical University of Denmark |
Keywords: Identification, Linear systems, Computational methods
Abstract: This paper proposes a methodology for scalable kernel-based regularized system identification based on indirect methods. It leverages stochastic trace estimation methods and an iterative solver such as LSQR for the efficient evaluation of hyperparameter selection criteria. It also uses a derivative-free optimization approach to hyperparameter estimation, which avoids the need for computing gradients or Hessians of the objective function. Moreover, the method is matrix-free, which means it only relies on a matrix-vector oracle and exploits fast routines for various structured matrix-vector products. Our preliminary numerical experiments indicate that the methodology scales significantly better than direct methods, especially when dealing with large datasets and slowly decaying impulse responses.
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15:10-15:30, Paper WeB14.6 | |
>On the Relation between Discrete and Continuous-Time Refined Instrumental Variable Methods |
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González, Rodrigo A. | Eindhoven University of Technology |
Rojas, Cristian R. | KTH Royal Institute of Technology |
Pan, Siqi | University of Newcastle |
Welsh, James S. | University of Newcastle |
Keywords: Identification, Linear systems, Estimation
Abstract: The Refined Instrumental Variable method for discrete-time systems (RIV) and its variant for continuous-time systems (RIVC) are popular methods for the identification of linear systems in open-loop. The continuous-time equivalent of the transfer function estimate given by the RIV method is commonly used as an initialization point for the RIVC estimator. In this paper, we prove that these estimators share the same converging points for finite sample size when the continuous-time model has relative degree zero or one. This relation does not hold for higher relative degrees. Then, we propose a modification of the RIV method whose continuous-time equivalent is equal to the RIVC estimator for any non-negative relative degree. The implications of the theoretical results are illustrated via a simulation example.
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WeB16 |
Peony Junior 4512 |
Energy Systems I |
Regular Session |
Chair: Gießler, Armin | Karlsruhe Institute of Technology |
Co-Chair: Jané Soneira, Pol | Karlsruher Institute Für Technology |
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13:30-13:50, Paper WeB16.1 | |
>Passivity-Based Economic Ports for Optimal Operation of Networked DC Microgrids |
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Jané Soneira, Pol | Karlsruher Institute Für Technology |
Malan, Albertus J. | Karlsruhe Institute of Technology |
Prodan, Ionela | Grenoble Institute of Technology (Grenoble INP) - Esisar |
Hohmann, Soeren | KIT |
Keywords: Energy systems, Optimal control, Distributed control
Abstract: In this paper, we introduce the novel concept of economic ports, allowing modular and distributed optimal operation of networked microgrids. Firstly, we design a novel price-based controller for optimal operation of a single microgrid and show asymptotic stability. Secondly, we define novel physical and economic interconnection ports for the microgrid and study the dissipativity properties of these ports. Lastly, we propose an interconnection scheme for microgrids via the economic ports. This interconnection scheme requires only an exchange of the local prices and allows a globally economic optimal operation of networked microgrids at steady state, while guaranteeing asymptotic stability of the networked microgrids via the passivity properties of economic ports. The methods are demonstrated through various academic examples.
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13:50-14:10, Paper WeB16.2 | |
>Economic Dispatch for DC Microgrids: An Optimal Power Sharing Approach with Batteries |
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Gießler, Armin | Karlsruhe Institute of Technology |
Jané Soneira, Pol | Karlsruher Institute Für Technology |
Malan, Albertus J. | Karlsruhe Institute of Technology |
Hohmann, Soeren | KIT |
Keywords: Energy systems, Power generation, Optimal control
Abstract: In this paper, we propose a hierarchical control structure comprising three layers which is able to (i) achieve economic dispatch for islanded DC microgrids, (ii) compensate load and generation disturbances with batteries performing power sharing and (iii) stabilize non-passive constant power loads. The batteries are charged economically optimally by the third layer controller such the state of charges (SOCs) remain constant. The proportional power sharing of the batteries is achieved by employing a novel control law which solves the linearized steady-state power flow equations in real time. The microgrid is stabilized by using voltage controllers for batteries and active damping elements. A numeric method to verify closed-loop asymptotic stability is derived. The power sharing of the batteries and stability achieved with the proposed control is demonstrated in a simulation.
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14:10-14:30, Paper WeB16.3 | |
>On the Optimality of Procrastination Policy for EV Charging under Net Energy Metering |
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Jeon, Minjae | Cornell University |
Tong, Lang | Cornell University |
Zhao, Qing | Cornell University |
Keywords: Energy systems, Stochastic optimal control, Smart grid
Abstract: We consider the problem of behind-the-meter EV charging by a prosumer, co-optimized with rooftop solar, electric battery, and flexible consumptions such as water heaters and HVAC. Under the time-of-use net energy metering tariff with the stochastic solar production and random EV charging demand, a finite-horizon surplus-maximization problem is formulated. We show that a procrastination threshold policy that delays EV charging to the last possible moment is optimal when EV charging is co-optimized with flexible demand, and the policy thresholds can be computed easily offline. When battery storage is part of the co-optimization, it is shown that the net consumption of the prosumer is a two-threshold piecewise linear function of the behind-the-meter renewable generation under the optimal policy, and the procrastination threshold policy remains optimal, although the thresholds cannot be computed easily. We propose a simple myopic solution and demonstrate in simulations that the performance gap between the myopic policy and an oracle upper bound appears to be 0.5-7.5%.
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14:30-14:50, Paper WeB16.4 | |
>Online Learning of Effective Turbine Wind Speed in Wind Farms |
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Henry, Aoife | University of Colorado Boulder |
Sinner, Michael | National Renewable Energy Laboratory |
King, Jennifer | National Renewable Energy Laboratory |
Pao, Lucy Y. | University of Colorado Boulder |
Keywords: Energy systems, Statistical learning, Identification for control
Abstract: To develop better wind farm controllers that can meet more complex objectives, methods of modeling the wind turbine wakes at low computational expense are needed. Gaussian Process (GP) regression offers a computationally inexpensive framework for learning complex functions from noisy measurements with very few datapoints. In this work, an online learning approach is presented to learn the rotor-averaged wind velocity at downstream wind turbines with GPs, using the available datastream of wind field measurements and wind turbine control set-points. This framework can readily be integrated into model-based controls methods because the model a) is updated online at low computational expense, b) assumes a mathematically favorable Gaussian form, and c) explicitly quantifies the stochastic nature of the wake field so that the trade-off between exploration and exploitation, and the uncertainty in the prediction, can be utilized. We show that a GP-learned model can match true values with errors within 0.5 % on average, with as few as 5 training data points.
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14:50-15:10, Paper WeB16.5 | |
>Emission-Constrained Optimization of Gas Networks: Input-Convex Neural Network Approach |
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Dvorkin, Vladimir | Massachusetts Institute of Technology |
Chevalier, Samuel | MIT |
Chatzivasileiadis, Spyros | Technical University of Denmark |
Keywords: Energy systems, Smart grid, Neural networks
Abstract: Planning optimization of gas networks under emission constraints prioritizes gas supply with the smallest emission footprint. As this problem includes complex gas flow physical laws, standard optimization solvers cannot guarantee convergence to a feasible solution, especially under strict emission constraints. To address this issue, we develop an input-convex neural network (ICNN) aided optimization routine which incorporates a set of trained ICNNs approximating the gas flow equations with high precision. Numerical tests on the Belgium gas network demonstrate that the ICNN-aided optimization dominates non-convex and relaxation-based solvers, with larger optimality gains pertaining to stricter emission targets.
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15:10-15:30, Paper WeB16.6 | |
>Pricing Uncertainty in Stochastic Multi-Stage Electricity Markets |
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Werner, Lucien | California Institute of Technology |
Christianson, Nicolas | California Institute of Technology |
Zocca, Alessandro | VU Amsterdam |
Wierman, Adam | California Institute of Technology |
Low, Steven | California Institute of Technology |
Keywords: Power systems, Smart grid, Stochastic systems
Abstract: This work proposes a pricing mechanism for multi-stage electricity markets that does not explicitly depend on the choice of dispatch procedure or optimization method. Our approach is applicable to a wide range of methodologies for the economic dispatch of power systems under uncertainty, including multi-interval dispatch, multi-settlement markets, scenario-based dispatch, and chance-constrained dispatch policies. We prove that our pricing scheme provides both ex-ante and ex-post dispatch-following incentives by simultaneously supporting per-stage and ex-post competitive equilibria. In numerical experiments on a ramp-constrained test system, we demonstrate the benefits of scheduling under uncertainty and show how our price decomposes into components corresponding to energy, intertemporal coupling, and uncertainty.
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WeB19 |
Peony Junior 4411 |
Linear Systems II |
Regular Session |
Chair: Besselink, Bart | University of Groningen |
Co-Chair: Grussler, Christian | Technion - Israel Institute of Technology |
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13:30-13:50, Paper WeB19.1 | |
>Reachable Set Estimation for Discrete-Time Periodic Piecewise Systems |
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Liu, Yun | East China University of Science and Technolog |
Yang, Wen | East China University of Science and Technology |
Yang, Chao | East China University of Science and Technology |
Zhao, Zhiyun | East China University of Science and Technology |
Keywords: Linear systems, Hybrid systems, Optimization
Abstract: This paper investigates the reachable set estimation problem for discrete-time periodic piecewise systems subject to bounded-peak disturbances for the first time. Based on the periodic linear-interpolative formulation, the discrete time-scheduling Lyapunov functions with continuous or jumping modes at the switching instant are constructed to develop criteria of reachable set estimation that can ensure the asymptotic stability and reachability of the investigated system. Moreover, an index optimizing the bounding region of the desirable reachable set is given via resorting to the ellipsoid technique, and their results are compared. Finally, numerical examples are given to validate the effectiveness of the proposed results.
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13:50-14:10, Paper WeB19.2 | |
>Control of Linear Systems with Guarantee of Outputs in Given Sets at Any Time |
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Nguyen, Ba Huy | ITMO University |
Furtat, Igor | Institute of Problems of Mechanical Engineering Russian Academy |
Vrazhevsky, Sergey | ITMO University |
Keywords: Linear systems, Nonlinear output feedback, LMIs
Abstract: A new method for designing the control law for linear plants with a guarantee of finding outputs in given sets under conditions of unknown bounded disturbances is proposed. The problem is solved in two stages. In the first stage, a coordinate transformation is used to reduce the original constrained problem to the problem of studying the input-to-state stability of a new extended system without constraints. In the second stage, the control law for the transformed system is designed, where the adjustable parameters are selected from the solution of linear matrix inequalities (LMI). The simulations, which are performed in MATLAB, show the method’s efficiency and confirm the theoretical results.
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14:10-14:30, Paper WeB19.3 | |
>Relaxation Systems and Cyclic Monotonicity |
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Chaffey, Thomas Lawrence | University of Cambridge |
van Waarde, Henk J. | University of Groningen |
Sepulchre, Rodolphe | University of Cambridge |
Keywords: Linear systems, Variational methods, Optimization
Abstract: It is shown that an LTI system is a relaxation system if and only if its Hankel operator is cyclic monotone. Cyclic monotonicity of the Hankel operator implies the existence of a storage function whose gradient is the Hankel operator. This storage is a function of past inputs alone, is independent of the state space realization, and admits a generalization to nonlinear circuit elements.
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14:30-14:50, Paper WeB19.4 | |
>Characterizing Compositionality of LQR from the Categorical Perspective |
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She, Baike | University of Florida |
Hanks, Tyler | University of Florida |
Fairbanks, James | University of Florida |
Hale, Matthew | University of Florida |
Keywords: Linear systems, Optimal control
Abstract: Composing systems is a fundamental concept in modern control systems, yet it remains challenging to formally analyze how controllers designed for individual subsystems can differ from controllers designed for the composition of those subsystems. To address this challenge, we propose a novel approach to composing control systems based on resource sharing machines, a concept from applied category theory. We use resource sharing machines to investigate the differences between (i) the linear-quadratic regulator (LQR) designed directly for a composite system and (ii) the LQR that is attained through the composition of LQRs designed for each subsystem. We first establish novel formalisms to compose LQR control designs using resource sharing machines. Then we develop new sufficient conditions to guarantee that the LQR designed for a composite system is equal to the LQR attained through composition of LQRs for its subsystems. In addition, we reduce the developed condition to that of checking the controllability and observability of a certain linear, time-invariant system, which provides a simple, computationally efficient procedure for evaluating the equivalence of controllers for composed systems.
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14:50-15:10, Paper WeB19.5 | |
>On the Monotonicity of Frequency Response Gains |
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Grussler, Christian | Technion - Israel Institute of Technology |
B. Burghi, Thiago | University of Cambridge |
Keywords: Compartmental and Positive systems, Linear systems, PID control
Abstract: Linear time-invariant single-input-single-output systems with nonnegative impulse responses, commonly called externally positive systems, carry well-known monotonicity properties such as: (i) the static gain equals the H_infty-norm (peak of the Bode magnitude diagram), (ii) monotone inputs are mapped to monotone outputs, (iii) the transfer function is totally monotone on the positive reals. In this paper, we complement these properties by proving monotonicity properties of the frequency response gain with the help of variation diminishing theory. While our results give new insights into proving monotonicity properties of the gains of positive systems, they are not limited to such systems, and extend to systems that preserve the periodic monotonicity of their inputs. In particular, our results also provide an interesting sufficient condition for positive dominance.
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15:10-15:30, Paper WeB19.6 | |
>Specification Verification and Controller Synthesis Using (gamma, Delta)-Similarity (I) |
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Pirastehzad, Armin | University of Groningen |
van der Schaft, Arjan | Univ. of Groningen |
Besselink, Bart | University of Groningen |
Keywords: Linear systems, LMIs, Formal Verification/Synthesis
Abstract: We address the problems of specification verification and controller synthesis in the context of (gamma,delta)-similarity, a notion of approximate system comparison that measures to what extent the external behaviors of two potentially non-deterministic systems are similar in an L2 sense. Expressing specifications in terms of input-output trajectories of a dynamical system, we use (gamma,delta)-similarity to verify whether the external behavior of a system satisfies such specifications in an approximate sense. We characterize this problem as a linear matrix inequality feasibility problem. In case a control system fails to satisfy specifications with a desired accuracy, we synthesize a dynamic controller that enforces specification satisfaction. We characterize the synthesis problem in terms of a bilinear matrix inequality feasibility problem. Aware of the computational costs for solving such problem, we obtain a sufficient condition for the existence of the controller that can be expressed in terms of a linear matrix inequality. Based on this, we propose an algorithm to construct the controller.
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WeB20 |
Orchid Junior 4312 |
Biological Systems II |
Regular Session |
Chair: Borri, Alessandro | CNR-IASI |
Co-Chair: Niazi, Muhammad Umar B. | Massachusetts Institute of Technology |
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13:30-13:50, Paper WeB20.1 | |
>Undetectable Attacks on Boolean Networks (I) |
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Zhu, Shiyong | Southeast University |
Lin, Lin | The University of Hong Kong |
Lam, James | The University of Hong Kong |
Ng, Michael | Hong Kong Baptist University |
Lu, Jianquan | Southeast University |
Azuma, Shun-ichi | Kyoto University |
Cao, Jinde | Southeast University |
Keywords: Biological systems, Network analysis and control, Attack Detection
Abstract: In this paper, driven by the ever-increasing cyber-security threats, we study the undetectable attack problems for Boolean networks (BNs), which model distributed systems with a limited capacity of storage and bandwidth of communication. Given a consistent monitor, undetectable attacks are formalized for BNs as those do not yield an output sequence out of the nominal output sequence set. By the graph-theoretic approach, undetectable attacks are characterized by a reachability problem of a directed cycle in the augmented transition graph. On the other hand, the algebraic approach also derives a necessary and sufficient criterion for undetectable attacks by testing the existence of the nonzero elements in the constructed matrix. While all these derived results are only computationally efficient for relatively small-size BNs. The detection of attack signals is indeed NP-hard. In other words, there is no polynomial-time algorithm to check the detectability of an attack signal or an attack node set unless NP=P.
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13:50-14:10, Paper WeB20.2 | |
>Optimal Safety-Critical Control of Epidemics |
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Butler, Brooks A. | Purdue University |
Pare, Philip E. | Purdue University |
Keywords: Biological systems, Emerging control applications, Optimal control
Abstract: We present a generalized model for epidemic processes that partitions control into changes in linear and non-linear flow rates between compartments, respectively. We then define an optimal control problem that minimizes the weighted cost of rate control on the generalized model while maintaining conditions that guarantee system safety at any time using control barrier functions. Using this formulation, we prove that under homogeneous penalties the optimal controller will always favor increasing the linear flow out of an infectious process over reducing nonlinear flow in. Further, in the case of heterogeneous penalties, we provide necessary and sufficient conditions under which the optimal controller will set control of non-linear rates (i.e., the reduction of flow rate into the infection process) to zero. We then illustrate these results through the simulation of a bi-virus SEIQRS model.
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14:10-14:30, Paper WeB20.3 | |
>The Long-Term Effects of Physical Activity on Blood Glucose Regulation: A Model to Unravel Diabetes Progression |
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De Paola, Pierluigi Francesco | Consiglio Nazionale Delle Ricerche (CNR) |
Paglialonga, Alessia | Consiglio Nazionale Delle Ricerche (CNR) |
Palumbo, Pasquale | University of Milano-Bicocca |
Keshavjee, Karim | University of Toronto |
Dabbene, Fabrizio | CNR-IEIIT |
Borri, Alessandro | CNR-IASI |
Keywords: Modeling, Biomedical, Metabolic systems
Abstract: Physical activity plays a key role in the prevention of type 2 diabetes. However, despite the numerous clinical evidences, there are still no mathematical models that satisfactorily describe the effects of physical activity on the progression of diabetes, preventing its onset or slowing down its course. Instead, there are models describing the influence of single training sessions of physical activity on blood glucose and insulin levels in the short term. In this article we propose a novel model for the long term effects of physical activity on diabetes progression, by exploiting and adapting an existing short-term model of physical activity. A pivotal role in the proposed model is played by interleukin-6 released during physical activity and known to be fundamental in maintaining pancreatic beta cells production and therefore satisfactory insulin secretion. The proposed simulation scenarios show how a modeling approach of physical activity that neglects the interleukin-6 action is not sufficient to capture the cumulative effects of physical exercise on disease progression. Indeed, preliminary results pave the way to natural extensions of the model to account for model-based control techniques for the long-term control of diabetes through personalized lifestyle interventions, properly accounting for the effects of physical activity on the long-term dynamics of blood glucose.
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14:30-14:50, Paper WeB20.4 | |
>A Probabilistic Finite-State Automata Framework for Monitoring Long-Term Activities of Daily Living |
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Li, Mianjun | National University of Singapore |
Chen, Peter C. Y. | National University of Singapore |
Keywords: Healthcare and medical systems, Modeling, Automata
Abstract: Aging is an increasingly challenging healthcare issue with long-term sociopolitical implications, requiring more sophisticated management of healthcare services for the elderly. A key element in managing such services is the knowledge about a typical elderly person’s Activities of Daily Living (ADLs). However, there is little study on the model-based objective and standardized ADLs assessment. This paper presents the concept of tracking the health status of the elderly by monitoring their individual patterns of ADLs: the specific pattern of the elderly model as probabilistic state-transition structures, and the transition probabilities in such a probabilistic model consider as a representation of the health status of a typical older person. The typical pattern of ADLs changes with the health status due to changes in the residential environment, progressive aging, or the onset of certain diseases. Such changes are reflected (over time) in the model, and therefore monitoring the transition probabilities to assess ADLs represents a possible way to track the health status of an older person and to alert relevant health service professionals if some change that warrants subsequent careful medical attention.
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14:50-15:10, Paper WeB20.5 | |
>Observer Design for Nonlinear Systems without Parameterizing Nonlinearities: Application to Networked SIR Model (I) |
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Niazi, M. Umar B. | MIT |
Johansson, Karl H. | KTH Royal Institute of Technology |
Keywords: Observers for nonlinear systems, Nonlinear systems, Biological systems
Abstract: Traditional observer design methods rely on certain properties of the system's nonlinearity, such as Lipschitz continuity, one-sided Lipschitzness, a bounded Jacobian, or quadratic boundedness. These properties are described by parameterized inequalities. However, enforcing these inequalities globally can lead to very large parameters, resulting in overly conservative observer design criteria. These criteria become infeasible for highly nonlinear applications, such as networked epidemic processes. In this paper, we present an observer design approach for estimating the state of nonlinear systems, without requiring any parameterization of the system's nonlinearities. The proposed observer design depends only on systems' matrices and applies to systems with any nonlinearity. We establish different design criteria for ensuring both asymptotic and exponential convergence of the estimation error to zero. To demonstrate the efficacy of our approach, we employ it for estimating the state of a networked SIR epidemic model. We show that, even in the presence of measurement noise, the observer can accurately estimate the epidemic state of each node in the network. To the best of our knowledge, the proposed observer is the first that is capable of estimating the state of networked SIR models.
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15:10-15:30, Paper WeB20.6 | |
>Data-Driven Forward Stochastic Reachability Analysis for Human-In-The-Loop Systems |
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Choi, Joonwon | Purdue University |
Byeon, Sooyung | Purdue University |
Hwang, Inseok | Purdue University |
Keywords: Human-in-the-loop control, Linear systems, Data driven control
Abstract: We propose a data-driven forward stochastic reachability analysis algorithm for Human-In-The-Loop (HITL) systems. We focus on a certain type of HITL system whose behavior is dominated by a human operator, for example, a multi-rotor controlled by a human operator. In such a system, the intervention of the human operator may generate a conservative reachable set due to the unpredictable control strategy of the human operator. The proposed algorithm computes a less conservative reachable set of the HITL system by accounting for the human operator’s behavior, i.e., we present the data-driven reachability analysis algorithm that considers the unknown controller information of the HITL system. The behavior of the human operator is trained as a Gaussian Mixture Model (GMM) from the state and input trajectories of the system. Then, the conditional probability distribution of the human operator’s behavior is obtained from the Gaussian Mixture Regression (GMR) for the closed-loop reachability analysis. The proposed algorithm is tested and demonstrated by the data collected from human subject experiments.
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WeB21 |
Orchid Junior 4311 |
Constrained Control II |
Regular Session |
Chair: Khorrami, Farshad | NYU Tandon School of Engineering |
Co-Chair: Tzes, Anthony | New York University Abu Dhabi |
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13:30-13:50, Paper WeB21.1 | |
>An Interval Predictor--Based Robust Control for a Class of Constrained Nonlinear Systems |
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Gutiérrez, Ariana | Tecnológico Nacional De México/I.T. De La Laguna |
Ríos, Héctor | Tecnológico Nacional De México/I.T. La Laguna |
Mera, Manuel | Esime Upt Ipn |
Efimov, Denis | Inria |
Ushirobira, Rosane | Inria |
Keywords: Constrained control, Nonlinear systems, Predictive control for nonlinear systems
Abstract: This paper proposes the design of a robust sampled–time controller to stabilize continuous–time nonlinear systems, taking into account state and input constraints. The proposed controller comprises the design of a robust control law, which is based on an interval predictor–based state–feedback controller and a Model Predictive Control (MPC) approach, which deals with the state and input constraints. The interval predictor–based state–feedback controller is designed based on a Lyapunov function approach that provides a safe set, where the state constraints are not transgressed. Out this set, the MPC is activated guaranteeing the fulfillment of the state and input constraints. The proposed switched control strategy guarantees the practical Uniform Asymptotic Stability of the considered nonlinear systems. A constructive method, based on linear matrix inequalities (LMIs), is proposed to compute the controller gains and the state of the system is not required. Some simulation results illustrate the feasibility of the proposed scheme.
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13:50-14:10, Paper WeB21.2 | |
>On Enlarging the Domain of Attraction for Linear Systems Subject to Asymmetric Actuator Saturation |
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Lai, Wenxin | Shanghai Jiao Tong University |
Li, Yuanlong | Shanghai Jiao Tong University |
Lin, Zongli | University of Virginia |
Keywords: Constrained control, Nonlinear systems
Abstract: In this paper, we revisit the problem of enlarging the domain of attraction for linear systems with asymmetric actuator saturation. We partition the state space into several regions according to the sign of each input and rewrite the linear system subject to asymmetric actuator saturation as an equivalent switched system, each subsystem of which is associated with one partition of the state space and is a linear system subject to symmetric actuator saturation. Based on this equivalent representation of the system, we present a Lyapunov function, which is composed of a set of quadratic functions associated with matrices that are not required to be positive definite. We establish sufficient conditions for regional stability and, based on them, formulate optimization problems to enlarge the estimate of the domain of attraction. Simulation results illustrate the effectiveness of the proposed approach.
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14:10-14:30, Paper WeB21.3 | |
>Safety-Critical Control under Multiple State and Input Constraints and Application to Fixed-Wing UAV |
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Oh, Donggeon David | Seoul National University |
Lee, Dongjae | Seoul National University |
Kim, H. Jin | Seoul National University |
Keywords: Constrained control, Optimal control, Control applications
Abstract: This study presents a framework to guarantee safety for a class of second-order nonlinear systems under multiple state and input constraints. To facilitate real-world applications, a safety-critical controller must consider multiple constraints simultaneously, while being able to impose general forms of constraints designed for various tasks (e.g., obstacle avoidance). With this in mind, we first devise a zeroing control barrier function (ZCBF) using a newly proposed nominal evading maneuver. By designing the nominal evading maneuver to 1) be continuously differentiable, 2) satisfy input constraints, and 3) be capable of handling other state constraints, we deduce an ultimate invariant set, a subset of the safe set that can be rendered forward invariant with admissible control inputs. Thanks to the development of the ultimate invariant set, we then propose a safety-critical controller, which is a computationally tractable one-step model predictive controller (MPC) with guaranteed recursive feasibility. We validate the proposed framework in simulation, where a fixed-wing UAV tracks a circular trajectory while satisfying multiple safety constraints including collision avoidance, bounds on flight speed and flight path angle, and input constraints.
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14:30-14:50, Paper WeB21.4 | |
>PWA Control Functions: From the Projection of mpQP Solution and Back to the Convexification by Lifting |
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Yang, Songlin | CentraleSupele, Paris Saclay University |
Olaru, Sorin | CentraleSupélec |
Rodriguez-Ayerbe, Pedro | CentraleSupelec |
Keywords: Constrained control, Optimal control, Model/Controller reduction
Abstract: This paper focuses on the geometric properties of the Piece-Wise Affine (PWA) feedback function as they appear from the optimal solution of the multi-parameter quadratic programming (mpQP) problem. Such optimization problems are popular formulations, for example, in the design of model- based predictive controllers (MPC) for discrete linear systems subject to input and state constraints. The paper considers such a PWA function as input data and provides a method for reconstructing a feasible convex set and a PWA curve within it, which retrieves the identical structure of the solution in the original parametric feasible set. The proposed method involves establishing and decomposing the topology structure of the polyhedral critical regions, which form the domain of the PWA function by means of a graph of interconnections. The regions are split into the boundary and interior collections using convex- concave lifting. The explicit solution is then merged based on the convex-concave liftings to reconstruct the feasible domain and the PWA curves.
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14:50-15:10, Paper WeB21.5 | |
>Constraint Inference in Control Tasks from Expert Demonstrations Via Inverse Optimization |
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Papadimitriou, Dimitris | UC Berkeley |
Li, Jingqi | University of California, Berkeley |
Keywords: Constrained control, Optimization, Estimation
Abstract: Inferring unknown constraints is a challenging and crucial problem in many robotics applications. When only expert demonstrations are available, it becomes essential to infer the unknown domain constraints to deploy additional agents effectively. In this work, we propose an approach to infer affine constraints in control tasks after observing expert demonstrations. We formulate the constraint inference problem as an inverse optimization problem, and we propose an alternating optimization scheme that infers the unknown constraints by minimizing a KKT residual objective. We demonstrate the effectiveness of our method in a number of simulations, and show that our method can infer less conservative constraints than a recent baseline method while maintaining comparable safety guarantees.
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15:10-15:30, Paper WeB21.6 | |
>Using Circulation to Mitigate Spurious Equilibria in Control Barrier Function |
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Goncalves, Vinicius Mariano | New York University Abu Dhabi, United Arab Emirates |
Krishnamurthy, Prashanth | NYU Tandon School of Engineering |
Tzes, Anthony | New York University Abu Dhabi |
Khorrami, Farshad | NYU Tandon School of Engineering |
Keywords: Constrained control, Optimization, Nonlinear systems
Abstract: Control Barrier Functions and Quadratic Programming are increasingly used for designing controllers that consider critical safety constraints. However, like Artificial Potential Fields, they can suffer from the stable spurious equilibrium point problem, which can result in the controller failing to reach the goal. To address this issue, we propose introducing circulation inequalities as a constraint. These inequalities force the system to explicitly circulate the obstacle region in configuration space, thus avoiding undesirable equilibria. We conduct a theoretical analysis of the proposed framework and demonstrate its efficacy through simulation studies. By mitigating spurious equilibria, our approach enhances the reliability of CBF-based controllers, making them more suitable for real-world applications.
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WeB22 |
Orchid Junior 4212 |
Stochastic Optimal Control II |
Regular Session |
Chair: Tsiotras, Panagiotis | Georgia Institute of Technology |
Co-Chair: Khonji, Majid | Khalifa University of Science and Technology |
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13:30-13:50, Paper WeB22.1 | |
>Optimal Stopping Problems in Low-Dimensional Feature Spaces: Lossless Conditions and Approximations |
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van Zutphen, Menno Johannes Theodorus Cornelis | Eindhoven University of Technology |
Heemels, W.P.M.H. | Eindhoven University of Technology |
Antunes, Duarte | Eindhoven University of Technology, the Netherlands |
Keywords: Stochastic optimal control, Markov processes, Model/Controller reduction
Abstract: Optimal control problems can be solved by dynamic programming. However, this method suffers from the curse of dimensionality. To resolve this, simplified versions of the original problem are often constructed in lower-dimensional feature spaces, leading to approximate policies. Yet, the connections between the original and the approximate policy and costs are rarely formalized. This paper addresses this challenge for optimal stopping problems. We start by providing conditions for lossless feature representations. This means that from an optimal policy obtained in feature space, an optimal policy in the original space can be constructed. Then, we search for modified versions of the original problem that (i) admit a lossless feature representation of far lower dimension; and (ii) provide upper and lower bounds on the optimal cost of the original problem. We can then use policies obtained in feature space using these modified problems to provide approximate policies for the original problem that are guaranteed to perform better than or equal to this aforementioned cost upper bound. We apply our tools in a high-dimensional precision farming intervention problem, where our tools allow for a dramatic decrease in complexity with only a small increase in the cost.
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13:50-14:10, Paper WeB22.2 | |
>A Fully Polynomial Time Approximation Scheme for Constrained MDPs under Local Transitions |
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Khonji, Majid | Khalifa University of Science and Technology |
Keywords: Stochastic optimal control, Markov processes, Uncertain systems
Abstract: The fixed-horizon constrained Markov Decision Process (C-MDP) is a well-known model for planning in stochastic environments under operating constraints. Chance-constrained MDP (CC-MDP) is a variant that allows bounding the probability of constraint violation, which is desired in many safety-critical applications. CC-MDP can also model a class of MDPs, called Stochastic Shortest Path (SSP), under dead-ends, where there is a trade-off between the probability-to-goal and cost-to-goal. This work studies the structure of (C)C-MDP, particularly an important variant that involves local transition. In this variant, the state reachability exhibits a certain degree of locality and independence from the remaining states. More precisely, the number of states, at a given time, that share some reachable future states is always constant. (C)C-MDP under local transition is NP-Hard even for a planning horizon of two. In this work, we propose a fully polynomial-time approximation scheme for (C)C-MDP that computes (near) optimal deterministic policies. Such an algorithm is among the best approximation algorithms attainable in theory and gives insights into the approximability of constrained MDP and its variants.
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14:10-14:30, Paper WeB22.3 | |
>Covariance Steering for Systems Subject to Unknown Parameters |
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Knaup, Jacob | Georgia Institute of Technology |
Tsiotras, Panagiotis | Georgia Institute of Technology |
Keywords: Stochastic optimal control, Optimal control, Uncertain systems
Abstract: This work considers the optimal covariance steering problem for systems subject to both additive noise and uncertain parameters which may enter multiplicatively with the state and the control. The unknown parameters are modeled as constant random variables sampled from distributions with known moments. The optimal covariance steering problem is formulated to include dependence between the unknown parameters and future states, and is solved using sequential convex programming. The proposed approach is demonstrated numerically using a spacecraft control application.
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14:30-14:50, Paper WeB22.4 | |
>Computationally Efficient Covariance Steering for Systems Subject to Parametric Disturbances and Chance Constraints |
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Knaup, Jacob | Georgia Institute of Technology |
Tsiotras, Panagiotis | Georgia Institute of Technology |
Keywords: Stochastic optimal control, Optimal control
Abstract: This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a tractable convex approximation of the optimal covariance steering problem is developed by tightening the chance constraints and by introducing a suitable change of variables. The solution of the convex approximation is shown to be a valid (albeit potentially suboptimal) solution to the original chance-constrained covariance steering problem.
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14:50-15:10, Paper WeB22.5 | |
>Discrete-Time Optimal Covariance Steering Via Semidefinite Programming |
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Rapakoulias, George | Georgia Institute of Technology |
Tsiotras, Panagiotis | Georgia Institute of Technology |
Keywords: Stochastic optimal control, Optimization, Linear systems
Abstract: This paper addresses the optimal covariance steering problem for stochastic discrete-time linear systems subject to probabilistic state and control constraints. A method is presented to efficiently attain the exact solution of the problem based on a lossless convex relaxation of the original non-linear program using semidefinite programming. Both the constrained and the unconstrained versions of the problem with either equality or inequality terminal covariance boundary conditions are addressed. We first prove that the proposed relaxation is lossless for all of the above cases. Numerical examples are then provided to illustrate the proposed method. Finally, a comparative study is performed on systems of various sizes and steering horizons to illustrate the advantages of the proposed method in terms of computational resources compared to the state of the art.
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15:10-15:30, Paper WeB22.6 | |
>Safe Stochastic Model-Based Policy Iteration with Chance Constraints |
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Zhai, Lijing | Georgia Institute of Technology |
Vamvoudakis, Kyriakos G. | Georgia Inst. of Tech |
Hugues, Jerome | Carnegie Mellon University / Software Engineering Institute |
Keywords: Stochastic optimal control, Resilient Control Systems, Learning
Abstract: In this paper, we consider optimal control problems of stochastic discrete-time systems subject to additive disturbances. Safety of such systems is guaranteed in a probabilistic sense via chance constraints. We solve the corresponding chance constrained stochastic control problems by extending the unconstrained model-based Policy Iteration (PI), and thus chance constrained PI with safety guarantees is proposed. Additionally, the stability of generated control policies is analyzed in the mean square sense. Numerical simulations are provided to validate the proposed algorithm performance.
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WeB23 |
Orchid Junior 4211 |
Cyber-Physical Security II |
Regular Session |
Chair: Li, Yuzhe | Northeastern University |
Co-Chair: Zamani, Majid | University of Colorado Boulder |
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13:30-13:50, Paper WeB23.1 | |
>Model-Unknown Spoofing Attack Via False Data Injections (I) |
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Yang, Nachuan | Hong Kong University of Science and Technology |
Zhong, Yuxing | The Hong Kong University of Science and Technology |
Li, Yuzhe | Northeastern University |
Shi, Ling | Hong Kong University of Science and Technology |
Keywords: Cyber-Physical Security, Attack Detection, Computer/Network Security
Abstract: This conference paper studies the spoofing attack via false data injections, where the adversarial attacker aims at misleading a cyber-physical system by distorting its sensor data. Such type of attacks has not been explored in the existing work on false data injection attacks. Besides, the existing research usually assumes an adversary with full knowledge of the target system. In this paper, we consider the case that the attacker does not know the system’s parameters. More specifically, we construct an adaptive estimator for the adversary and prove its convergence to the plant’s state estimate under adaptive laws. We also show that the convergence of the adaptive estimator is independent of the adversary’s strategy. Based on this “separation principle”, we propose two false data injection methods to implement online spoofing attacks by solving online linear equations and quadratic programming, respectively, and more can be developed using our proposed adaptive scheme in future research. Finally, we provide a benchmark numerical example of an L-1011 aircraft to illustrate the attack performance.
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13:50-14:10, Paper WeB23.2 | |
>Optimal Sequential False Data Injection Attack Scheme: Finite-Time Inverse Convergence (I) |
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Luo, Xiaoyu | Shanghai Jiao Tong University |
Fang, Chongrong | Shanghai Jiao Tong University |
Zhao, Chengcheng | Zhejiang University |
Cheng, Peng | Zhejiang University |
He, Jianping | Shanghai Jiao Tong University |
Keywords: Cyber-Physical Security, Networked control systems, Linear systems
Abstract: In this paper, we explore the relationship between the injected attack signal and the attack selection strategy in networked control systems where the adversary desires to steer the system state to the expected malicious one. We construct a sequential attack framework, i.e., the injected false data varies with the sampling time in discrete-time systems, and then derive an optimal sequential FDI attack strategy. The optimal sequential FDI attack strategy reveals the strongly coupled relationship between the injected attack signal and the attack selection strategy. Furthermore, we prove the finite-time inverse convergence of the critical parameters in the injected optimal attack signal by discrete-time Lyapunov analysis, which enables the efficient off-line design of the attack strategy and saves computing sources. Extensive simulations are conducted to show the effectiveness of the injected optimal sequential attack and the relationship between the attack signal and the attack selection strategy.
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14:10-14:30, Paper WeB23.3 | |
>Resilient State Estimation for Nonlinear Discrete-Time Systems Via Input and State Interval Observer Synthesis (I) |
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Khajenejad, Mohammad | University of California, San Diego |
Jin, Zeyuan | Arizona State University |
Dinh, Thach N. | CNAM Paris |
Yong, Sze Zheng | Northeastern University |
Keywords: Resilient Control Systems, Observers for nonlinear systems, Attack Detection
Abstract: This paper addresses the problem of resilient state estimation and attack reconstruction for boundederror nonlinear discrete-time systems with nonlinear observations/ constraints, where both sensors and actuators can be compromised by false data injection attack signals/unknown inputs. By leveraging mixed-monotone decomposition of nonlinear functions, as well as affine parallel outer-approximation of the observation functions, along with introducing auxiliary states to cancel out the effect of the attacks/unknown inputs, our proposed observer recursively computes interval estimates that by construction, contain the true states and unknown inputs of the system. Moreover, we provide several semi-definite programs to synthesize observer gains to ensure input-to-state stability of the proposed observer and optimality of the design in the sense of minimum mathcal{H}_{infty} gain.
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14:30-14:50, Paper WeB23.4 | |
>Towards Trustworthy AI: Sandboxing AI-Based Unverified Controllers for Safe and Secure Cyber-Physical Systems (I) |
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Zhong, Bingzhuo | Technical University of Munich |
Liu, Siyuan | KTH Royal Institute of Technology |
Caccamo, Marco | Technical University of Munich |
Zamani, Majid | University of Colorado Boulder |
Keywords: Supervisory control, Formal Verification/Synthesis, Hybrid systems
Abstract: In the past decade, artificial-intelligence-based (AI-based) techniques have been widely applied to design controllers over cyber-physical systems (CPSs) for complex control missions (e.g., motion planning in robotics). Nevertheless, AI-based controllers, particularly those developed based on deep neural networks, are typically very complex and are challenging to be formally verified. To cope with this issue, we propose a secure-by-construction architecture, namely Safe-Sec-visor architecture, to sandbox AI-based unverified controllers. By applying this architecture, the overall safety and security of CPSs can be ensured simultaneously, while formal verification over the AI-based controllers is not required. Here, we consider invariance and opacity properties as the desired safety and security properties, respectively. Accordingly, by leveraging a notion of (augmented) control barrier functions, we design a supervisor to check the control inputs provided by the AI-based controller and decide whether to accept them. At the same time, a safety-security advisor runs in parallel and provides fallback control inputs whenever the AI-based controller is rejected for safety and security reasons. To show the effectiveness of our approaches, we apply them to a case study on a quadrotor controlled by an AI-based controller. Here, the initial state of the quadrotor contains secret information which should not be revealed while the safety of the quadrotor should be ensured.
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14:50-15:10, Paper WeB23.5 | |
>Zero-Sum Game Based Secure Tracking Control of UAV against FDI Attacks Using Fixed-Time Convergent Reinforcement Learning (I) |
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Gong, Zhenyu | Northwestern Polytechnical University |
Yang, Feisheng | Northwestern Polytechnical University |
Wu, Dongrui | Huazhong University of Science and Technology |
Keywords: Cyber-Physical Security, Game theory, Learning
Abstract: In this paper, a fixed-time convergent reinforcement learning (RL) algorithm is developed to realize the secure tracking control of the unmanned aerial vehicle (UAV) via the zero-sum game for the first time. To mitigate FDI attack on actuators that may cause the UAV to deviate from the reference trajectory, a zero-sum differential game framework is built in which the secure controller tries to minimize the common performance function, yet the attacker plays a contrary role. Obtaining the optimal secure tracking controller depends on solving the Hamilton-Jacobi-Issacs (HJI) equation related to the zero-sum game. Therefore, a critic-only online RL algorithm is proposed that can converge in a fixed time interval, with the corresponding convergence proof provided. A simulation example is given to show the effectiveness of the raised method.
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15:10-15:30, Paper WeB23.6 | |
>Infinite Horizon Privacy in Networked Control Systems: Utility/Privacy Tradeoffs and Design Tools (I) |
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Hayati, Haleh | Eindhoven University of Technology |
Van De Wouw, Nathan | Eindhoven University of Technology |
Murguia, Carlos | Eindhoven University of Technology |
Keywords: Control Systems Privacy, Information theory and control, Optimal control
Abstract: We address the problem of synthesizing distorting mechanisms that maximize infinite horizon privacy for Networked Control Systems (NCSs). We consider stochastic LTI systems where information about the system state is obtained through noisy sensor measurements and transmitted to a (possibly adversarial) remote station via unsecured/public communication networks to compute control actions (a remote LQR controller). Because the network/station is untrustworthy, adversaries might access sensors and control data, and estimate the system state. To mitigate this risk, we pass sensor and control data through distorting (privacy-preserving) mechanisms before transmission and send the distorted data through the communication network. These mechanisms consist of a linear coordinate transformation and additive-dependent Gaussian vectors. We formulate the synthesis of the distorting mechanisms as a convex program where we minimize the infinite horizon mutual information (our privacy metric) between the system state and its optimal estimate at the remote station for a desired upper bound on the control performance (LQR cost) degradation induced by the distortion mechanism.
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WeB24 |
Orchid Main 4201AB |
Hybrid Systems I |
Regular Session |
Chair: Zaccarian, Luca | LAAS-CNRS and University of Trento |
Co-Chair: Poveda, Jorge I. | University of California, San Diego |
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13:30-13:50, Paper WeB24.1 | |
>A Hybrid Redesign for Robust Stabilization without Unit Input |
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Ballaben, Riccardo | University of Trento |
Sutulovic, Uros | Università Degli Studi Di Trento |
Invernizzi, Davide | Politecnico Di Milano |
Zaccarian, Luca | LAAS-CNRS |
Keywords: Hybrid systems, Aerospace, Lyapunov methods
Abstract: We redesign a linear stabilizer while avoiding an arbitrary value of the input signal. With a hybrid architecture based on a switching logic with two modes we obtain robust global exponential stability while ensuring that the input never takes the unwanted value, while preserving the nominal closed-loop behaviour in a neighbourhood of the origin. In the case where the minimization problem is too computationally expensive, we provide a simpler, albeit more conservative, way to determine the scaling factor. We also present a nonlinear case study to show that the proposed hybrid redesign can be extended to deal with nonlinear systems. Numerical examples are used to illustrate the theoretical results.
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13:50-14:10, Paper WeB24.2 | |
>On Invariants for Open Hybrid Systems and Their Interconnections |
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Sanfelice, Ricardo G. | University of California at Santa Cruz |
Teel, Andrew R. | Univ. of California at Santa Barbara |
Keywords: Hybrid systems, Network analysis and control, Networked control systems
Abstract: For a broad class of hybrid dynamical systems with inputs, termed open hybrid inclusions, a general interconnection model and solution concept are introduced. This model is employed to certify forward invariance of a set for the interconnection. The forward invariance notion allows for Zeno solutions and solutions that end prematurely – namely, maximal solutions that are not complete. Sufficient conditions for forward invariance of a set that are compositional and involve a properly defined scalar-valued barrier function are proposed. An example illustrates the ideas.
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14:10-14:30, Paper WeB24.3 | |
>Kalman-Like Observer for Hybrid Systems with Linear Maps and Known Jump Times |
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Tran, Gia Quoc Bao | Mines Paris, Université PSL |
Bernard, Pauline | Mines Paris - PSL |
Keywords: Hybrid systems, Observers for Linear systems, Kalman filtering
Abstract: We propose a hybrid Kalman-like observer for general hybrid systems with linear (time-varying) dynamics and output maps, where the solutions' jump times are exactly known. After defining a hybrid observability Gramian and the corresponding hybrid uniform complete observability, we show that the estimate provided by this observer converges asymptotically to the system solution if this observability holds together with some boundedness and invertibility conditions along the considered system solution. Then, under additional uniformity and strictness of the forgetting factors, we show exponential stability of the estimation error with an arbitrarily fast rate. The robust stability of this error against input disturbances and measurement noise is also studied. The results are illustrated on several benchmark examples, including switched systems, hybrid systems with discontinuous solutions, and continuous-time systems with multi-rate sporadic outputs.
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14:30-14:50, Paper WeB24.4 | |
>A Trajectory Based Optimization Approach for Hybrid Observer Design |
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Oliva, Federico | University of Rome Tor Vergata |
Mattogno, Simone | University of Rome Tor Vergata |
Tenaglia, Alessandro | University of Rome Tor Vergata |
Masocco, Roberto | University of Rome "Tor Vergata" |
Martinelli, Francesco | Univ. Di Roma Tor Vergata |
Carnevale, Daniele | Universita' Di Roma |
Keywords: Hybrid systems, Optimization, Estimation
Abstract: This paper presents a study on developing a hybrid 3D position observer for a rover with acceleration and relative distance measurements. The observer design utilizes two different methodologies; a Trajectory Based Optimization Design (TBOD) and a Linear Matrix Inequality (LMI) method. We prove that, under the proposed solutions, the boundedness of the estimation error is guaranteed. The performance of the observer is evaluated and compared to a standard EKF using comprehensive Monte Carlo simulations.
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14:50-15:10, Paper WeB24.5 | |
>Humanoid Robot Co-Design: Coupling Hardware Design with Gait Generation Via Hybrid Zero Dynamics |
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Ghansah, Adrian Boedtker | California Institute of Technology |
Kim, Jeeseop | California Institute of Technology |
Tucker, Maegan | California Institute of Technology |
Ames, Aaron D. | California Institute of Technology |
Keywords: Hybrid systems, Robotics, Optimization
Abstract: Selecting robot design parameters can be challenging since these parameters are often coupled with the performance of the controller and, therefore, the resulting capabilities of the robot. This leads to a time-consuming and often expensive process whereby one iterates between designing the robot and manually evaluating its capabilities. This is particularly challenging for bipedal robots, where it can be difficult to evaluate the behavior of the system due to the underlying nonlinear and hybrid dynamics. Thus, in an effort to streamline the design process of bipedal robots, and maximize their performance, this paper presents a systematic framework for the co-design of humanoid robots and their associated walking gaits. To this end, we leverage the framework of hybrid zero dynamic (HZD) gait generation, which gives a formal approach to the generation of dynamic walking gaits. The key novelty of this paper is to consider both virtual constraints associated with the actuators of the robot, coupled with emph{design} virtual constraints that encode the associated parameters of the robot to be designed. These virtual constraints are combined in an HZD optimization problem which simultaneously determines the design parameters while finding a stable walking gait that minimizes a given cost function. The proposed approach is demonstrated through the design of a novel humanoid robot, ADAM, wherein its thigh and shin are co-designed so as to yield energy efficient bipedal locomotion.
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15:10-15:30, Paper WeB24.6 | |
>Averaging in a Class of Stochastic Hybrid Dynamical Systems with Time-Varying Flow Maps |
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Poveda, Jorge I. | University of California, San Diego |
Keywords: Hybrid systems, Stability of hybrid systems, Adaptive systems
Abstract: We present stability and recurrence results for a class of stochastic hybrid dynamical systems with oscillating flow maps. These results are developed by introducing averaging tools that parallel those already existing for ordinary differential equations and deterministic hybrid dynamical systems. Such tools can be used to examine the stability properties of the original dynamics based on the properties of a simpler dynamical system constructed from the average of the original oscillating vector field. In this work, we focus on a class of systems for which global stability and recurrence results are achievable under suitable smoothness assumptions on the dynamics. By studying the average stochastic hybrid dynamics using Lyapunov-Foster functions, we derive similar stability and recurrence results for the original stochastic hybrid system.
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WeB26 |
Orchid Main 4301AB |
Distributed Parameter Systems I |
Regular Session |
Chair: Macchelli, Alessandro | University of Bologna - Italy |
Co-Chair: Le Gorrec, Yann | Cnrs, Ensmm, Femto-St / As2m |
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13:30-13:50, Paper WeB26.1 | |
>Adaptive Estimation of the Pennes’ Bio-Heat Equation - I: Observer Design |
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Cristofaro, Andrea | Sapienza University of Rome |
Cappellini, Guglielmo | Sapienza University of Rome |
Staffetti, Ernesto | Universidad Rey Juan Carlos |
Trappolini, Giovanni | Sapienza University of Rome |
Vendittelli, Marilena | Sapienza University of Rome |
Keywords: Distributed parameter systems, Adaptive systems, Healthcare and medical systems
Abstract: In this paper, we propose a multiple-model adaptive estimation setup for a class of uncertain parabolic reaction-diffusion PDEs encompassing the Pennes’ bio-heat equation, which is a motivating case study from the perspective of biomedical applications such as hyperthermia. The efficacy of the approach in estimating the system solution and recovering the value of the reaction coefficient is validated through numerical simulations in MATLAB. The validation step has highlited some limitations of classical numerical simulation tools that we propose to handle through an implementation of the estimator relying on Deep Learning libraries. This alternative approach is reported in a companion paper (Part II of this work).
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13:50-14:10, Paper WeB26.2 | |
>Incrementally Passive Infinite Dimensional Systems with a Constrained State Variable |
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Singh, Shantanu | Tel Aviv University |
Fueyo, Sebastien | Tel Aviv University |
Weiss, George | Tel Aviv University |
Keywords: Distributed parameter systems, Constrained control, Nonlinear systems
Abstract: In this paper, we show that the passivity property of a linear infinite dimensional system, with respect to a given supply rate, is preserved in the presence of a saturating integrator, which restricts a one dimensional component of the state to a compact interval. The resulting nonlinear system is incrementally passive with the same supply rate. We give an application of our main result to a boundary controlled string equation, where the displacement of the string at some interior point is restricted to a compact interval.
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14:10-14:30, Paper WeB26.3 | |
>The Power Function for Adaptive Control in Native Space Embedding |
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Wang, Haoran | Virginia Tech |
Powell, Nathan | Virginia Tech |
L'Afflitto, Andrea | Virginia Tech |
Kurdila, Andrew J. | Virginia Tech |
Burns, John A | Virginia Tech |
Keywords: Distributed parameter systems, Data driven control, Adaptive control
Abstract: This paper studies how the power function in a reproducing kernel Hilbert space (RKHS) can be used system- atically to design error bounding methods of adaptive estima- tion and control via the native space embedding method. The approach is based on viewing the original system of ordinary differential equations (ODEs) as a type of distributed parameter system (DPS), and subsequently defining realizable controllers by approximating the DPS with scattered bases over a domain of interest. The approach provides rigorous bounds on ultimate performance guarantees for uncertainty classes defined in the native space. One result derives an upper bound on the ultimate performance of the adaptive controller in terms of the power function. Another version of this upper bound shows how the ultimate performance can bounded in terms of a fill distance of centers of approximation in subsets that contain the closed loop trajectory. In contrast to the general theory for error bounding adaptive controllers in Euclidean space, the general approach in this paper works for functional uncertainties in any RKHS.
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14:30-14:50, Paper WeB26.4 | |
>Frequency Domain Approach for the Stability Analysis of a Fast Hyperbolic PDE Coupled with a Slow ODE |
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Arias, Gonzalo | Pontificia Universidad Católica De Chile |
Marx, Swann | LS2N |
Mazanti, Guilherme | Inria, Université Paris-Saclay, CentraleSupélec, CNRS |
Keywords: Distributed parameter systems, Delay systems, Stability of linear systems
Abstract: This paper deals with the exponential stability of systems made of a hyperbolic PDE coupled with an ODE with different time scales, the dynamics of the PDE being much faster than that of the ODE. Such a difference of time scales is modeled though a small parameter varepsilon multiplying the time derivative in the PDE, and our stability analysis relies on the singular perturbation method. More precisely, we define two subsystems: a reduced order system, representing the dynamics of the full system in the limit varepsilon = 0, and a boundary-layer system, which represents the dynamics of the PDE in the fast time scale. Our main result shows that, if both the reduced order and the boundary-layer systems are exponentially stable, then the full system is also exponentially stable for varepsilon small enough, and our strategy is based on a spectral analysis of the systems under consideration. Our main result improves a previous result in the literature, which was proved using a Lyapunov approach and required a stronger assumption on the boundary-layer system to obtain the same conclusion.
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14:50-15:10, Paper WeB26.5 | |
>Port-Hamiltonian Control Design for an IPMC Actuated Highly Flexible Endoscope |
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Macchelli, Alessandro | University of Bologna - Italy |
Wu, Yongxin | FEMTO-ST/ENSMM |
Le Gorrec, Yann | Cnrs, Ensmm, Femto-St / As2m |
Keywords: Distributed parameter systems, Flexible structures, Smart structures
Abstract: This paper deals with modelling and control of an endoscope actuated by Ionic Polymer Metal Composites (IPMC) patches. The endoscope is modelled by a nonlinear partial differential equation (PDE) capable to describe large deformations. The dynamics of the flexible structure and of the IPMC patches are in port-Hamiltonian form, with the actuators interconnected to the mechanical device in power-conserving way. Thus, the complete model is a port-Hamiltonian system in which a PDE with fixed boundary conditions is coupled with a set of ordinary differential equations. The control inputs are the voltages applied to the patches, and the feedback law is designed within the Interconnection and Damping Assignment Passivity-based Control (IDA-PBC) framework. The asymptotic stability of the closed-loop system is proved, and the effectiveness of the design procedure is illustrated by a numerical example.
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15:10-15:30, Paper WeB26.6 | |
>Disturbance Attenuation in the Euler-Bernoulli Beam with Viscous and Kelvin-Voigt Damping Via Piezoelectric Actuators |
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Selivanov, Anton | The University of Sheffield |
Fridman, Emilia | Tel-Aviv Univ |
Keywords: Distributed parameter systems, LMIs
Abstract: We design a state-feedback controller, applied via piezoelectric actuators, that suppresses the effect of a distributed disturbance in the Euler-Bernoulli beam with viscous and Kelvin-Voigt damping. The controller is designed to improve performance on a finite number of modes. Its effect on the remaining (infinitely many) modes is analysed by constructing an appropriate Lyapunov functional, whose properties are guaranteed by the feasibility of linear matrix inequalities (LMIs). The LMIs allow us to design suitable controller gain and estimate the induced L2 gain. A numerical example demonstrates how this modal decomposition approach leads to a controller that significantly reduces the L2 gain.
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WeC01 |
Orchid Main 4202-4306 |
Learning, Optimization, and Game Theory I |
Invited Session |
Chair: Doan, Thinh T. | Virginia Tech |
Co-Chair: Vamvoudakis, Kyriakos G. | Georgia Inst. of Tech |
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 WeC01.1 | |
>Revisiting LQR Control from the Perspective of Receding-Horizon Policy Gradient |
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Zhang, Xiangyuan | University of Illinois at Urbana-Champaign |
Basar, Tamer | Univ of Illinois, Urbana-Champaign |
Keywords: Optimal control, Machine learning, Optimization
Abstract: We revisit in this paper the discrete-time linear quadratic regulator (LQR) problem from the perspective of receding-horizon policy gradient (RHPG), a newly developed model-free learning framework for control applications. We provide a fine-grained sample complexity analysis for RHPG to learn a control policy that is both stabilizing and epsilon-close to the optimal LQR solution, and our algorithm does not require knowing a stabilizing control policy for initialization. Combined with the recent application of RHPG in learning the Kalman filter, we demonstrate the general applicability of RHPG in linear control and estimation with streamlined analyses.
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16:20-16:40, Paper WeC01.2 | |
>Online Reinforcement Learning in Markov Decision Process Using Linear Programming (I) |
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Leon, Vincent | University of Illinois at Urbana-Champaign |
Etesami, Rasoul | University of Illinois at Urbana-Champaign |
Keywords: Learning, Markov processes, Optimization algorithms
Abstract: We consider online reinforcement learning in episodic Markov decision process (MDP) with unknown transition function and stochastic rewards drawn from some fixed but unknown distribution. The learner aims to learn the optimal policy and minimize their regret over a finite time horizon through interacting with the environment. We devise a simple and efficient model-based algorithm that achieves O~(LX(TA)^(1/2)) regret with high probability, where L is the episode length, T is the number of episodes, and X and A are the cardinalities of the state space and the action space, respectively. The proposed algorithm, which is based on the concept of "optimism in the face of uncertainty", maintains confidence sets of transition and reward functions and uses occupancy measures to connect the online MDP with linear programming. It achieves a tighter regret bound compared to the existing works that use a similar confidence set framework and improves computational effort compared to those that use a different framework but with a slightly tighter regret bound.
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16:40-17:00, Paper WeC01.3 | |
>On the Convergence of Natural Policy Gradient and Mirror Descent-Like Policy Methods for Average-Reward MDPs (I) |
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Murthy, Yashaswini | University of Illinois, Urbana-Champaign |
Srikant, R | Univ of Illinois, Urbana-Champaign |
Keywords: Learning, Stochastic optimal control, Stochastic systems
Abstract: It is now well known that Natural Policy Gradient (NPG) globally converges for discounted-reward MDPs in the tabular setting, with perfect value function estimates. However, the result cannot be directly used to obtain a corresponding convergence result for average-reward MDPs by letting the discount factor tend to one. In this paper, we prove that NPG also converges for average-reward MDPs in which each policy leads to an irreducible Markov chain. Since NPG can also be interpreted as a mirror descent based policy method, we then discuss extensions to non-tabular settings for mirror descent-based methods.
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17:00-17:20, Paper WeC01.4 | |
>Episodic Logit-Q Dynamics for Efficient Learning in Stochastic Teams (I) |
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Unlu, Onur | Bilkent University |
Sayin, Muhammed Omer | Bilkent University |
Keywords: Game theory, Markov processes, Learning
Abstract: We present new learning dynamics combining (independent) log-linear learning and value iteration for stochastic games within the auxiliary stage game framework. The dynamics presented provably attain the efficient equilibrium (also known as optimal equilibrium) in identical-interest stochastic games, beyond the recent concentration of progress on provable convergence to some (possibly inefficient) equilibrium. The dynamics are also independent in the sense that agents take actions consistent with their local viewpoint to a reasonable extent rather than seeking equilibrium. These aspects can be of practical interest in the control applications of intelligent and autonomous systems. The key challenges are the convergence to an inefficient equilibrium and the non-stationarity of the environment from a single agent's viewpoint due to the adaptation of others. The log-linear update plays an important role in addressing the former. We address the latter through the play-in-episodes scheme in which the agents update their Q-function estimates only at the end of the episodes.
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17:20-17:40, Paper WeC01.5 | |
>Gradient Dynamics in Linear Quadratic Network Games with Time-Varying Connectivity and Population Fluctuation (I) |
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Al Taha, Feras | Cornell University |
Rokade, Kiran | Cornell University |
Parise, Francesca | Cornell University |
Keywords: Game theory, Learning, Large-scale systems
Abstract: In this paper, we consider a learning problem among non-cooperative agents interacting in a time-varying system. Specifically, we focus on repeated linear quadratic network games, in which the network of interactions changes with time and agents may not be present at each iteration. To get tractability, we assume that at each iteration, the network of interactions is sampled from an underlying random network model and agents participate at random with a given probability. Under these assumptions, we consider a gradient-based learning algorithm and establish almost sure convergence of the agents' strategies to the Nash equilibrium of the game played over the expected network. Additionally, we prove, in the large population regime, that the learned strategy is an epsilon-Nash equilibrium for each stage game with high probability. We validate our results over an online market application.
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17:40-18:00, Paper WeC01.6 | |
>Policy Gradient Play Over Time-Varying Networks in Markov Potential Games (I) |
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Aydin, Sarper | Texas A&M University |
Eksin, Ceyhun | Texas A&M University |
Keywords: Game theory, Learning, Optimization algorithms
Abstract: We design a multi-agent and networked policy gradient algorithm in Markov potential games. Each agent has its own rewards and utility as functions of joint actions and a shared state among agents. The state dynamics depend on the joint actions taken. Differentiable Markov potential games are defined based on the existence of a potential (value) function having partial gradients equal to the local gradients of agents' individual value functions. Agents implement continuous parameterized policies defined over the state and other agents' parameters to maximize their utilities against each other. Agents compute their stochastic policy gradients to update their parameters with respect to their local estimates of Q-functions and joint parameters. The updated parameters are shared with neighbors over a time-varying network. We prove the convergence of joint parameters to a first-order stationary point of the potential function in probability for any type of state and action spaces. Numerical results illustrate the potential advantages of using networked policies compared to independent policies.
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WeC02 |
Melati Main 4001AB-4104 |
Data-Driven Distributionally Robust Optimization and Control |
Invited Session |
Chair: Aolaritei, Ioan-Liviu | ETH Zurich |
Co-Chair: Dörfler, Florian | Swiss Federal Institute of Technology (ETH) Zurich |
Organizer: Aolaritei, Liviu | ETH Zurich |
Organizer: Dörfler, Florian | Swiss Federal Institute of Technology (ETH) Zurich |
Organizer: Cherukuri, Ashish | University of Groningen |
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16:00-16:20, Paper WeC02.1 | |
>Ordered Risk Minimization: Learning More from Less Data (I) |
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Coppens, Peter | KU Leuven |
Patrinos, Panagiotis | KU Leuven |
Keywords: Optimization, Statistical learning, Machine learning
Abstract: We consider the worst-case expectation of a permutation invariant ambiguity set of discrete distributions as a proxy-cost for data-driven expected risk minimization. For this framework, we coin the term ordered risk minimization to highlight how results from order statistics inspired the proxy-cost. Specifically, we show how such costs serve as point-wise high-confidence upper bounds of the expected risk. The confidence level can be determined tightly for any sample size. Conversely we also illustrate how to calibrate the size of the ambiguity set such that the high-confidence upper bound has some user specified confidence. This calibration procedure notably supports phi-divergence based ambiguity sets. Numerical experiments then illustrate how the resulting scheme both generalizes better and is less sensitive to tuning parameters compared to the empirical risk minimization approach.
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16:20-16:40, Paper WeC02.2 | |
>Distributionally Robust Differential Dynamic Programming with Wasserstein Distance |
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Hakobyan, Astghik | Seoul National University |
Yang, Insoon | Seoul National University |
Keywords: Stochastic optimal control, Optimal control
Abstract: Differential dynamic programming (DDP) is a popular technique for solving nonlinear optimal control problems with locally quadratic approximations. However, existing DDP methods are not designed for stochastic systems with unknown disturbance distributions. To address this limitation, we propose a novel DDP method that approximately solves the Wasserstein distributionally robust control (WDRC) problem, where the true disturbance distribution is unknown but a disturbance sample dataset is given. Our approach aims to develop a practical and computationally efficient DDP solution. To achieve this, we use the Kantrovich duality principle to decompose the value function in a novel way and derive closed-form expressions of the distributionally robust control and worst-case distribution policies to be used in each iteration of our DDP algorithm. This characterization makes our method tractable and scalable without the need for numerically solving any minimax optimization problems. The superior out-of-sample performance and scalability of our algorithm are demonstrated through kinematic car navigation and coupled oscillator problems.
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16:40-17:00, Paper WeC02.3 | |
>Distributionally Robust Optimal and Safe Control of Stochastic Systems Via Kernel Conditional Mean Embedding (I) |
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Romao, Licio | University of Oxford |
Hota, Ashish Ranjan | Indian Institute of Technology (IIT), Kharagpur |
Abate, Alessandro | University of Oxford |
Keywords: Stochastic optimal control, Stochastic systems, Machine learning
Abstract: We present a distributionally robust framework for dynamic programming that uses kernel methods to design control policies satisfying both safety and optimality specifications. Specifically, we leverage kernel mean embedding to map the transition probabilities governing state evolution into an associated reproducing kernel Hilbert space. Our key idea lies in combining conditional mean embedding estimated from past data of system trajectories with the maximum mean discrepancy distance to construct an ambiguity set, and then design a robust control policy using techniques from distributionally robust optimization. The main theoretical contribution of this paper is to leverage functional analytical tools to prove that optimal policies for this infinite-dimensional min-max problem are Markovian. Additionally, we discuss approximation schemes based on discretization of inputs to make the approach computationally tractable. We validate the main theoretical findings of the paper in a benchmark control problem involving safe control of thermostatically controlled loads.
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17:00-17:20, Paper WeC02.4 | |
>Wasserstein Distributionally Robust Risk-Constrained Iterative MPC for Motion Planning: Computationally Efficient Approximations (I) |
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Zolanvari, Alireza | University of Groningen |
Cherukuri, Ashish | University of Groningen |
Keywords: Predictive control for nonlinear systems, Iterative learning control, Robotics
Abstract: This paper considers a risk-constrained motion planning problem and aims to find the solution combining the concepts of iterative model predictive control (MPC) and data-driven distributionally robust (DR) risk-constrained optimization. In the iterative MPC, at each iteration, safe states visited and stored in the previous iterations are imposed as terminal constraints. Furthermore, samples collected during the iteration are used in the subsequent iterations to tune the ambiguity set of the DR constraints employed in the MPC. In this method, the MPC problem becomes computationally burdensome when the iteration number goes high. To overcome this challenge, the emphasis of this paper is to reduce the real-time computational effort using two approximations. First one involves clustering of data at the beginning of each iteration and modifying the ambiguity set for the MPC scheme so that safety guarantees still holds. The second approximation considers determining DR-safe regions at the start of iteration and constraining the state in the MPC scheme to such safe sets. We analyze the computational tractability of these approximations and present a simulation example that considers path planning in the presence of randomly moving obstacle.
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17:20-17:40, Paper WeC02.5 | |
>Data-Driven Distributionally Robust Coverage Control by Mobile Robots (I) |
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Boskos, Dimitris | TU Delft |
Cortes, Jorge | University of California, San Diego |
Martinez, Sonia | University of California at San Diego |
Keywords: Autonomous robots, Uncertain systems, Optimization algorithms
Abstract: This paper provides a data-driven solution to the problem of coverage control by which a team of robots aims to optimally deploy in a spatial region where certain event of interest may occur. This event is random and described by a probability density function, which is unknown and can only be learned by collecting data. In this work, we hedge against this uncertainty by designing a distributionally robust algorithm that optimizes the locations of the robots against the worst-case probability density from an ambiguity set. This ambiguity set is constructed from data initially collected by the agents, and contains the true density function with prescribed confidence. However, the objective function that the robots seek to minimize is non-smooth. To address this issue, we employ the so-called gradient sampling algorithm, which approximates the Clarke generalized gradient by sampling the derivative of the objective function at nearby locations and stabilizes the choice of descent directions around points where the function may fail to be differentiable. This enables us to prove that the algorithm converges to a stationary point from any initial location of the robots, in analogy to the well-known Lloyd algorithm for differentiable costs when the spatial density is known.
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17:40-18:00, Paper WeC02.6 | |
>Wasserstein Tube MPC with Exact Uncertainty Propagation (I) |
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Aolaritei, Liviu | ETH Zurich |
Fochesato, Marta | ETH Zurich |
Lygeros, John | ETH Zurich |
Dörfler, Florian | Swiss Federal Institute of Technology (ETH) Zurich |
Keywords: Stochastic systems, Robust control, Optimal control
Abstract: We study model predictive control (MPC) problems for stochastic LTI systems, where the noise distribution is unknown, compactly supported, and only observable through a limited number of i.i.d. noise realizations. Building upon recent results in the literature, which show that distributional uncertainty can be efficiently captured within a Wasserstein ambiguity set, and that such ambiguity sets propagate exactly through the system dynamics, we start by formulating a novel Wasserstein Tube MPC (WT-MPC) problem, with distributionally robust CVaR constraints. We then show that the WT-MPC problem: (1) is a direct generalization of the (deterministic) Robust Tube MPC (RT-MPC) to the stochastic setting; (2) through a scalar parameter, it interpolates between the data-driven formulation based on sample average approximation and the RT-MPC formulation, allowing us to optimally trade between safety and performance; (3) admits a tractable convex reformulation, which grows linearly in the number of available noise samples; and (4) is recursively feasible. Finally, we conclude the paper with a numerical comparison of WT-MPC and RT-MPC.
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WeC03 |
Melati Junior 4010A-4111 |
Cyber-Physical Systems: Resilience |
Invited Session |
Chair: Zhu, Quanyan | New York University |
Co-Chair: Sadabadi, Mahdieh S. | Queen Mary University of London |
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 WeC03.1 | |
>Identification of Malicious Activity in Distributed Average Consensus Via Non-Concurrent Checking |
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Hadjicostis, Christoforos N. | University of Cyprus |
Dominguez-Garcia, Alejandro D. | University of Illinois at Urbana-Champaign |
Keywords: Agents-based systems, Distributed control, Fault diagnosis
Abstract: We consider the problem of average consensus in a network system under a fixed, undirected communication topology, when there are malicious nodes present that may try to influence the average calculation. In the setting considered, the average consensus is performed by the nodes in a distributed fashion using a linear iterative algorithm. We assume malicious nodes can manipulate, in an arbitrary manner, the value of their state in the aforementioned algorithm; the problem is then to check whether or not each node is correctly performing the updates of its state. To address this problem, we propose a distributed algorithm whereby each node is in charge of checking the updates performed by its neighboring nodes based on information that it receives from them and also from the neighbors of its neighbors. The algorithm leverages ideas from non-concurrent error detection schemes and its main advantage is that information from two-hop neighbors is only needed infrequently—a relaxation that significantly reduces the communication overhead associated with the requirement to make such information available.
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16:20-16:40, Paper WeC03.2 | |
>Distributed Resilient Observer: Blended Dynamics Theory Meets L1-Minimization Approach |
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Lee, Donggil | Seoul National University |
Kim, Junsoo | Seoul National University of Science and Technology |
Shim, Hyungbo | Seoul National University |
Keywords: Networked control systems, Observers for Linear systems, Distributed control
Abstract: This paper presents a distributed resilient observer for continuous-time linear time-invariant plants that remains functional even under sensor attacks. The proposed method aims to determine the estimation outcome that matches the majority of sensor measurements, which is formulated as an l1-minimization problem considering all the observable components of each sensor measurement. A distributed observer based on the blended dynamics theory is then proposed to solve the l1-minimization problem in a distributed manner. As a result, the distributed resilient estimation is enabled for a broader class of systems compared to previous works. The design procedure is constructive with parameters obtained from a specified condition that is equivalent to the well-known null-space property.
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16:40-17:00, Paper WeC03.3 | |
>Leader-Follower Formations Subject to False Data Injections: A Resilient Distributed Model Predictive Approach (I) |
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Famularo, Domenico | Università Degli Studi Della Calabria |
Franze, Giuseppe | Universita' Della Calabria |
Tedesco, Francesco | Università Della Calabria |
Venturino, Antonello | Università Della Calabria |
Keywords: Resilient Control Systems, Cyber-Physical Security, Predictive control for nonlinear systems
Abstract: In this paper, resilience issues for platoons of autonomous agents are addressed when false data injections affect the information exchanged among the neighbors via a communication medium. A distributed model predictive control scheme is used for dealing with the overall regulation task. Conversely, the core of this study relies on the design of an efficient anomaly detector and viable attack countermeasures. In particular, it is formally proven that the proposed device is capable to uncover in finite time malicious actions by simple set-containment set-membership conditions arising from the concept of k-step ahead state predictions convex sets. Moreover, the attack countermeasures have a twofold nature: the first one is conceived by exploiting feasibility arguments of the model predictive philosophy; while the second resilient operation takes inspiration from rejuvenation ideas by leading to safe splitting and/or queuing the initial multi-agent formation.
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17:00-17:20, Paper WeC03.4 | |
>Resilient Quantized Consensus with Multi-Hop Communication (I) |
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Yuan, Liwei | Hunan University |
Ishii, Hideaki | Tokyo Institute of Technology |
Keywords: Networked control systems, Cyber-Physical Security, Agents-based systems
Abstract: In this paper, we study the problem of resilient quantized consensus problem where some of the agents may behave maliciously. The network consists of agents taking quantized/integer-valued states with asynchronous updates and time delays in the communication between agents. We propose a quantized weighted mean subsequence reduced (QW-MSR) algorithm where agents are capable to communicate with multi-hop neighbors. We provide necessary and sufficient conditions for our algorithm to achieve resilient quantized consensus for synchronous/asynchronous updates under the malicious attacks. Compared to existing methods in the literature, our algorithm has tighter graph condition and, in particular, we establish that with multi-hop communication, the requirement for achieving resilient quantized consensus is less stringent. Numerical examples are given to verify the efficacy of the proposed algorithm.
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17:20-17:40, Paper WeC03.5 | |
>Temporal Logic Resilience for Cyber-Physical Systems (I) |
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Saoud, Adnane | CentraleSupelec |
Jagtap, Pushpak | Indian Institute of Science |
Soudjani, Sadegh | Newcastle University |
Keywords: Resilient Control Systems, Formal Verification/Synthesis, Hybrid systems
Abstract: We consider the notion of resilience for cyber-physical systems, that is, the ability of the system to withstand adverse events while maintaining acceptable functionality. We use temporal logic to express the requirements on the acceptable functionality and define the resilience metric as the maximum disturbance under which the system satisfies the temporal requirements. We fix a parameterized template for the set of disturbances and form a robust optimization problem under the system dynamics and the temporal specifications to find the maximum value of the parameter. From the computational point of view, we show how this optimization can be solved for linear systems and provide under-approximations of the resilience metric for nonlinear systems using linear programs. The computations are demonstrated on the temperature regulation of buildings and adaptive cruise control.
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17:40-18:00, Paper WeC03.6 | |
>Resilient Integral Control for Regulating Systems with Convex Input Constraints (I) |
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Konstantopoulos, George | University of Patras |
Bechlioulis, Charalampos P. | University of Patras |
Keywords: Nonlinear systems, Output regulation, Constrained control
Abstract: In this paper, a novel integral control that can maintain the control input vector trajectory of a generic ISS linear or nonlinear plant within a prescribed compact and convex set is proposed. During normal operating conditions, the proposed controller can regulate the plant to the desired setpoint, while in the case of abnormal conditions, e.g. sensor faults, unrealistic reference input command, the controller introduces an inherent resilience property by maintaining the entire control input vector of the plant within a desired convex set. The boundedness of the control input vector is analytically proven using invariant set theory and vector field analysis (Nagumo’s theorem). Opposed to conventional and more advanced integral controllers that either restrict each element of the control input vector independently or bound its Euclidean norm, in this paper, a detailed methodology for designing a resilient integral control to guarantee a generic compact and convex input constraint for a plant with unknown structure or dynamics is presented for the first time. A practical example of an underwater vehicle is investigated to validate the efficiency and resilience of the proposed controller under changes of the reference signal and under sensor faults.
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WeC04 |
Simpor Junior 4913 |
Efficient Communication for Networked Control Systems & Games |
Invited Session |
Chair: Aggarwal, Shubham | University of Illinois, Urbana Champaign |
Co-Chair: Basar, Tamer | Univ of Illinois, Urbana-Champaign |
Organizer: Aggarwal, Shubham | University of Illinois, Urbana Champaign |
Organizer: Zaman, Muhammad Aneeq uz | UIUC |
Organizer: Bastopcu, Melih | University of Illinois Urbana Champaign |
Organizer: Basar, Tamer | Univ of Illinois, Urbana-Champaign |
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16:00-16:20, Paper WeC04.1 | |
>Event-Based Admission Control Over Multi-Hop Networks with Self-Interference (I) |
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Ayan, Onur | Huawei Technologies |
Kutsevol, Polina | Technical University of Munich |
Kellerer, Wolfgang | Technical University of Munich |
An, Xueli | Huawei Technologies |
Keywords: Control of networks, Networked control systems, Control over communications
Abstract: In this work, we investigate the application of event-triggering in a multi-hop networked control scenario with interference constraints. In particular, we consider a line network comprised of H nodes with neighboring nodes affecting the reliability of each other, hence, introducing packet loss and non-negligible end-to-end latency. Having the practical feasibility in mind, we focus on admission control mechanisms at the sensor without assuming a centralized scheduling entity that has the perfect and global knowledge of the entire network. We demonstrate that, if the limitations of the network are neglected, the event-triggering mechanism may lead to low end-to-end reliability causing a significant degradation of the control performance. As a solution, we propose two novel admission control policies that aim to find a minimum inter-event time (MIET) in order to prevent a network congestion followed by a control performance deterioration. While the first policy follows an analytical approach combining the core principles of event-triggering and congestion control, the second policy learns the MIET adaptively without the knowledge of the network model. We show through numerical evaluation that the proposed strategies improve the control performance by more than 20% if the event criterion is selected appropriately.
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16:20-16:40, Paper WeC04.2 | |
>A Group Formation Game for Local Anomaly Detection (I) |
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Ye, Zixin | University of Melbourne |
Alpcan, Tansu | The University of Melbourne |
Leckie, Christopher Andrew | The University of Melbourne |
Keywords: Game theory, Machine learning, Computer/Network Security
Abstract: This paper studies strategic group formation for local anomaly detection with potential applications to Cognitive Radio Networks (CRN) and the Internet-of-Things (IoT). The problem comprises multiple local anomaly detection tasks which use machine learning (ML) models and partial data. We consider a two-layer network structure with anomaly detectors in the lower layer acting as local anomaly detectors and central nodes at the upper layer as data aggregators, which train the ML models used by local anomaly detectors. The problem is addressed using a strategic (non-cooperative) game formulation, where all central nodes and detectors are players. The players interactively learn one or multiple optimal machine learning models for their dynamically identified local anomaly detection problems. The game is next formulated as a successive optimization problem and solved using the player's best responses to compute a Nash equilibrium. Under mild conditions, we prove that this group formation game is also a potential game, and any acquired solution achieving the local optima corresponds to a Nash Equilibrium. Experimental results are consistent with theoretical ones and show fast convergence to the solution.
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16:40-17:00, Paper WeC04.3 | |
>Timely Tracking of a Remote Dynamic Source Via Multi-Hop Renewal Updates (I) |
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Kaswan, Priyanka | University of Maryland |
Ulukus, Sennur | University of Maryland |
Keywords: Communication networks, Stochastic systems, Network analysis and control
Abstract: We study the version age of information in a multi-hop multi-cast cache-enabled network, where updates at the source are marked with incrementing version numbers, and the inter-update times on the links are not necessarily exponentially distributed. We focus on the set of non-arithmetic distributions, which includes continuous probability distributions as a subset, with finite first and second moments for inter-update times. We first characterize the instantaneous version age of information at each node for an arbitrary network. We then explicate the recursive equations for instantaneous version age of information in multi-hop networks and employ semi-martingale representation of renewal processes to derive closed form expressions for the expected version age of information at an end user. We show that the expected age in a multi-hop network exhibits an additive structure. Further, we show that the expected age at each user is proportional to the variance of inter-update times at all links between a user and the source. Thus, end user nodes should request packet updates at constant intervals.
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17:00-17:20, Paper WeC04.4 | |
>Communication-Efficient Local SGD for Over-Parametrized Models with Partial Participation (I) |
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Qin, Tiancheng | University of Illinois at Urbana-Champaign |
Yevale, Jayesh | University of Illinois at Urbana-Champaign |
Etesami, Rasoul | University of Illinois at Urbana-Champaign |
Keywords: Optimization, Distributed parameter systems, Machine learning
Abstract: We analyze the convergence rate of Local stochastic gradient descent (SGD) for over-parameterized models, which is at the core of federated learning. In this model, we allow the server to randomly select a subset of agents and communicate with them at each communication round to optimize a global objective function. This captures the realistic scenarios where the communication link between the server and the agents may break down due to random link failures or adversarial attacks. Under such an elaborate setting, we establish convergence guarantees for smooth objective functions without the convexity assumption that is the first for the regime. We also consider an extension of our results under a different random participation setting over general network structures (rather than a star network) in which an agent participates in the local optimization steps of its neighbors by some edge-dependent probability. We characterize the convergence rate of the proposed algorithm in terms of the number of communication rounds which confirms the communication efficiency of our methods.
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17:20-17:40, Paper WeC04.5 | |
>Efficient Communication for Pursuit-Evasion Games with Asymmetric Information (I) |
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Maity, Dipankar | University of North Carolina at Charlotte |
Keywords: Agents-based systems, Control over communications, Game theory
Abstract: We consider a class of pursuit-evasion differential games in which the evader has continuous access to the pursuer’s location but not vice-versa. There is an immobile sensor (e.g., a ground radar station) that can sense the evader’s location and communicate that information intermittently to the pursuer. Transmitting the information from the sensor to the pursuer is costly and only a finite number of transmissions can happen throughout the entire game. The outcome of the game is determined by the control strategies of the players and the communication strategy between the sensor and the pursuer. We obtain the (Nash) equilibrium control strategies for both the players as well as the optimal communication strategy between the static sensor and the pursuer. We discuss a dilemma for the evader that emerges in this game. We also discuss the emergence of implicit communication where the absence of communication from the sensor can also convey some actionable information to the pursuer.
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17:40-18:00, Paper WeC04.6 | |
>A Privacy-Preserving Finite-Time Push-Sum Based Gradient Method for Distributed Optimization Over Digraphs |
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Chen, Xiaomeng | Hong Kong University of Science and Technology |
Jiang, Wei | Aalto University, Finland |
Charalambous, Themistoklis | University of Cyprus |
Shi, Ling | Hong Kong University of Science and Technology |
Keywords: Optimization, Decentralized control, Optimization algorithms
Abstract: This paper addresses the problem of distributed optimization, where a network of agents represented as a directed graph (digraph) aims to collaboratively minimize the sum of their individual cost functions. Existing approaches for distributed optimization over digraphs, such as Push-Pull, require agents to exchange explicit state values with their neighbors in order to reach an optimal solution. However, this can result in the disclosure of sensitive and private information. To overcome this issue, we propose a state-decomposition-based privacy-preserving finite-time push-sum (PrFTPS) algorithm without any global information, such as network size or graph diameter. Then, based on PrFTPS, we design a gradient descent algorithm (PrFTPS-GD) to solve the distributed optimization problem. It is proved that under PrFTPS-GD, the privacy of each agent is preserved and the linear convergence rate related to the optimization iteration number is achieved. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed approach.
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WeC05 |
Simpor Junior 4912 |
Control with Learning for Autonomous Robots |
Invited Session |
Chair: Zhao, Lin | National University of Singapore |
Co-Chair: Wang, Chen | State University of New York at Buffalo |
Organizer: Zhao, Lin | National University of Singapore |
Organizer: Wang, Chen | State University of New York at Buffalo |
Organizer: Shi, Guanya | Carnegie Mellon University |
Organizer: Liu, Changliu | Carnegie Mellon University |
Organizer: Mou, Shaoshuai | Purdue University |
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16:00-16:20, Paper WeC05.1 | |
>Learning for Online Mixed-Integer Model Predictive Control with Parametric Optimality Certificates |
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Nair, Siddharth | University of California, Berkeley |
Russo, Luigi | Università Del Sannio |
Glielmo, Luigi | University of Napoli Federico II |
Borrelli, Francesco | Unversity of California at Berkeley |
Keywords: Constrained control, Machine learning, Autonomous systems
Abstract: We propose a supervised learning framework for computing solutions of multi-parametric Mixed Integer Linear Programs (MILPs) that arise in Model Predictive Control. Our approach also quantifies sub-optimality for the computed solutions. Inspired by Branch-and-Bound techniques, the key idea is to train a Neural Network/Random Forest, which for a given parameter, predicts a strategy consisting of (1) a set of Linear Programs (LPs) such that their feasible sets form a partition of the feasible set of the MILP and (2) a candidate integer solution. For control computation and sub-optimality quantification, we solve a set of LPs online in parallel. We demonstrate our approach for a motion planning example and compare it against various commercial and open-source mixed-integer programming solvers.
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16:20-16:40, Paper WeC05.2 | |
>Nonlinear MPC for Quadrotors in Close-Proximity Flight with Neural Network Downwash Prediction (I) |
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Li, Jinjie | Beihang University |
Han, Liang | Beihang University |
Yu, Haoyang | Beihang University |
Lin, Yuheng | Beihang University |
Li, Qingdong | Beihang University |
Ren, Zhang | Beijing University of Aeronautics and Astronautics |
Keywords: Data driven control, Predictive control for nonlinear systems, Flight control
Abstract: Swarm aerial robots are required to maintain close proximity to successfully traverse narrow areas in cluttered environments. However, this movement is affected by the downwash effect generated by the other quadrotors in the swarm. This aerodynamic effect is highly nonlinear and hard to model by classic mathematical methods. In addition, the motor speeds of quadrotors are risky to reach the limit when resisting the effect. To solve these problems, we integrate a Neural network Downwash Predictor with Nonlinear Model Predictive Control (NDP-NMPC) to propose a trajectory-tracking approach. The network is trained with spectral normalization to ensure robustness and safety on uncollected cases. The predicted disturbances are then incorporated into the optimization scheme in NMPC, which handles constraints to ensure that the motor speed remains within safe limits. We also design a quadrotor system, identify its parameters, and implement the proposed method onboard. Finally, we conduct an open-loop prediction experiment to verify the safety and effectiveness of the network, and a real-time closed-loop trajectory tracking experiment which demonstrates a 75.37% reduction of tracking error in height under the downwash effect.
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16:40-17:00, Paper WeC05.3 | |
>Optimal Scheduling for Remote Estimation with an Auxiliary Transmission Scheme (I) |
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Li, Zitian | Guangdong University of Technology |
Yang, Lixin | Queensland University of Technology |
Jia, Yijin | Guangdong University of Technology |
Huang, Zenghong | Guangdong University of Technology |
Lv, Weijun | Guangdong University of Technology |
Xu, Yong | Guangdong University of Technology |
Keywords: Networked control systems, Kalman filtering, Learning
Abstract: The remote estimation for multiple systems is considered in this paper. Some smart sensors observe the systems and run Kalman filters to compute their state estimates, which are then transmitted to a remote estimator via high frequency wave band. The path loss and signal attenuation make communication at high frequency unreliable. To improve estimation performance, an auxiliary transmission scheme is proposed, where a complementary channel with low frequency wave band is deployed to transmit a duplication of a local state estimate. Since the auxiliary channel consumes extra energy and occupies limited bandwidth, the optimal scheduling needs to be studied, i.e., to determine whether or which sensor to use the auxiliary channel. To tackle this issue, we establish a Markov decision process (MDP) to formulate the optimal scheduling, and prove that the optimal policy is deterministic and stationary. Furthermore, the threshold structure is verified for the optimal policy. The deep reinforcement learning is introduced to approximate an optimal policy. Finally, the threshold structure and the deep reinforcement learning is validated by a numerical example.
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17:00-17:20, Paper WeC05.4 | |
>Deriving Rewards for Reinforcement Learning from Symbolic Behaviour Descriptions of Bipedal Walking (I) |
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Harnack, Daniel | German Research Center for Artificial Intelligence (DFKI) |
Lüth, Christoph | Deutsches Forschungszentrum Für Künstliche Intelligenz (DFKI) |
Gross, Lukas | DFKI |
Kumar, Shivesh | German Research Center for Artificial Intelligence (DFKI GmbH) |
Kirchner, Frank | Robotics Innovation Center, DFKI and Department of Mathematics |
Keywords: Robotics, Learning, Hybrid systems
Abstract: Generating physical movement behaviours from their symbolic description is a long-standing challenge in artificial intelligence (AI) and robotics, requiring insights into numerical optimization methods as well as into formalizations from symbolic AI and reasoning. In this paper, a novel approach to finding a reward function from a symbolic description is proposed. The intended system behaviour is modelled as a hybrid automaton, which reduces the system state space to allow more efficient reinforcement learning. The approach is applied to bipedal walking, by modelling the walking robot as a hybrid automaton over state space orthants, and used with the compass walker to derive a reward that incentivizes following the hybrid automaton cycle. As a result, training times of reinforcement learning controllers are reduced while final walking speed is increased. The approach can serve as a blueprint how to generate reward functions from symbolic AI and reasoning.
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17:20-17:40, Paper WeC05.5 | |
>Optimizing Field-Of-View for Multi-Agent Path Finding Via Reinforcement Learning: A Performance and Communication Overhead Study |
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Cheng, Hoi Chuen | The Hong Kong University of Science and Technology |
Shi, Ling | Hong Kong University of Science and Technology |
Yue, Chik Patrick | The Hong Kong University of Science and Technology |
Keywords: Agents-based systems, Machine learning, Autonomous robots
Abstract: This work investigates the impact of Field-of-View (FOV) on the performance of Reinforcement Learning (RL) models in Multi-Agent Path Finding (MAPF) problems. The study measures the effects of different FOV settings on RL performance, communication overhead, and computation time. Results show that the tested smallest FOV (3 x 3) reduces communication frequency by 28.9% with only a 1.65% reduction in success rate compared to the baseline (9 x 9). The study also compares computation time for different FOV for efficiency analysis and provides insights into FOV selection considering computation cost.
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17:40-18:00, Paper WeC05.6 | |
>Learning Koopman Operators with Control Using Bi-Level Optimization (I) |
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Huang, Daning | Pennsylvania State University |
Prasetyo, Muhammad Bayu | The Pennsylvania State University |
Yu, Yin | Penn State University |
Geng, Junyi | Pennsylvania State University |
Keywords: Machine learning, Data driven control, Nonlinear systems identification
Abstract: The accurate modeling and control of nonlinear dynamical effects are crucial for numerous robotic systems. The Koopman formalism emerges as a valuable tool for linear control design in nonlinear systems within unknown environments. However, it still remains a challenging task to learn the Koopman operator with control from data, and in particular, the simultaneous identification of the Koopman linear dynamics and the mapping between the physical and Koopman states. Conventionally, the simultaneous learning of the dynamics and mapping is achieved via single-level optimization based on one-step or multi-step discrete-time predictions, but the learned model may lack model robustness, training efficiency, and/or long-term predictive accuracy. This paper presents a bi-level optimization framework that jointly learns the Koopman embedding mapping and Koopman dynamics with exact long-term dynamical constraints. Our formulation allows back-propagation in standard learning framework and the use of state-of-the-art optimizers, yielding more accurate and stable system prediction in long-time horizon over various applications compared to conventional methods.
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WeC06 |
Simpor Junior 4911 |
Estimation III |
Regular Session |
Chair: Pangborn, Herschel | The Pennsylvania State University |
Co-Chair: Shames, Iman | Australian National University |
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16:00-16:20, Paper WeC06.1 | |
>Parameter Estimation of Some Special Classes of Dynamical Nonlinear Systems with Non-Separable Nonlinear Parameterizations |
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Ortega, Romeo | ITAM |
Bobtsov, Alexey | ITMO University |
Costa-Castelló, Ramon | Universitat Politècnica De Catalunya (UPC) |
Nikolaev, Nikolay | ITMO University |
Pyrkin, Anton | ITMO University |
Keywords: Estimation, Nonlinear systems, Observers for nonlinear systems
Abstract: In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical applications, and none of the existing parameter estimators is able to deal with them in an efficient way. The proposed estimation procedure is illustrated with two modern applications: fuel cells and human musculoskeletal dynamics. The procedure does not assume that the parameters live in known compact sets, that the nonlinearities satisfy some Lipschitzian properties, nor rely on injection of high-gain or the use of complex, computationally demanding methodologies. Instead, we propose to design a classical on-line estimator whose dynamics is described by an ordinary differential equation given in a compact precise form. A further contribution of the paper is the proof that parameter convergence is guaranteed with the extremely weak interval excitation requirement.
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16:20-16:40, Paper WeC06.2 | |
>A Koopman Operator-Based Finite Impulse Response Filter for Nonlinear Systems |
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Pan, ZhiChao | Jiangnan University |
Huang, Biao | Univ. of Alberta |
Liu, Fei | Jiangnan University |
Keywords: Estimation, Nonlinear systems, Optimization
Abstract: This paper proposes a novel Koopman operator-based finite impulse response (KFIR) filter for nonlinear dynamic systems. This filter is generalized from the minimum variance unbiased (MVU) FIR filter for linear systems by using a global linear approximation of the nonlinear dynamics obtained from Koopman operator theory and the extended dynamic mode decomposition (EDMD) algorithm. Based on the recursive linear model, a reduced-order FIR filtering structure is proposed, and the optimal gain is derived to minimize the trace of the estimation error covariance. Unlike traditional methods, the KFIR filter requires no prior knowledge of the initial state and fully utilizes the data of a moving horizon. Simulation results show that the proposed filter has excellent robustness against unexpected modeling uncertainties and inaccurate noise information, making it suitable for real applications.
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16:40-17:00, Paper WeC06.3 | |
>Bayesian Estimation for Linear Systems with Nonlinear Output and General Noise Distribution Using Fourier Basis Functions |
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van Zuijlen, Roy | Eindhoven University of Technology |
van Hulst, Jilles | Eindhoven University of Technology |
Heemels, W.P.M.H. | Eindhoven University of Technology |
Antunes, Duarte | Eindhoven University of Technology, the Netherlands |
Keywords: Estimation, Observers for nonlinear systems, Control applications
Abstract: Bayesian estimation can be used to estimate the state of dynamical systems, but its applicability is hampered due to the curse of dimensionality. This paper aims to mitigate this bottleneck for a relevant class of systems consisting of a linear plant with bounded input, driven by stochastic disturbances with non-linear noisy output; the distributions of the disturbances and noise have a bounded support but are otherwise general. Using a frequency-domain interpretation of the operations of the Bayes' filter, we show that, under mild assumptions, exact Bayesian estimation can be pursued in a countable space of Fourier series coefficients, rather than in the usual functional space of probability densities. This fact leads to a natural approximate method, where the Fourier series coefficients corresponding to high frequencies are discarded. For this approximate method, the complexity of the conditioned state distribution, measured by the number of Fourier coefficients, remains constant at prediction steps and grows only linearly at each update step. The applicability of the results is illustrated in the context of electron microscopy, where a residual error analysis indicates that the approximation is accurate.
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17:00-17:20, Paper WeC06.4 | |
>Set-Valued State Estimation for Nonlinear Systems Using Hybrid Zonotopes |
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Siefert, Jacob | Pennsylvania State University |
Thompson, Andrew | The Pennsylvania State University |
Glunt, Jonah | The Pennsylvania State University |
Pangborn, Herschel | The Pennsylvania State University |
Keywords: Estimation, Observers for nonlinear systems
Abstract: This paper proposes a method for set-valued state estimation of nonlinear, discrete-time systems. This is achieved by combining graphs of functions representing system dynamics and measurements with the hybrid zonotope set representation that can efficiently represent nonconvex and disjoint sets. Tight over-approximations of complex nonlinear functions are efficiently produced by leveraging special ordered sets and neural networks, which enable computation of set-valued state estimates that grow linearly in memory complexity with time. A numerical example demonstrates significant reduction of conservatism in the set-valued state estimates using the proposed method as compared to an idealized convex approach.
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17:20-17:40, Paper WeC06.5 | |
>Distributed Block Coordinate Moving Horizon Estimation for 2D Visual-Inertial-Odometry SLAM |
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Flayac, Emilien | ISAE Supaero |
Shames, Iman | Australian National University |
Keywords: Estimation, Robotics, Optimization algorithms
Abstract: This paper presents a Visual Inertial Odometry Landmark-based Simultaneous Localisation and Mapping algorithm based on a distributed block coordinate nonlinear Moving Horizon Estimation scheme. The main advantage of the proposed method is that the updates on the position of the landmarks are based on a Bundle Adjustment technique that can be parallelised over the landmarks. The performance of the method are demonstrated in simulations in different environments and with different types of robot trajectory. Circular and wiggling patterns in the trajectory lead to better estimation performance than straight ones, confirming what is expected from recent nonlinear observability theory.
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17:40-18:00, Paper WeC06.6 | |
>Sub-Optimal Moving Horizon Estimation in Feedback Control of Linear Constrained Systems |
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Yang, Yujia | University of Melbourne |
Manzie, Chris | The University of Melbourne |
Pu, Ye | The University of Melbourne |
Keywords: Estimation, Stability of linear systems, Optimization
Abstract: Moving horizon estimation (MHE) offers benefits relative to other estimation approaches by its ability to explicitly handle constraints, but suffers increased computation cost. To help enable MHE on platforms with limited computation power, we propose to solve the optimization problem underlying MHE sub-optimally for a fixed number of optimization iterations per time step. The stability of the closed-loop system is analyzed using the small-gain theorem by considering the closed-loop controlled system, the optimization algorithm dynamics, and the estimation error dynamics as three interconnected subsystems. By assuming incremental input/output-to-state stability (delta-IOSS) of the system and imposing standard ISS conditions on the controller, we derive conditions on the iteration number such that the interconnected system is input-to-state stable (ISS) w.r.t. the external disturbances. A simulation using an MHE-MPC estimator-controller pair is used to validate the results.
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WeC07 |
Simpor Junior 4813 |
Game Theory III |
Regular Session |
Chair: Jaleel, Hassan | Lahore University of Management Sciences |
Co-Chair: Stella, Leonardo | University of Birmingham |
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16:00-16:20, Paper WeC07.1 | |
>Consistent Conjectural Variations Equilibria: Characterization & Stability for a Class of Continuous Games |
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Calderone, Daniel J. | University of Washington |
Chasnov, Benjamin J. | University of Washington |
Burden, Samuel A. | University of Washington |
Ratliff, Lillian J. | University of Washington |
Keywords: Game theory, Linear systems, Optimization
Abstract: Leveraging tools from the study of linear fractional transformations and algebraic Riccati equations, a local characterization of consistent conjectural variations equilibrium is given for two player games on continuous action spaces with costs approximated by quadratic functions. A discrete time dynamical system in the space of conjectures is derived; a solution method for computing fixed points of these dynamics (equilibria) is given via solving an eigenvalue problem; local stability properties of the dynamics around the equilibria are characterized; and conditions are given that guarantee a unique stable equilibrium.
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16:20-16:40, Paper WeC07.2 | |
>A Multi-Agent Reinforcement Learning Approach to Promote Cooperation in Evolutionary Games on Networks with Environmental Feedback |
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Zhang, Tuo | University of Birmingham |
Gupta, Harsh | Indian Institute of Technology Kharagpur |
Suprabhat, Kumar | Indian Institute of Technology Kharagpur |
Stella, Leonardo | University of Birmingham |
Keywords: Game theory, Machine learning, Stability of nonlinear systems
Abstract: A prominent feature of biological organization in many species of social animals is the ability to achieve cooperation. However, despite its predominance in natural evolution, cooperative behaviors come at a cost, typically in the form of do ut des mechanisms (e.g., reciprocal altruism in vampire bats) with given thresholds for sharing resources or communication efforts. In this paper, we investigate the conditions of cooperation through the evolutionary dynamics of the prisoner's dilemma (PD) game as well as the learning dynamics resulting from the corresponding multi-agent reinforcement learning (MARL) model. In both cases, the interactions in the population are captured by a regular network and the impact of the players' actions is reflected through the evolution of an environmental resource, which also acts as a feedback on the dynamics. The following is a list of contributions: i) we provide a full characterization of the stability properties of the networked feedback-evolving PD game; ii) we determine a set of threshold values below which cooperation is promoted; iii) we develop the corresponding cross-learning model, which is a stateless MARL model, and we show that this model is equivalent to the networked PD game with environmental feedback.
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16:40-17:00, Paper WeC07.3 | |
>Soft-Bellman Equilibrium in Affine Markov Games: Forward Solutions and Inverse Learning |
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Chen, Shenghui | University of Texas at Austin |
Yu, Yue | The University of Texas at Austin |
Fridovich-Keil, David | The University of Texas at Austin |
Topcu, Ufuk | The University of Texas at Austin |
Keywords: Game theory, Markov processes, Optimization
Abstract: Markov games model interactions among multiple players in a stochastic, dynamic environment. Each player in a Markov game maximizes its expected total discounted reward, which depends upon the policies of the other players. We formulate a class of Markov games, termed affine Markov games, where an affine reward function couples the players' actions. We introduce a novel solution concept, the soft-Bellman equilibrium, where each player is boundedly rational and chooses a soft-Bellman policy rather than a purely rational policy as in the well-known Nash equilibrium concept. We provide conditions for the existence and uniqueness of the soft-Bellman equilibrium and propose a nonlinear least-squares algorithm to compute such an equilibrium in the forward problem. We then solve the inverse game problem of inferring the players’ reward parameters from observed state-action trajectories via a projected-gradient algorithm. Experiments in a predator-prey OpenAI Gym environment show that the reward parameters inferred by the proposed algorithm outperform those inferred by a baseline algorithm: they reduce the Kullback-Leibler divergence between the equilibrium policies and observed policies by at least two orders of magnitude.
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17:00-17:20, Paper WeC07.4 | |
>Robustness of Log-Linear Learning in Network Coordination Games with Stubborn Players |
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Akber, Aqsa Shehzadi | Lahore University of Management Sciences |
Jaleel, Hassan | Lahore University of Management Sciences |
Keywords: Game theory, Markov processes, Randomized algorithms
Abstract: We analyze Log-Linear Learning (LLL) in a networked multi-agent system with stubborn agents who can influence other players but do not update their actions. We are interested in the robustness of LLL against stubborn players in a coordination game setup in which the players have to decide between a status quo and an innovative practice that is inherently superior to the status quo. We investigate the impact of interaction network topology and the payoff gain offered by the innovation on the steady state behavior of the population in the presence of stubborn agent/s. We present conditions for the robustness of various networks, namely a class of 3-regular networks, n×n grid networks, and Erd˝os-R´enyi (ER) random networks. For these networks, we derive the threshold values of the payoff gain for which the system behavior is robust to the presence of stubborn players under LLL. Although the results in this work are for network coordination games, our framework can be generalized to a wider class of normal-form games in the presence of multiple heterogeneous players.
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17:20-17:40, Paper WeC07.5 | |
>Cooperation and Competition: A Sequential Game Model of Flocking |
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Wang, Chenlan | University of Michigan, Ann Arbor |
DuBay, Shane | University of Texas at Arlington |
Liu, Mingyan | University of Michigan |
Keywords: Game theory, Modeling
Abstract: We study a sequential game model on how groups form in time. In particular, agents make asynchronous decisions on a time of arrival; those choosing the same arrival time are considered to travel together or belong to the same flock. Flocking reduces travel costs but arriving early allows one to obtain a higher reward. Our model is primarily motivated by commonly observed flocking behavior among migratory birds, but it can also be applied to other areas of competition and cooperation, e.g., in the case of rideshare to a common destination with a limited supply of goods. Given the model's sequential nature, the solution concept we study is the subgame perfect equilibrium (SPE). We present in detail the nature of the SPE in a 2-agent and 3-agent game, respectively, and its properties in the more general n-agent game. Of particular interest are observations on when and what types of groups emerge in an SPE.
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17:40-18:00, Paper WeC07.6 | |
>Beyond the ‘Enemy-Of-My-Enemy’ Alliances: Coalitions in Networked Contest Games |
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Diaz-Garcia, Gilberto | University of California, Santa Barbara |
Bullo, Francesco | Univ of California at Santa Barbara |
Marden, Jason R. | University of California, Santa Barbara |
Keywords: Game theory, Network analysis and control, Cyber-Physical Security
Abstract: Competitive resource allocation describes scenarios where multiple agents compete by spending their limited resources. For these settings, contest games offer a game-theoretic framework to analyze how players can efficiently invest their assets. Moreover, for this family of games, the resulting behavior can be modified through external interactions among the players. For instance, players could be able to make coalitions that allow budgetary transfers among them, trying to improve their outcomes. In this work, we study budgetary transfers in contest games played over networks. In particular, we aim to characterize the networks and players that guarantee that a transfer is beneficial for all players in the coalition. For this, we provide conditions for the existence of beneficial transfers. In addition, we provide a construction that guarantees that the benefit of making coalitions is independent of the graph structure and the chosen player to make an alliance.
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WeC08 |
Simpor Junior 4812 |
Optimal Control III |
Regular Session |
Chair: Wang, Fu-Cheng | National Taiwan University |
Co-Chair: Oguri, Kenshiro | Purdue University |
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16:00-16:20, Paper WeC08.1 | |
>Multiple Output Responses Decoupling: With Application to Vibration Suppression of Optical Tables |
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Lee, Chung-Hsien | National Taiwan University |
Wang, Fu-Cheng | National Taiwan University |
Keywords: Optimal control, Linear systems, Control applications
Abstract: This paper proposes a novel control theorem called multiple output response decoupling (MORD) and applies it to optical-table vibration control. Optical tables need to isolate environmental vibrations by limited suspension travels. Soft suspensions can significantly isolate ground disturbances but need large strut displacements, while stiff suspensions can reduce suspension displacements but allow significant table vibrations. Passive suspensions are usually trade-offs between these conflicting requirements. Though active suspensions could relieve the compromises, the coupling system dynamics might cause difficulties in control designs. Therefore, this paper proposes the MORD theorem, which allows simultaneous performance improvement by independent control design. First, we review the disturbance response decoupling (DRD) theorem and simplify it as the output response decoupling (ORD) lemma. We then develop the MORD theorem, which can integrate independent ORD control designs without affecting each other. Finally, we apply the MORD theorem to the optical table systems. We design optimal controllers to suppress ground disturbances and other optimal controllers to minimize strut travels. We then integrate these controllers to achieve optimal performance simultaneously as the individual designs with the MORD control design.
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16:20-16:40, Paper WeC08.2 | |
>Linear Programming Approach to Relative-Orbit Control with Element-Wise Quantized Thrust |
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Echigo, Kazuya | University of Washington |
Hayner, Christopher | University of Washington |
Mittal, Avi | University of Washington |
Sarsilmaz, Selahattin Burak | Utah State University |
Harris, Matthew W. | Utah State University |
Acikmese, Behcet | University of Washington |
Keywords: Optimal control, Linear systems, Control applications
Abstract: This paper considers the problem of close-proximity relative-orbit control of spacecraft with thrust quantization constraints, models the problem as a mixed-integer program, and reformulates the problem as a linear program. The reformulation uses linearized relative orbital element dynamics with a sum-of-absolute-values objective, and it is proved that optimal controls for the reformulated problem satisfy the quantization constraint, that is, the quantization constraints are convexified for the reformulated continuous-time optimal control problem. This problem is then discretized, converted to a finite-dimensional linear program, and solved using commercially available convex optimization solvers with polynomial time convergence guarantees. Since the mathematical proofs of convexification are available only for continuous-time case, their validity for discrete-time is demonstrated with extensive simulations. To this end, Monte Carlo simulations indicate that quantization is achieved with high probability while keeping spacecraft slew rates low relative to other proposed approaches.
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16:40-17:00, Paper WeC08.3 | |
>Imitation and Transfer Learning for LQG Control |
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Guo, Taosha | University of California, Riverside |
Al Makdah, Abed AlRahman | University of California Riverside |
Krishnan, Vishaal | University of California, Riverside |
Pasqualetti, Fabio | University of California, Riverside |
Keywords: Optimal control, Linear systems, Machine learning
Abstract: In this paper we study an imitation and transfer learning setting for Linear Quadratic Gaussian (LQG) control, where (i) the system dynamics, noise statistics and cost function are unknown and expert data is provided (that is, sequences of optimal inputs and outputs) to learn the LQG controller, and (ii) multiple control tasks are performed for the same system but with different LQG costs. We show that the LQG controller can be learned from a set of expert trajectories of length n(l+2)-1, with n and l the dimension of the system state and output, respectively. Further, the controller can be decomposed as the product of an estimation matrix, which depends only on the system dynamics, and a control matrix, which depends on the LQG cost. This data-based separation principle allows us to transfer the estimation matrix across different LQG tasks, and to reduce the length of the expert trajectories needed to learn the LQG controller to~2n+m-1 with m the dimension of the inputs (for single-input systems with l=2, this yields approximately a 50% reduction of the required expert data).
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17:00-17:20, Paper WeC08.4 | |
>Optimizing Pre-Scheduled, Intermittently-Observed MDPs |
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Zhong, Patrick | Texas A&M University |
Rossi, Federico | Jet Propulsion Laboratory - California Institute of Technology |
Shell, Dylan | Texas A&M University |
Keywords: Optimal control, Markov processes, Autonomous robots
Abstract: A challenging category of robotics problems arises when sensing incurs substantial costs. This paper examines settings in which a robot wishes to limit its observations of state, for instance, motivated by specific considerations of energy management, stealth, or implicit coordination. We formulate the problem of planning under uncertainty when the robot’s observations are intermittent but their timing is known via a pre-declared schedule. After having established the appropriate notion of an optimal policy for such settings, we tackle the problem of joint optimization of the cumulative execution cost and the number of state observations, both in expectation under discounts. To approach this multi-objective optimization problem, we introduce an algorithm that can identify the Pareto front for a class of schedules that are advantageous in the discounted setting. The algorithm proceeds in an accumulative fashion, prepending additions to a working set of schedules and then computing incremental changes to the value functions. Because full exhaustive construction becomes computationally prohibitive for moderate-sized problems, we propose a filtering approach to prune the working set. Empirical results demonstrate that this filtering is effective at reducing computation while incurring only negligible reduction in quality. In summarizing our findings, we provide a characterization of the run-time vs quality trade-off involved.
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17:20-17:40, Paper WeC08.5 | |
>Geometry Enhanced Finite Time Near Optimal Control Strategy for Acrobatic Flip Motion of Quadcopter Unmanned Aerial Vehicles |
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Yao, Jie | University of Minnesota, Twin Cities |
Zezhong, Zhang | Nanyang Technological University/ MAE |
Zhao, Gaonan | University of Minnesota |
Keywords: Optimal control, Nonlinear systems, Control applications
Abstract: A nonlinear optimal control strategy, named the geometry enhanced finite time θ−D technique, is proposed to manipulate the acrobatic flip flight of variable pitch (VP) quadcopter unmanned aerial vehicles (abbreviated as VP copter). A unique superiority of the VP copter, which can provide the thrust in both positive and negative vertical directions by varying the pitch angles of blades, facilitates the acrobatic flip motion. The finite time θ−D technique can offer a closed-form near-optimal state feedback control law with online computational efficiency as compared with the finite time state-dependent Riccati equation (SDRE) technique. Meanwhile, by virtue of the geometric technique, the singularity issue of the rotation matrix in the acrobatic flip maneuver can be avoided. The simulation experiments verify the proposed control strategy is effective and efficient.
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17:40-18:00, Paper WeC08.6 | |
>Adaptive Optimal Control of Nonlinear Systems with Multiple Time-Scale Eligibility Traces |
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Rao, Jun | Shanghai Jiao Tong University |
Wang, Jingcheng | Shanghai Jiao Tong University |
Xu, Jiahui | Shanghai Jiao Tong University |
Wu, Shunyu | Shanghai Jiaotong University |
Keywords: Optimal control, Nonlinear systems, Iterative learning control
Abstract: Adaptive dynamic programming (ADP) is one of the main methods to solve the optimal control problem of nonlinear systems. Eligibility traces are utilized in recent years to reduce the computing burden of the value function, but the existing fixed eligibility trace is difficult to ensure stable convergence especially when facing environmental changes and complex neural network structures. To solve the above issues, a novel off-policy algorithm, T-HDP(lambda) with Multiple Time-scale Eligibility Traces (MET), is proposed. By utilizing MET, the new algorithm can adaptively accumulate gradients and include more gradient information, which guides the control faster in the optimal direction. T-step Truncated lambda-returns are utilized to solve the infinite-horizon optimal control problems, and a new importance sampling ratio is designed to correct the value function. Furthermore, the convergence and boundedness of the algorithm are proved. Based on the actor-critic network architecture, the optimal value function and policy are well approximated. Finally, compared with the original algorithm by a simulation example, the proposed algorithm has a faster convergence speed and lower variance.
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WeC09 |
Simpor Junior 4811 |
Optimization Algorithms III |
Regular Session |
Chair: Ornik, Melkior | University of Illinois Urbana-Champaign |
Co-Chair: Axehill, Daniel | Linköping University |
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16:00-16:20, Paper WeC09.1 | |
>Welfare Maximization Algorithm for Solving Budget-Constrained Multi-Component POMDPs |
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Vora, Manav Ketan | University of Illinois Urbana Champaign |
Thangeda, Pranay | University of Illinois Urbana-Champaign |
Grussing, Michael N. | US Army Corps of Engineers |
Ornik, Melkior | University of Illinois Urbana-Champaign |
Keywords: Optimization algorithms, Markov processes, Distributed control
Abstract: Partially Observable Markov Decision Processes (POMDPs) provide an efficient way to model real-world sequential decision making processes. Motivated by the problem of maintenance and inspection of a group of infrastructure components with independent dynamics, this paper presents an algorithm to find the optimal policy for a multi-component budget-constrained POMDP. We first introduce a budgeted-POMDP model (textit{b-POMDP}) which enables us to find the optimal policy for a POMDP while adhering to budget constraints. Next, we prove that the value function or maximal collected reward for a b-POMDP is a concave function of the budget for the finite horizon case. Our second contribution is an algorithm to calculate the optimal policy for a multi-component budget-constrained POMDP by finding the optimal budget split among the individual component POMDPs. The optimal budget split is posed as a welfare maximization problem and the solution is computed by exploiting the concavity of the value function. We illustrate the effectiveness of the proposed algorithm by proposing a maintenance and inspection policy for a group of real-world infrastructure components with different deterioration dynamics, inspection and maintenance costs. We show that the proposed algorithm vastly outperforms the policies currently used in practice.
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16:20-16:40, Paper WeC09.2 | |
>A Quantization Procedure for Nonlinear Pricing with an Application to Electricity Markets |
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Jacquet, Quentin | EDF R&D, INRIA, CMAP, Ecole Polytechnique |
van Ackooij, Wim Stefanus | EDF R&D |
Alasseur, Clemence | EDF R&D |
Gaubert, Stephane | INRIA and Ecole Polytechnique |
Keywords: Optimization algorithms, Mean field games, Finance
Abstract: We consider a revenue maximization model, in which a company aims at designing a menu of contracts, given a population of customers. A standard approach consists in constructing an incentive-compatible continuum of contracts, i.e., a menu composed of an infinite number of contracts, where each contract is especially adapted to an infinitesimal customer, taking his type into account. Nonetheless, in many applications, the company is constrained to offering a limited number of contracts. We show that this question reduces to an optimal quantization problem, similar to McEneaney's pruning problem that appeared in the max-plus based numerical methods in optimal control. We develop a new quantization algorithm, which, given an initial menu of contracts, iteratively prunes the less important contracts, to construct an implementable menu of the desired cardinality, while minimizing the revenue loss. We apply this algorithm to solve a pricing problem with price-elastic demand, originating from the electricity retail market. Numerical results show an improved performance by comparison with earlier pruning algorithms.
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16:40-17:00, Paper WeC09.3 | |
>Distributed Online Learning Algorithms for Aggregative Games Over Time-Varying Unbalanced Digraphs |
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Zuo, Xiaolong | Central South University |
Deng, Zhenhua | Central South University |
Keywords: Optimization algorithms, Network analysis and control, Time-varying systems
Abstract: In this paper, online aggregative games over time-varying unbalanced digraphs are studied, where the cost functions of players are time-varying and are gradually revealed to corresponding players only after decisions are made. Moreover, in the problems, players are subject to local convex set constraints and time-varying coupled nonlinear inequality constraints. To the best of our knowledge, no result about online games with unbalanced digraphs has been reported, let alone constrained online games. To solve the problem, a distributed online algorithm based on primal-dual, mirror descents and push-sum methods is developed. With the algorithm, sublinear dynamic regrets and constraint violations are established.
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17:00-17:20, Paper WeC09.4 | |
>Meta-Learning Parameterized First-Order Optimizers Using Differentiable Convex Optimization |
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Gautam, Tanmay | University of California, Berkeley |
Pfrommer, Samuel | University of California, Berkeley |
Sojoudi, Somayeh | UC Berkeley |
Keywords: Optimization algorithms, Neural networks, Machine learning
Abstract: Conventional optimization methods in machine learning and controls rely heavily on first-order update rules. Selecting the right method and hyperparameters for a particular task often involves trial-and-error or practitioner intuition, motivating the field of meta-learning. We generalize a broad family of preexisting update rules by proposing a meta-learning framework in which the inner loop optimization step involves solving a differentiable convex optimization (DCO). We illustrate the theoretical appeal of this approach by showing that it enables one-step optimization of a family of linear least squares problems, given that the meta-learner has sufficient exposure to similar tasks. Various instantiations of the DCO update rule are compared to conventional optimizers on a range of illustrative experimental settings.
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17:20-17:40, Paper WeC09.5 | |
>Exact Complexity Certification of Start Heuristics in Branch-And-Bound Methods for Mixed-Integer Linear Programming |
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Shoja, Shamisa | Linköping University |
Axehill, Daniel | Linköping University |
Keywords: Optimization algorithms, Optimal control, Hybrid systems
Abstract: Model predictive control (MPC) with linear performance measure for hybrid systems requires the solution of a mixed-integer linear program (MILP) at each time instance. A well-known method to solve MILP problems is branch-and-bound (B&B). To enhance the performance of B&B, start heuristic methods are often used, where they have shown to be useful supplementary tools to find good feasible solutions early in the B&B search tree, hence, reducing the overall effort in B&B to find optimal solutions. In this work, we extend the recently-presented complexity certification framework for B&B-based MILP solvers to also certify computational complexity of the start heuristics that are integrated into B&B. Therefore, the exact worst-case computational complexity of the three considered start heuristics and, consequently, the B&B method when applying each one can be determined offline, which is of significant importance for real-time applications of hybrid MPC. The proposed algorithms are validated by comparing against the corresponding online heuristic-based MILP solvers in numerical experiments.
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17:40-18:00, Paper WeC09.6 | |
>Time-Varying Optimization with Optimal Parametric Functions |
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Amidzadeh, Mohsen | Aalto University |
Keywords: Optimization algorithms, Optimal control, Optimization
Abstract: In this paper, we consider a class of nonlinear constrained optimization problems. We formulate this problem as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal solution. We then re-parameterize the dynamical system to express it as a linear combination of the parametric functions. Calculus of variations is applied to optimize the parametric functions, such that the optimality distance of the solution is minimized. Accordingly, an iterative dynamic algorithm is devised to find the solution with an efficient convergence rate. We benchmark the performance of the proposed algorithm with the prediction-correction method from the optimality and computational complexity point-of-views.
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WeC10 |
Roselle Junior 4713 |
Machine Learning III |
Regular Session |
Chair: Sojoudi, Somayeh | UC Berkeley |
Co-Chair: Das, Amritam | Eindhoven University of Technology |
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16:00-16:20, Paper WeC10.1 | |
>On Improved Commutation for Moving-Magnet Planar Actuators |
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Broens, Yorick | Eindhoven University of Technology |
Butler, Hans | ASML |
Tóth, Roland | Eindhoven University of Technology |
Keywords: Machine learning, Mechatronics, Control applications
Abstract: The demand for high-precision and high-throughput motion control systems has increased significantly in recent years. The use of moving-magnet planar actuators (MMPAs) is gaining popularity due to their advantageous characteristics, such as complete environmental decoupling and reduction of stage mass. Nonetheless, model-based commutation techniques for MMPAs are compromised by misalignment between the mover and coil array and mismatch between the ideal electromagnetic model and the physical system, often leading to decreased system performance. To address this issue, a novel improved commutation approach is proposed in this paper, which is applicable for general planar motor applications, by means of dynamic regulation of the position dependence of the ideal model-based commutation algorithm, which allows for attenuation of magnetic misalignment, manufacturing inaccuracies and other unmodelled phenomena. The effectiveness of the proposed approach is validated through experiments using a state-of-the-art moving-magnet planar actuator prototype.
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16:20-16:40, Paper WeC10.2 | |
>Initial State Interventions for Deconfounded Imitation Learning |
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Pfrommer, Samuel | University of California, Berkeley |
Bai, Yatong | University of California, Berkeley |
Lee, Hyunin | University of California, Berkeley |
Sojoudi, Somayeh | UC Berkeley |
Keywords: Machine learning, Neural networks, Data driven control
Abstract: Imitation learning suffers from causal confusion. This phenomenon occurs when learned policies attend to features that do not causally influence the expert actions but are instead spuriously correlated. Causally confused agents produce low open-loop supervised loss but poor closed-loop performance upon deployment. We consider the problem of masking observed confounders in a disentangled representation of the observation space. Our novel masking algorithm leverages the usual ability to intervene in the initial system state, avoiding any requirement involving expert querying, expert reward functions, or causal graph specification. Under certain assumptions, we theoretically prove that this algorithm is conservative in the sense that it does not incorrectly mask observations that causally influence the expert; furthermore, intervening on the initial state serves to strictly reduce excess conservatism. The masking algorithm is applied to behavior cloning for two illustrative control systems: CartPole and Reacher.
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16:40-17:00, Paper WeC10.3 | |
>Universal Approximation of Flows of Control Systems by Recurrent Neural Networks |
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Aguiar, Miguel | KTH Royal Institute of Technology |
Das, Amritam | Eindhoven University of Technology |
Johansson, Karl H. | KTH Royal Institute of Technology |
Keywords: Machine learning, Neural networks, Nonlinear systems
Abstract: We consider the problem of approximating flow functions of continuous-time dynamical systems with inputs. It is well-known that continuous-time recurrent neural networks are universal approximators of this type of system. In this paper, we prove that an architecture based on discrete-time recurrent neural networks universally approximates flows of continuous-time dynamical systems with inputs. The required assumptions are shown to hold for systems whose dynamics are well-behaved ordinary differential equations and with practically relevant classes of input signals. This enables the use of off-the-shelf solutions for learning such flow functions in continuous-time from sampled trajectory data.
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17:00-17:20, Paper WeC10.4 | |
>Backward Reachability Analysis of Neural Feedback Systems Using Hybrid Zonotopes |
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Zhang, Yuhao | University of Wisconsin-Madison |
Zhang, Hang | University of Wisconsin-Madison |
Xu, Xiangru | University of Wisconsin-Madison |
Keywords: Machine learning, Neural networks, Optimization algorithms
Abstract: The proliferation of neural networks in safety-critical applications necessitates the development of effective methods to ensure their safety. This letter presents a novel approach for computing the exact backward reachable sets of neural feedback systems based on hybrid zonotopes. It is shown that the input-output relationship imposed by a ReLU-activated neural network can be exactly described by a hybrid zonotope-represented graph set. Based on that, the one-step exact backward reachable set of a neural feedback system is computed as a hybrid zonotope in the closed form. In addition, a necessary and sufficient condition is formulated as a mixed-integer linear program to certify whether the trajectories of a neural feedback system can avoid unsafe regions in finite time. Numerical examples are provided to demonstrate the efficiency of the proposed approach.
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17:20-17:40, Paper WeC10.5 | |
>Computationally Efficient Reinforcement Learning: Targeted Exploration Leveraging Simple Rules |
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Di Natale, Loris | Empa / EPFL |
Svetozarevic, Bratislav | University of Zurich |
Heer, Philipp | Empa |
Jones, Colin N. | EPFL |
Keywords: Machine learning, Neural networks
Abstract: Model-free Reinforcement Learning (RL) generally suffers from poor sample complexity, mostly due to the need to exhaustively explore the state-action space to find well-performing policies. On the other hand, we postulate that expert knowledge of the system often allows us to design simple rules we expect good policies to follow at all times. In this work, we hence propose a simple yet effective modification of continuous actor-critic frameworks to incorporate such rules and avoid regions of the state-action space that are known to be suboptimal, thereby significantly accelerating the convergence of RL agents. Concretely, we saturate the actions chosen by the agent if they do not comply with our intuition and, critically, modify the gradient update step of the policy to ensure the learning process is not affected by the saturation step. On a room temperature control case study, it allows agents to converge to well-performing policies up to 6 − 7× faster than classical agents without computational overhead and while retaining good final performance.
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17:40-18:00, Paper WeC10.6 | |
>G-Learning: Equivariant Indirect Optimal Control with Generating Function |
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Lee, Taeyoung | George Washington University |
Keywords: Machine learning, Optimal control, Learning
Abstract: This paper presents a new formulation of data-driven, learning-based optimal control with the Hamilton-Jacobi theory. In contrast to the common practice of reinforcement learning for dynamical systems, where the control policy is parameterized by deep neural network and the control parameters are optimized directly, we propose to adopt the indirect optimal control where the necessary conditions for optimality are first constructed by Pontryagin's minimum principle. Then, the resulting two-point boundary value problem is solved by learning the generating function associated with the optimality conditions that are considered as a Hamiltonian system. Further, it is shown that the sampling efficiency can be improved when there exists an invariance in the dynamics. The foremost benefit is that this provides a set of optimal controls for varying boundary conditions, which cannot be systematically addressed in the policy gradient.
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WeC11 |
Roselle Junior 4712 |
Agent-Based Systems III |
Regular Session |
Chair: Maity, Dipankar | University of North Carolina at Charlotte |
Co-Chair: D'Alfonso, Luigi | Università Della Calabria |
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16:00-16:20, Paper WeC11.1 | |
>Tug of Peace: Distributed Learning for Quality of Service Guarantees |
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Chandak, Siddharth | Stanford University |
Bistritz, Ilai | Tel Aviv University |
Bambos, Nicholas | Stanford University |
Keywords: Agents-based systems, Game theory, Learning
Abstract: Consider N players, where the action of player n is a number in the interval [0,B_n] that is interpreted as its ``pull''. Each player has a reward function that depends on all actions. We define Tug-of-War (ToW) games where increasing the action of one player decreases the rewards of all others. Tug-of-War games can model networking scenarios such as transmission power control and activation in sensor networks. We propose Tug-of-Peace algorithm, a simple stochastic approximation, and prove that in Tug-of-War games, it converges to a equilibrium that satisfies a target feasible Quality of Service reward vector for the players. Moreover, with high probability it converges to the ``minimal pull'' equilibrium. Our algorithm uses infrequent 1-bit communication between the players, but we also propose a fully distributed modification that does not require any communication at all and achieves almost the same guarantees. We then simulate our algorithms in the power control and sensor activation scenarios.
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16:20-16:40, Paper WeC11.2 | |
>Optimal Intermittent Sensing for Pursuit-Evasion Games |
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Maity, Dipankar | University of North Carolina at Charlotte |
Keywords: Agents-based systems, Game theory, Sampled-data control
Abstract: We consider a class of pursuit-evasion differential games in which the evader has continuous access to the pursuer’s location, but not vice-versa. There is a remote sensor (e.g., a radar station) that can sense the evader’s location upon a request from the pursuer and communicate that sensed location to the pursuer. The pursuer has a budget on the total number of sensing requests. The outcome of the game is determined by the players’ sensing and motion strategies. We obtain the equilibrium sensing and motion strategies for the players. We quantify the degradation in the pursuer’s pay-off due to its sensing limitations.
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16:40-17:00, Paper WeC11.3 | |
>Data-Driven Dynamic Input Transfer for Learning Control in Multi-Agent Systems with Heterogeneous Unknown Dynamics |
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Lehmann, Dustin | TU Berlin |
Drebinger, Philipp | Technische Universität Berlin |
Seel, Thomas | Leibniz Universität Erlangen |
Raisch, Joerg | Technical University Berlin |
Keywords: Agents-based systems, Learning, Iterative learning control
Abstract: Learning input signals that make a dynamic system respond with a desired output is often data intensive and time consuming. It is therefore natural to ask whether, in a heterogeneous multi-agent scenario, an input signal learned by one agent can be suitably adapted and transferred to make the other agents respond with the same desired output, despite exhibiting different dynamics. In this paper, we propose a novel method to achieve this by employing a dynamic input transfer map. The method does not require any a-priori knowledge of the individual agents’ dynamics. Instead, a small amount of experimental data from the source and target systems are used to estimate the transfer map. We evaluate the proposed method and compare it to existing approaches using static input transfer maps by investigating two example scenarios: (i) a simulation scenario for muscle dynamics, (ii) an experimental setting with a group of two-wheeled inverted pendulum robots and a sim-to-real motion learning problem.
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17:00-17:20, Paper WeC11.4 | |
>MAPPG: Multi-Agent Phasic Policy Gradient |
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Zhang, Qi | Dalian University of Technology |
Zhang, Xuetao | Dalian University of Technology |
Liu, Yisha | Dalian Maritime University |
Zhang, Xuebo | Nankai University |
Zhuang, Yan | School of Control Science and Engineering |
Keywords: Agents-based systems, Learning, Neural networks
Abstract: We propose a Multi-Agent Phasic Policy Gradient (MAPPG) algorithm, which can assist agents to further alleviate the non-stationarity of the environment. Different from the existing methods, the auxiliary phase is introduced to train the local policy directly by using the environment state, which can be naturally integrated into other algorithms. Specifically, the hidden layer feature sharing is proposed, which ensures feature sharing between global value network and local policy network for the first time. Meanwhile, mirror descent is utilized to iteratively update the policy in the auxiliary stage, which makes the policy update more robust. Through a series of evaluations on multi-agent Particle and multi-agent Mujoco benchmark environments, the experimental results show that our method achieves higher reward than state-of-the-art benchmarks.
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17:20-17:40, Paper WeC11.5 | |
>Non-Stationary Policy Learning for Multi-Timescale Multi-Agent Reinforcement Learning |
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Emami, Patrick | National Renewable Energy Lab |
Zhang, Xiangyu | National Renewable Energy Laboratory |
Biagioni, David | National Renewable Energy Laboratory |
Zamzam, Ahmed S. | National Renewable Energy Laboratory |
Keywords: Agents-based systems, Neural networks, Machine learning
Abstract: In multi-timescale multi-agent reinforcement learning (MARL), agents interact across different timescales. In general, policies for time-dependent behaviors, such as those induced by multiple timescales, are non-stationary. Learning non-stationary policies is challenging and typically requires sophisticated or inefficient algorithms. Motivated by the prevalence of this control problem in real-world complex systems, we introduce a simple framework for learning non-stationary policies for multi-timescale MARL. Our approach uses available information about agent timescales to define and learn periodic multi-agent policies. In detail, we theoretically demonstrate that the effects of non-stationarity introduced by multiple timescales can be learned by a periodic multi-agent policy. To learn such policies, we propose a policy gradient algorithm that parameterizes the actor and critic with phase-functioned neural networks, which provide an inductive bias for periodicity. The framework's ability to effectively learn multi-timescale policies is validated on a gridworld and building energy management environment.
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17:40-18:00, Paper WeC11.6 | |
>On the Impact of Agents with Influenced Opinions in the Swarm Social Behavior |
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Fedele, Giuseppe | University of Calabria |
Bozzo, Enrico | Università Degli Studi Di Udine |
D'Alfonso, Luigi | Università Della Calabria |
Keywords: Agents-based systems, Network analysis and control, Cooperative control
Abstract: We consider a simplified version of the Taylor model, typically used in the collective dynamics of continuous exchange of opinions, to describe the properties of swarm formation in the presence of external sources of influence or prejudices affecting a number of agents in the network. Such external sources are responsible for the breakdown of the consensus equilibrium and directly influence certain other individuals in the network, which we denote as quasi-stubborn agents. These quasi-stubborn agents participate in consensus with other individuals, but are able to indirectly influence the opinions of the entire system. In particular, we show that the swarm in steady-state moves towards the convex hull of the opinions of the quasi-stubborn agents. This is an interesting result that allows a more accurate estimation of the final opinions in a social network. In the case of two prejudiced agents, an explicit expression of the stationary opinions is provided in terms of the Moore-Penrose inverse of the Laplacian of the graph. Numerical simulations are presented to illustrate the properties of the considered model.
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WeC12 |
Roselle Junior 4711 |
Cooperative Control III |
Regular Session |
Chair: Yu, Xiao | Xiamen University |
Co-Chair: Su, Rong | Nanyang Technological University |
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16:00-16:20, Paper WeC12.1 | |
>Distributed Adaptive Tracking Control of Pure-Feedback Multi-Agent Systems with Full State and Control Input Constraints |
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Chen, Gang | Chongqing University |
Zhou, Yaoyao | Chongqing University |
Keywords: Cooperative control, Distributed control, Adaptive control
Abstract: The distributed tracking control of multi-agent systems with the general pure-feedback agent dynamics, the full state constraints, and the control input constraints is investigated in this paper. Based on the one-to-one nonlinear mapping, the saturation function transformation, and the degree elevation techniques, the pure-feedback multi-agent system with full state constraints and control input constrains is firstly transformed into a novel one without constraints. Considering the unknown control sign and the unknown dynamic models, a distributed adaptive control law is proposed by leveraging the merits of Nussbaum function and neural networks. The rigorous Lyapunov stability analysis shows that the agent constraints are always satisfied, and the cooperative tracking errors can be made as small as possible by appropriately setting the control parameters. Finally, a numerical simulation is conducted to clarify the effectiveness of the proposed control strategy.
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16:20-16:40, Paper WeC12.2 | |
>Distributed Observer-Based Dynamic Event-Triggered Control of Multi-Agent Systems with Adjustable Inter-Event Time |
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Wang, Zeyuan | University of Paris-Saclay |
Chadli, M. | University of Paris-Saclay - UEVE |
Keywords: Cooperative control, Distributed control, Networked control systems
Abstract: This paper proposes a dynamic event-triggered control strategy for the leader-following multi-agent control under directed topology. A synthesis approach combining distributed controllers and observers design is developed under a dynamic sampling scheme, and only local information is required for each agent to implement the proposed method. The control protocol incorporates model-based estimation and clock-like auxiliary dynamic variables to prolong the inter-event time as long as possible. Sufficient conditions for leader-following consensus control are established by linear matrix inequalities, and an explicit inter-event time is given to enable flexible tuning. Due to the carefully selected Lyapunov function, the proposed method exhibits significant advantages over the dynamic event-triggered control methods described in the existing literature. Compared to the existing static event-triggered strategy, the proposed approach significantly reduces the utilization of communication resources while preserving asymptotic convergence to the state consensus. The validity and effectiveness of the proposed theoretical results are demonstrated by comparative simulations.
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16:40-17:00, Paper WeC12.3 | |
>Composite Nonlinear Feedback Control for Cooperative Output Regulation of Linear Multi-Agent Systems with Input Saturation |
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Wu, Xinfei | Xiamen University |
Lan, Weiyao | Xiamen University |
Guan, Jinting | Xiamen University |
Yu, Xiao | Xiamen University |
Keywords: Cooperative control, Distributed control, Output regulation
Abstract: This paper investigates the cooperative output regulation problem of multi-agent systems. Each agent is modeled as a general linear system with input saturation, and the network topology among agents is represented by a directed graph containing a directed spanning tree. A distributed dynamic control law based on composite nonlinear feedback (CNF) control technique is developed, which consists of a distributed dynamic compensator and a controller with a linear feedback law leading to small damping ratio and a nonlinear feedback law making the system to be highly damped as the tracking error decreases to reduce the overshoot. It is shown that the cooperative output regulation problem can be solved and the transient performance of the multi-agent systems can be improved by properly tuning the parameters of the nonlinear feedback. The effectiveness of the theoretical results is illustrated by a numerical example.
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17:00-17:20, Paper WeC12.4 | |
>Passivity-Based Attack Detection and Mitigation with Switching Adaptive Controller and Quadratic Storage Function |
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Purohit, Pushkal | Indian Institute of Technology Jodhpur |
Jain, Anoop | Indian Institute of Technology, Jodhpur, India |
Keywords: Cooperative control, Distributed control, Resilient Control Systems
Abstract: This paper studies the consensus problem in a networked multi-agent system subject to actuator attacks. The concept of passivity is leveraged for the detection of destabilizing attacks, which relies on satisfying the dissipation-inequality with the quadratic storage functions. On identification of an attack, the controller switches to the defense mode, where the attack signal is mitigated via an estimator based on available measurements. We show that the state error, incurred due to an attack, remains bounded with bounded attack signals, and the system achieves consensus once the attack is mitigated. Simulations are provided to illustrate the theoretical findings.
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17:20-17:40, Paper WeC12.5 | |
>Fully Distributed Adaptive Consensus of Multiple Manipulators with Elastic Joints under a Directed Graph |
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Meng, Xiangzheng | Harbin Institute of Technology |
Mei, Jie | Harbin Institute of Technology, Shenzhen |
Wu, Ai-Guo | Harbin Institute of University, Shenzhen |
Ma, Guangfu | Harbin Institute of Technology, Shenzhen |
Keywords: Cooperative control, Distributed control, Uncertain systems
Abstract: In this paper, the distributed leaderless consensus problem of multiple manipulators with elastic joints under a directed graph is investigated, which extends existing results on the coordination of multiple second-order Euler-Lagrange systems to fourth-order manipulators with elastic joints. We use the model reference adaptive consensus scheme to transform the consensus problem into two subproblems. A trajectory tracking algorithm is designed based on the command filter adaptive backstepping approach, and it is shown that the joint positions of the manipulators achieve ultimately bounded consensus. The proposed algorithm only requires the interaction of the relative joint position information.
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17:40-18:00, Paper WeC12.6 | |
>Preserving Data-Privacy Cooperative Control of Discrete-Time Multi-Agent Systems |
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Huang, Lingying | Nanyang Technological University |
Su, Rong | Nanyang Technological University |
Ma, Maode | Education |
Lu, Yun | Nanyang Technological University |
Wang, Bohui | Nanyang Technological University |
Hu, Zhijian | Nanyang Technological University |
Keywords: Cooperative control, Estimation
Abstract: With the rapid advancements of communication technology, distributed cooperative control has emerged as a promising approach, enabling participants to perform control based on their neighbouring agents, thereby facilitating a faster response and more flexibility. However, the privacy concerns must be addressed not only on the external adversaries but also on the internal adversaries, to encourage the participant to join this cooperative network. In contrast to existing literature, our study considers the scenario where participating agents are unaware of whether their neighbouring nodes inject noises, leading them to directly use the received data in control. We first design the noise injection scheme to ensure the mean-square consensus while preserving privacy in discrete-time multi-agent systems (MASs) and then derive the upper and lower bounds of the convergence rate. After that, we study the covariance matrix of the maximum likelihood estimate on the initial state of other agents based on the internal adversary’s local information. The feasibility of (ε, δ)-differential privacy is characterized. Simulations of a practical cooperative adaptive cruise control illustrate the effectiveness of the Privacy-Preserving Cooperative Control (PPCC).
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WeC16 |
Peony Junior 4512 |
Energy Systems II |
Regular Session |
Chair: Tomar, Nutan Kumar | Indian Institute of Technology Patna |
Co-Chair: Richter, Hanz | Cleveland State University |
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16:00-16:20, Paper WeC16.1 | |
>Thermodynamic H_infinity Control of Multidomain Power Networks |
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Richter, Hanz | Cleveland State University |
Keywords: Energy systems, Optimal control, Robust control
Abstract: The problem of achieving disturbance attenuation while maximizing energy efficiency in multidomain power networks is considered. Recent results generalizing principles from thermodynamics, in particular those associated with the second law and exergy are used as a basis to define a cost function. A full-information H-infinity approach is used to guarantee a prescribed level of disturbance attenuation, and a secondary, energy-oriented optimization is carried out over the degree of freedom associated with the non-uniqueness of the H-infinity solution. The secondary problem is non-convex, requiring a global search. A comprehensive simulation example is included demonstrating the superiority of the optimized controllers, in particular relative to the the central solution of H-infinity control.
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16:20-16:40, Paper WeC16.2 | |
>Risk-Sensitive Control of Vibratory Energy Harvesters (I) |
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Ligeikis, Connor | University of Michigan |
Scruggs, Jeff | University of Michigan |
Keywords: Energy systems, Stochastic optimal control, Mechatronics
Abstract: Linear-quadratic-Gaussian (LQG) optimal control theory can be used to maximize the average electrical power generated by a vibratory energy harvester subjected to random disturbances. However, feedback controllers designed using the LQG framework often require large peak power flows for their successful implementation, which may be undesirable for several reasons. In this paper, we propose using a risk-sensitive performance measure to synthesize control laws for stochastic vibratory energy harvesters. The proposed methodology is applied in two examples, in which we show how the risk-sensitive parameter can be systematically tuned to maximize power generation and mitigate excessive power flows. The first example involves a simple single-degree-of-freedom oscillator subjected to a bandpass filtered noise excitation, and the second pertains to ocean wave energy harvesting.
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16:40-17:00, Paper WeC16.3 | |
>Co-Optimization of Electrical and District Heating Networks: Bornholm Case Study (I) |
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Polisetty, Sai Pavan | Imperial College London |
Joseph, Thomas | Imperial College London |
Turk, Ana | Technical University of Denmark |
Batzelis, Efstratios I. | University of Southampton |
Pal, Bikash C | Imperial College London |
Yang, Guangya | Technical University of Denmark |
Kotsampopoulos, Panos | National Technical University of Athens |
Keywords: Energy systems, Optimization
Abstract: With the growing energy demands, the interdependence among multiple energy domains is increasing rapidly. The optimal dispatch of the different energy sources, storage systems, and flexible loads in a multi-energy system is a challenging problem. This paper focuses on the co-optimization of a multi-energy system consisting of electrical and district heating networks to address the challenge. The electric boilers and heaters act as interconnecting elements between the two systems. Utilizing the available flexibilities in both systems, the co-optimization focuses on energy management to achieve economical operation and reduction in renewable curtailment. The algorithm uses the day-ahead forecast of renewable generation as well as electrical and heating demands to determine the optimal schedule for the various generation, storage, and flexible loads in both systems. A case study based on the multi-energy system at Bornholm Island, Denmark is presented in this paper. The results show a significant reduction in renewable power curtailment and a reduction in CO2 emissions achieved via the interconnected systems.
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17:00-17:20, Paper WeC16.4 | |
>Unlocking Energy Flexibility from Thermal Inertia of Buildings: A Robust Optimization Approach |
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Li, Yun | TU Delft |
Yorke-Smith, Neil | TU Delft |
Keviczky, Tamas | Delft University of Technology |
Keywords: Building and facility automation, Smart cities/houses, Energy systems
Abstract: Towards integrating renewable electricity generation sources into the grid, an important facilitator is the energy flexibility provided by buildings' thermal inertia. Most of the existing research follows a single-step price- or incentive-based scheme for unlocking the flexibility potential of buildings. In contrast, this paper proposes a novel two-step design approach for better harnessing buildings' energy flexibility. In a first step, a robust optimization model is formulated for assessing the energy flexibility of buildings in the presence of uncertain predictions of external conditions, such as ambient temperature, solar irradiation, etc. In a second step, energy flexibility is activated in response to a feasible demand response (DR) request from grid operators without violating indoor temperature constraints, even in the presence of uncertain external conditions. The proposed approach is tested on a high-fidelity Modelica simulator to evaluate its effectiveness. Simulation results show that, compared with price-based demand-side management, the proposed approach achieves greater energy reduction during peak hours.
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17:20-17:40, Paper WeC16.5 | |
>On Solar Photovoltaic Parameter Estimation: Global Optimality Analysis and a Simple Efficient Differential Evolution Method |
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Gao, Shuhua | Shandong University |
Xiang, Cheng | National University of Singapore |
Yu, Ming | Power Automation Pte Ltd |
Tan, Kuan Tak | Singapore Institute of Technology |
Lee, Tong Heng | National University of Singapore |
Keywords: Energy systems, Identification, Optimization algorithms
Abstract: The literature presents a vast array of advanced metaheuristic methods for photovoltaic parameter estimation. However, the focus of this study is not to introduce another new method into this already crowded field. Instead, we examine two important but often overlooked questions: (i) are existing results globally optimal, and (ii) can a simpler method achieve comparable performance. We conduct case studies using two widely used I-V curve datasets. To address the first issue, we develop a branch and bound algorithm that, despite its sluggishness, either certifies the global minimum or provides a tight upper bound. These values serve as useful benchmarks for fair metaheuristic evaluation and further development. To answer the second question, our extensive examination and comparison surprisingly reveal that a basic differential evolution (DE) algorithm can achieve the certified global minimum or obtain the best known result. Additionally, the DE algorithm's runtime is much shorter than that of current state-of-the-art metaheuristic methods, making it a great choice for time-sensitive applications. This remarkable finding suggests that using increasingly complex metaheuristics in ordinary PV parameter estimation problems might be unnecessary. Finally, we discuss the implications of these outcomes and propose the simple DE method as the premier choice for industrial applications.
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17:40-18:00, Paper WeC16.6 | |
>Kalman Filtering for Descriptor Systems: An Alternative Approach and Application to Cell Level Estimation of a Lithium-Ion Battery |
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Lone, Jaffar Ali | Indian Institute of Technology Patna |
Goel, Ashna | Indian Institute of Technology, Patna |
Tomar, Nutan Kumar | Indian Institute of Technology Patna |
Bhaumik, Shovan | Indian Institute of Technology Patna |
Keywords: Differential-algebraic systems, Kalman filtering, Control applications
Abstract: This paper presents an alternative approach for the derivation of the Kalman filter for descriptor systems. The descriptor system is assumed to be regular and of index-one. The proposed filtering algorithm is designed based on the well-known projection theorem approach. The algorithm is simple and convenient for recursive estimation and can be easily extended to complex systems with additive/multiplicative random uncertainty. The developed results are applied to estimate the state of charge and local currents of a parallel connected Lithium-ion battery pack, whose modeling naturally comes out to be a descriptor system. Simulation results demonstrate a significant accuracy of our approach under different levels of initialization error and noise.
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WeC18 |
Peony Junior 4412 |
Nonlinear Systems III |
Regular Session |
Chair: Califano, Federico | University of Twente |
Co-Chair: Coates, Erlend M. | Norwegian University of Science and Technology |
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16:00-16:20, Paper WeC18.1 | |
>Utility of the Koopman Operator in Output Regulation of Disturbed Nonlinear Systems |
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Kieboom, Bart | Delft University of Technology |
Bartzioka, Maria | Delft University of Technology |
Jafarian, Matin | Delft University of Technology |
Keywords: Output regulation, Stability of nonlinear systems
Abstract: This paper studies the problem of output regulation for a class of nonlinear systems experiencing matched input disturbances. It is assumed that the disturbance signal is generated by an external autonomous dynamical system. First, we show that for a class of nonlinear systems admitting a finite-dimensional Koopman representation, the problem is equivalent to a bilinear output regulation. We then prove that a linear dynamic output feedback controller, inspired by the linear output regulation framework, locally solves the original nonlinear problem. Numerical results validate our analysis.
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16:20-16:40, Paper WeC18.2 | |
>Strictly Positive Realness-Based Feedback Gain Design under Imperfect Input-Output Feedback Linearization in Prioritized Control Problem |
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An, Sang-ik | University of Seoul |
Park, Gyunghoon | University of Seoul |
Lee, Dongheui | Technische Universität Wien (TU Wien) |
Keywords: Feedback linearization, Output regulation, Nonlinear output feedback
Abstract: The prioritized control problem is a process to find a control strategy for a dynamical system with prioritized multiple outputs, so that it can operate outside its nonsingular domain. Singularity typically leads to imperfect inversion in the prioritized control problem, which in turn results in imperfect input-output feedback linearization. In this paper, we propose a method based on the Kalman-Yakubovich-Popov lemma that compensates nonlinear feedback terms caused by the imperfect inversion of the prioritized control problem. In order to realize this idea, we prove existence of a feedback gain matrix that gives a strictly positive real transfer function whose output matrix is identical to the feedback gain matrix. Our proof is constructive so that a set of such matrices can be found. Also, we provide a numerical approach that gives a larger set of feedback gain matrices and validate the result with numerical examples.
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16:40-17:00, Paper WeC18.3 | |
>Almost Global Three-Dimensional Path-Following Guidance Law for Arbitrary Curved Paths |
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Coates, Erlend M. | Norwegian University of Science and Technology |
Hamel, Tarek | I3S-CNRS-UCA |
Fossen, Thor I. | Norwegain University of Science and Technology |
Keywords: Flight control, Autonomous vehicles, Nonlinear systems
Abstract: Motivated by aircraft applications, we revisit the path-following guidance problem in three dimensions. First, by formulating the path-following error directly in the inertial frame, we propose a class of guidance laws for regular parameterized paths that, unlike most approaches existing in the literature, do not require the explicit construction of a path frame. Based on an inner-outer loop control paradigm, the guidance law generates a normal acceleration command that is normal to the flow-relative velocity vector (as the lift force). This allows for a natural decomposition of the desired vehicle acceleration for aerial vehicles in coordinated turns: tangential acceleration for airspeed control and normal acceleration for guidance generated through bank-to-turn maneuvers, i.e., by tilting the lift vector. By using cascade arguments, we show that the proposed design leads to almost global stability results and thus relaxes the set of feasible initial conditions compared to existing methods. The efficacy of the proposed guidance law is demonstrated in a simulation study.
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17:00-17:20, Paper WeC18.4 | |
>On Roll Stabilisation Using a Canting Keel |
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Ramezani, Hossein | University of Southern Denmark (SDU) |
Chaudhuri, Shouvik | University of Southern Denmark (SDU) |
Jouffroy, Jerome | University of Southern Denmark (SDU) |
Baurichter, Arnd | Dacoma ApS |
Mattrup Hansen, Steen | Dacoma ApS |
Keywords: Maritime control, Nonlinear systems, Modeling
Abstract: This paper presents a study on the modeling and control of a roll stabilization mechanism based on a canting keel. Compared to several active anti-rolling systems, it has the advantage of working at zero and non-zero surge velocity, while taking minimal space in the hull of a considered ship. Using first principles, we describe a simple nonlinear model of the system representing the roll motion of a ship equipped with a canting keel system. We then consider a few dynamic properties of the system under consideration, including the non-minimum phase behavior occurring when the keel is positively buoyant, dubbed as "Airkeel". A controller is then proposed to stabilize the roll motion to compensate for load unbalance of the ship and decrease the influence of waves. A few simulations results are presented for illustration.
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17:20-17:40, Paper WeC18.5 | |
>LMI Feasibility Analysis in Observer Design for Some Families of Nonlinear Systems |
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Arezki, Hasni | University of Genova (Italy) University of Lorraine (France) |
Zemouche, Ali | CRAN UMR CNRS 7039 & Inria: EPI-DISCO |
Bagnerini, Patrizia | University of Genoa |
Djennoune, Saïd | University of Mouloud Mammeri, Tizi-Ouzou |
Keywords: LMIs, Observers for nonlinear systems, Estimation
Abstract: This note deals with observer design for nonlinear systems via Linear Matrix Inequalities (LMIs). The main goal consists in showing that for some families of nonlinear systems, the LMI-based observer design techniques always provide exponential convergent observer. Indeed, until now, this advantageous feature is unique to some types of observers/estimators, such as the high-gain observer, the sliding mode observer, and the moving horizon estimator, under certain conditions of detectability or observability. More specifically, the LMI conditions we propose in this paper always provide solutions to both systems in companion form and feedforward structure. An extension to a general class of nonlinear triangular systems without linear components is provided, which renders the applicability of LMI-based methods possible for a wide class of nonlinear systems without the need for nonlinear diffeomorphism-based transformations.
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17:40-18:00, Paper WeC18.6 | |
>Passivity-Preserving Safety-Critical Control Using Control Barrier Functions |
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Califano, Federico | University of Twente |
Keywords: Energy systems, Lyapunov methods, Optimal control
Abstract: In this letter we propose a holistic analysis merging the techniques of passivity-based control (PBC) and control barrier functions (CBF). We constructively find conditions under which passivity of the closed-loop system is preserved under CBF-based safety-critical control. The results provide an energetic interpretation of safety-critical control schemes, and induce novel passive designs with respect to standard methods based on damping injection. The results are specialised to port-Hamiltonian systems and simulations are performed on a cart-pole system.
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WeC20 |
Orchid Junior 4312 |
Biomolecular Systems |
Regular Session |
Chair: Borri, Alessandro | CNR-IASI |
Co-Chair: Darlington, Alexander | University of Warwick |
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16:00-16:20, Paper WeC20.1 | |
>Natural Host Feedback Simplifies the Design of Metabolic Switches |
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Darlington, Alexander P. S. | University of Warwick |
Mannan, Ahmad A. | Imperial College London |
Bates, Declan G. | Univ. of Warwick |
Keywords: Biomolecular systems, Biotechnology, Genetic regulatory systems
Abstract: The performance of microbial chemical production can be improved by incorporating inducible synthetic gene circuits which `switch' the microbial cell factories from growth to production. Here, we consider the design of an inducible switch, implemented as a small-scale gene regulatory network, in the context of host processes. We show that by accounting for the non-regulatory interactions which arise between host and circuit processes due to natural metabolic and ribosomal constraints the design of the gene circuit can be simplified with little cost to performance. We show that whilst optimal performance is achieved by engineering the full three-gene controller, a partial system composed of fewer regulated genes can still achieve near optimal performance. This may allow for engineering controllers in living cells with fewer time consuming and expensive experimental steps.
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16:20-16:40, Paper WeC20.2 | |
>Exploiting Resource Constraints for Controlling Biomolecular Circuits |
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Patel, Abhilash | Indian Institute of Technology Kanpur |
Stan, Guy-Bart Vincent | Imperial College London |
Keywords: Biomolecular systems, Cellular dynamics, Genetic regulatory systems
Abstract: Advances in synthetic biology depend on our ability to predictably engineer robust biomolecular systems in living cells. The functioning of these synthetic biomolecular systems requires the consumption of shared cellular resources, which imposes a gene expression burden that may impact the performance of the cell and the synthetic system. In this paper, we show the effect of resource constraints on quantitative and qualitative aspects of gene expression in multiple circuits. We utilise a resource-aware modelling framework to show that stabilization can be achieved in a class of integral controllers. The results open possibilities for the design of lean biomolecular controllers.
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16:40-17:00, Paper WeC20.3 | |
>Biomolecular Control Circuit with Inherent Bi-Stability Is Applicable for Automatic Detection of Gut Infection |
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Huang, Yulin | Stanford University |
Mayalu, Michaelle | Caltech, MIT, Stanford |
Keywords: Biomolecular systems, Genetic regulatory systems, Control applications
Abstract: Previously a variety of engineered biological circuits to control cell population have been developed. One possible implementation uses paradoxical feedback, where population control is achieved by using the same quorum sensing signal, produced and sensed by the cell population, to provide both positive (cell proliferation) and negative (cell death) feedback. Here, we extend the paradoxical feedback population control circuit with the addition of a detector to manipulate the activation of the circuit via modulation of an external signal. The detector design utilizes the inherent bi-stability within paradoxical feedback control to switch the cell population dynamics between two equilibrium states via an external signal. Through simulation, we first demonstrate that the bi-stability of the paradoxical feedback controller remains unaffected after the introduction of the detector. Also, the modified detector-population controller can automatically detect and respond to the external signal. We then show how the modified circuit can trigger the total elimination of the cell population using an additional external signal. Finally, we propose a solution for disturbance rejection by adjusting the concentration of a certain gene. Although the detector-population controller is used in the context of gut infection detection, it follows generalizable principles that can be used in various contexts.
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17:00-17:20, Paper WeC20.4 | |
>Robust Model Invalidation for Chemical Reaction Networks Using Generalized Moments |
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Grunberg, Theodore W. | Massachusetts Institute of Technology |
Del Vecchio, Domitilla | Massachusetts Institute of Technology |
Keywords: Biomolecular systems, Identification, Model Validation
Abstract: Many biomolecular systems can be described by chemical reaction networks, however, there may be several candidate networks based on the known biology for a particular system. Determining which chemical reaction network models are inconsistent with observed data can be done via model invalidation. In this work, we formulate and solve a robust version of the model invalidation problem for the case where only measurements from the stationary distribution are available. This problem corresponds to determining if an observed distribution could have been generated by the given chemical reaction network for some value of the parameters, plus a perturbation of bounded size with respect to total variation distance. The main technical tool we introduce to solve the problem is a set of generalized moments that make the problem amenable to an algorithmic solution.
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17:20-17:40, Paper WeC20.5 | |
>Quantitative Steady-State Bounds in Biomolecular Circuits Due to Bounded Multi-Parametric Perturbations |
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Chorasiya, Gunjan | Indian Institute of Technology Delhi, New Delhi |
Prakash, Rudra | Indian Institute of Technology Delhi, New Delhi |
Sen, Shaunak | Indian Institute of Technology Delhi |
Keywords: Biomolecular systems, Systems biology, Computational methods
Abstract: Biomolecular circuit performance depends upon the reaction rate parameters. Any perturbation in these parameters can propagate to the output of the system, altering its performance. A rigorous quantitation of the extent of such deviations in response to variations in one or more parameters, especially in nonlinear settings, is generally unclear. To address this, we developed theoretical frameworks based on the Banach Contraction Theorem and Interval Analysis. We used a parametrized version of the Banach Contraction Theorem to develop a method to bound steady-state variations in terms of variations in multiple parameters, in the linearized and in the nonlinear settings. We extended this to propose a solution to the design problem of obtaining parametric bounds given steady-state bound specifications. We developed a complementary method based on Interval Analysis to rigorously obtain steady-state intervals given parametric intervals. These methods are illustrated using benchmark biomolecular circuit examples. These results contribute to the analysis and design of biomolecular systems in the presence of uncertainties.
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17:40-18:00, Paper WeC20.6 | |
>Co-Design of Resource Limited Genetic Modules |
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Celeste Junior, Carlos Eduardo | Massachusetts Institute of Technology |
Di Loreto, Ilaria | University of L'Aquila |
Grunberg, Theodore W. | Massachusetts Institute of Technology |
Di Benedetto, Maria Domenica | University of L'Aquila |
Borri, Alessandro | CNR-IASI |
Del Vecchio, Domitilla | Massachusetts Institute of Technology |
Keywords: Biomolecular systems, Systems biology, Genetic regulatory systems
Abstract: Modular composition of systems through defined input/output interfaces is a wide-spread engineering approach that allows to make the design of complicated systems tractable. Although this approach has percolated to the design of synthetic genetic circuits, it has proved challenging to obtain predictable design outcomes. In particular, context-dependence due to sharing a limited pool of cellular resources is a major factor that confounds modular composition of genetic modules. Here, we propose the use of a systems framework in which resource sharing among different subsystems is explicitly modeled through disturbance inputs and outputs. Within this system description, resource sharing results in undesired connectivity among subsystems, which is explicitly accounted for in design. Accordingly, we propose to use this system framework to co-design stable systems, with constant input, based on steady state specifications that each subsystem should satisfy. To this end, we provide sufficient conditions on the system parameters such that the output of each subsystem in the network remains in a small interval around a desired value, as well as an algorithmic procedure to compute the feasible region for these parameters. In general, this framework can be used to design subsystems to satisfy a specification, while explicitly accounting for context-dependence.
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WeC24 |
Orchid Main 4201AB |
Hybrid Systems II |
Regular Session |
Chair: Tanwani, Aneel | Laas -- Cnrs |
Co-Chair: Sanfelice, Ricardo G. | University of California at Santa Cruz |
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16:00-16:20, Paper WeC24.1 | |
>Multi-Channel Hybrid Time Domains and Clustering Protocols for Large-Scale Interconnections |
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Teel, Andrew R. | Univ. of California at Santa Barbara |
Goebel, Rafal | Loyola University Chicago |
Sanfelice, Ricardo G. | University of California at Santa Cruz |
Keywords: Hybrid systems, Stability of hybrid systems, Large-scale systems
Abstract: Multi-channel hybrid time domains and clustering protocols are introduced. These concepts are shown to be well- suited for the modeling and description of interconnections of hybrid dynamical systems. Compared to a hybrid time domain, a multi-channel hybrid time domain incorporates multiple jump counters, one for each subsystem in an interconnection. The interconnection’s clustering protocol then determines how the different counters are coordinated. A distributed, hybrid average consensus algorithm is used to illustrate these concepts.
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16:20-16:40, Paper WeC24.2 | |
>An Input-To-State Stability Perspective on Robust Locomotion |
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Tucker, Maegan | California Institute of Technology |
Ames, Aaron D. | California Institute of Technology |
Keywords: Hybrid systems, Stability of nonlinear systems, Lyapunov methods
Abstract: Uneven terrain necessarily transforms periodic walking into a non-periodic motion. As such, traditional stability analysis tools no longer adequately capture the ability of a bipedal robot to locomote in the presence of such disturbances. This motivates the need for analytical tools aimed at generalized notions of stability --robustness. Towards this, we propose a novel definition of robustness, termed emph{delta-robustness}, to characterize the domain on which a nominal periodic orbit remains stable despite uncertain terrain. This definition is derived by treating perturbations in ground height as disturbances in the context of the input-to-state-stability (ISS) of the extended Poincar'{e} map associated with a periodic orbit. The main theoretic result is the formulation of robust Lyapunov functions that certify delta-robustness of periodic orbits. This yields an optimization framework for verifying delta-robustness, which is demonstrated in simulation with a bipedal robot walking on uneven terrain.
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16:40-17:00, Paper WeC24.3 | |
>Controller Synthesis of Signal Temporal Logical Tasks for Cyber-Physical Production Systems Via Acyclic Decomposition |
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Wang, Shuling | Shanghai Jiao Tong University |
Zhu, Shanying | Shanghai Jiao Tong University |
Chen, Cailian | Shanghai Jiao Tong University |
Xu, Liang | Shanghai University |
Keywords: Boolean control networks and logic networks, Formal Verification/Synthesis, Manufacturing systems and automation
Abstract: Modularization facilitates the adaptability of cyber-physical production systems (CPPSs) with a variety of collaborative tasks. Various production rules can be captured by signal temporal logic (STL) specifications imposed on interconnected multi-agent systems (MASs). In this paper, we focus on the controller synthesis of STL tasks for interconnected MASs to accomplish collaborative tasks in modular CPPSs. Firstly, a class of STL specifications characterizing tasks by the combination of fixed-time reachability and finite-time persistence tasks is proposed, which encompasses a large class of production specifications for the MAS. Secondly, the acyclic decomposition of the global STL formula is constructed to enable conflict-free collaborative tasks and unidirectional couplings between subsystems. By establishing the equivalence between the proposition and the state set of the MAS,necessary and sufficient conditions are respectively proposed for the satisfaction of reachability and persistence tasks. In addition, an algorithm is presented to synthesize controllers for the MAS with the global STL specification based on local controllers of subsystems. An illustrative example is given to show the effectiveness of the proposed method.
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17:00-17:20, Paper WeC24.4 | |
>HySST: An Asymptotically Near-Optimal Motion Planning Algorithm for Hybrid Systems |
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Wang, Nan | University of California, Santa Cruz |
Sanfelice, Ricardo G. | University of California at Santa Cruz |
Keywords: Hybrid systems
Abstract: This paper proposes a stable sparse rapidly-exploring random trees (SST) algorithm to solve the optimal motion planning problem for hybrid systems. At each iteration, the proposed algorithm, called HySST, selects a vertex with minimal cost among all the vertices within the neighborhood of a random sample, subsequently extending the search tree through flow or jump, which is also chosen randomly when both regimes are possible. In addition, HySST maintains a static set of witness points where all vertices within each witness's neighborhood are pruned, except for the ones with lowest cost. We show that HySST is asymptotically near-optimal, namely, the probability of failing to find a motion plan with cost close to the optimal approaches zero as the number of iterations of the algorithm increases to infinity. The proposed algorithm is applied to a collision-resilient tensegrity multicopter system so as to highlight its generality and computational features.
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17:20-17:40, Paper WeC24.5 | |
>A Trajectory-Based Stochastic Approach to Symbolic Control |
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Tenaglia, Alessandro | University of Rome Tor Vergata |
Possieri, Corrado | Università Degli Studi Di Roma "Tor Vergata" |
Carnevale, Daniele | Universita' Di Roma |
Keywords: Automata, Markov processes, Machine learning
Abstract: This paper presents two innovative approaches to design symbolic controllers for dynamical systems. The first novelty involves a new trajectory-based strategy for defining the states of a symbolic model, which provides a more accurate representation of the system's dynamics than the traditional grid-based technique. The second novelty concerns using a Bounded-parameter Markov Decision Process rather than a Finite Transition System to model the behavior of a symbolic model. This procedure allows for handling the system's stochastic behavior and considers uncertainties. The effectiveness of the novel approaches presented is demonstrated through numerical results.
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17:40-18:00, Paper WeC24.6 | |
>Existence and Completeness of Solutions to Extended Projected Dynamical Systems and Sector-Bounded Projection-Based Controllers |
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Heemels, W.P.M.H. | Eindhoven University of Technology |
Tanwani, Aneel | Laas -- Cnrs |
Keywords: Hybrid systems, Switched systems
Abstract: Projection-based control (PBC) systems have significant engineering impact and receive considerable scientific attention. To properly describe closed-loop PBC systems, extensions of classical projected dynamical systems are needed, because partial projection operators and irregular constraint sets (sectors) are crucial in PBC. These two features obstruct the application of existing results on existence and completeness of solutions. To establish a rigorous foundation for the analysis and design of PBC, we provide essential existence and completeness properties for this new class of discontinuous systems.
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WeC25 |
Lotus Junior 4DE |
Contraction Theory for Analysis, Synchronization and Regulation III |
Invited Session |
Chair: Astolfi, Daniele | Cnrs - Lagepp |
Co-Chair: Bullo, Francesco | Univ of California at Santa Barbara |
Organizer: Astolfi, Daniele | Cnrs - Lagepp |
Organizer: Bullo, Francesco | Univ of California at Santa Barbara |
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16:00-16:20, Paper WeC25.1 | |
>Design of Nonlinear Coupling for Efficient Synchronization in Networks of Nonlinear Systems (I) |
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Steur, Erik | Eindhoven University of Technology |
Pavlov, Alexey | Norwegian University of Science and Technology |
Van De Wouw, Nathan | Eindhoven University of Technology |
Keywords: Network analysis and control, Nonlinear output feedback, Stability of nonlinear systems
Abstract: This paper proposes a design methodology of nonlinear coupling functions for guaranteed network synchronization. Compared to commonly used linear coupling, the proposed nonlinear coupling allows for a significant reduction of coupling energy cost and output noise sensitivity. This is achieved by activating the coupling only where necessary. Using the novel concept of strict incremental feedback passivity with a nonlinear gain, we estimate the magnitude and state-space location of potential incremental instabilities present in the systems’ intrinsic dynamics, which could drive systems apart in the absence of coupling. Then we introduce a nonlinear coupling design that provides a gain only in the part of the coupled systems’ state-space where the estimated incremental instabilities need to be suppressed. We provide constructive methods to design the nonlinear couplings for guaranteed synchronization over any connected, undirected, weighted network. By means of a numerical example, we demonstrate that our nonlinear coupling design, compared to linear couplings, results in significant performance improvements in terms of noise sensitivity and required coupling energy.
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16:20-16:40, Paper WeC25.2 | |
>Nonlinear Repetitive Control for Mitigating Noise Amplification (I) |
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Aarnoudse, Leontine | TU Eindhoven |
Pavlov, Alexey | Norwegian University of Science and Technology |
Kon, Johan | Eindhoven University of Technology |
Oomen, Tom | Eindhoven University of Technology |
Keywords: Iterative learning control, Learning, Output regulation
Abstract: Repetitive control can lead to high performance by attenuating periodic disturbances completely, yet it may amplify non-periodic disturbances. The aim of this paper is to achieve both fast learning and low errors in repetitive control. To this end, a nonlinear learning filter is introduced that distinguishes between periodic and non-periodic errors based on their typical amplitude characteristics to adapt the extent to which they are included in the repetitive controller. Convergence conditions for the nonlinear repetitive control system are derived by casting the resulting closed-loop as a discrete-time convergent system. Simulation results of the proposed approach demonstrate fast learning and small errors.
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16:40-17:00, Paper WeC25.3 | |
>Kernel-Based Learning of Stable Nonlinear State-Space Models (I) |
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Shakib, Fahim | Imperial College London |
Tóth, Roland | Eindhoven University of Technology |
Pogromsky, A. Yu. | Eindhoven University of Technology |
Pavlov, Alexey | Norwegian University of Science and Technology |
Van De Wouw, Nathan | Eindhoven University of Technology |
Keywords: Learning, Stability of nonlinear systems, Nonlinear systems identification
Abstract: This paper presents a kernel-based learning approach for black-box nonlinear state-space models with a focus on enforcing model stability. Specifically, we aim to enforce a stability notion called convergence which guarantees that, for any bounded input from a user-defined class, the model responses converge to a unique steady-state solution that remains within a positively invariant set that is user-defined and bounded. Such a form of model stability provides robustness of the learned models to new inputs unseen during the training phase. The problem is cast as a convex optimization problem with convex constraints that enforce the targeted convergence property. The benefits of the approach are illustrated by a simulation example.
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17:00-17:20, Paper WeC25.4 | |
>Data-Driven Output Regulation Using Single-Gain Tuning Regulators (I) |
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Chen, Liangjie (Jeffrey) | University of Toronto |
Simpson-Porco, John W. | University of Toronto |
Keywords: Data driven control, Output regulation, Linear systems
Abstract: Current approaches to data-driven control are geared towards optimal performance, and often integrate aspects of machine learning and large-scale convex optimization, leading to complex implementations. In many applications, it may be preferable to sacrifice performance to obtain significantly simpler controller designs. We focus here on the problem of output regulation for linear systems, and revisit the so-called tuning regulator of E. J. Davison as a minimal-order data-driven design for tracking and disturbance rejection. Our proposed modification of the tuning regulator relies only on samples of the open-loop plant frequency response for design, is tuned online by adjusting a single scalar gain, and comes with a guaranteed margin of stability; this provides a faithful extension of tuning procedures for SISO integral controllers to MIMO systems with mixed constant and harmonic disturbances. The results are illustrated via application to a four-tank water control process.
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17:20-17:40, Paper WeC25.5 | |
>CaRT: Certified Safety and Robust Tracking in Learning-Based Motion Planning for Multi-Agent Systems (I) |
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Tsukamoto, Hiroyasu | California Institute of Technology |
Riviere, Benjamin | California Institute of Technology |
Choi, Changrak | NASA Jet Propulsion Lab |
Rahmani, Amir | Jet Propulsion Laboratory |
Chung, Soon-Jo | California Institute of Technology |
Keywords: Robust control, Autonomous systems, Machine learning
Abstract: The key innovation of our analytical method, CaRT, lies in establishing a new hierarchical, distributed architecture to guarantee the safety and robustness of a given learning-based motion planning policy. First, in a nominal setting, the analytical form of our CaRT safety filter formally ensures safe maneuvers of nonlinear multi-agent systems, optimally with minimal deviation from the learning-based policy. Second, in off-nominal settings, the analytical form of our CaRT robust filter optimally tracks the certified safe trajectory, generated by the previous layer in the hierarchy, the CaRT safety filter. We show using contraction theory that CaRT guarantees safety and the exponential boundedness of the trajectory tracking error, even under the presence of deterministic and stochastic disturbance. Also, the hierarchical nature of CaRT enables enhancing its robustness for safety just by its superior tracking to the certified safe trajectory, thereby making it suitable for off-nominal scenarios with large disturbances. This is a major distinction from conventional safety function-driven approaches, where the robustness originates from the stability of a safe set, which could pull the system over-conservatively to the interior of the safe set. Our log-barrier formulation in CaRT allows for its distributed implementation in multi-agent settings. We demonstrate the effectiveness of CaRT in several examples of nonlinear motion planning and control problems, including optimal, multi-spacecraft reconfiguration.
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17:40-18:00, Paper WeC25.6 | |
>A Contracting Dynamical System Perspective Toward Interval Markov Decision Processes (I) |
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Jafarpour, Saber | Georgia Institute of Technology |
Coogan, Samuel | Georgia Institute of Technology |
Keywords: Markov processes, Stochastic optimal control, Uncertain systems
Abstract: Interval Markov decision processes are a class of Markov models where the transition probabilities between the states belong to intervals. In this paper, we study the problem of efficient estimation of the optimal policies in Interval Markov Decision Processes (IMDPs) with continuous action-space. Given an IMDP, we show that the pessimistic (resp. the optimistic) value iterations, i.e., the value iterations under the assumption of a competitive adversary (resp. cooperative agent), are monotone dynamical systems and are contracting with respect to the ell_{infty}-norm. Inspired by this dynamical system viewpoint, we introduce another IMDP, called the action-space relaxation IMDP. We show that the action-space relaxation IMDP has two key features: (i) its optimal value is an upper bound for the optimal value of the original IMDP, and (ii) its value iterations can be efficiently solved using tools and techniques from convex optimization. We then consider the policy optimization problems at each step of the value iterations as a feedback controller of the value function. Using this system-theoretic perspective, we propose an iteration-distributed implementation of the value iterations for approximating the optimal value of the action-space relaxation IMDP.
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WeC26 |
Orchid Main 4301AB |
Distributed Parameter Systems II |
Regular Session |
Chair: Macchelli, Alessandro | University of Bologna - Italy |
Co-Chair: Prieur, Christophe | CNRS |
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16:00-16:20, Paper WeC26.1 | |
>Boundary Control with Integral Action for a Class of Gantry Crane Systems |
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Ma, Ling | Jiangnan University |
Andrieu, Vincent | Université De Lyon |
Astolfi, Daniele | Cnrs - Lagepp |
Xu, Chengzhong | University Claude Bernard - Lyon1 |
Lou, Xuyang | Jiangnan University |
Keywords: Distributed parameter systems, Output regulation, PID control
Abstract: In this paper, we focus on the output regulation problem of a class of gantry crane systems governed by partial differential equations (PDEs) in the presence of unknown constant disturbances. We first design a preliminary state-feedback controller for the system without perturbations and establish the existence of a strict Lyapunov function under the preliminary control law. By employing the forwarding method, we then add an integral action to the preliminary controller and analyze the well-posedness of the resulting closed-loop system, demonstrating its exponential stability. Furthermore, we extend our analysis to consider the system with perturbations, solving the output regulation problem. Finally, we provide numerical simulation results to demonstrate the effectiveness of our proposed strategy.
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16:20-16:40, Paper WeC26.2 | |
>Distributed-Parameter Port-Hamiltonian Systems in Discrete-Time |
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Macchelli, Alessandro | University of Bologna - Italy |
Keywords: Distributed parameter systems, Sampled-data control, Stability of linear systems
Abstract: This paper presents a design framework of discrete-time regulators for linear, port-Hamiltonian, boundary control systems. The contribution is twofold. At first, a discrete-time approximation of the plant dynamics originally described by a linear PDE with boundary actuation is introduced. The discretisation is performed in time only. Thus, the "distributed nature" of the state is maintained. Such a system inherits the passivity of the original one and is well-posed, namely the "next" state always exists. The second result is the characterisation of discrete-time, linear controllers in the port-Hamiltonian form that render the closed-loop dynamics asymptotically stable. A numerical example illustrates the effectiveness of the proposed framework.
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16:40-17:00, Paper WeC26.3 | |
>A Case Study of Port-Hamiltonian Systems with a Moving Interface |
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Kilian, Alexander | University of Passau |
Maschke, Bernhard | University Claude Bernard of Lyon |
Mironchenko, Andrii | University of Passau |
Wirth, Fabian | University of Passau |
Keywords: Distributed parameter systems, Stability of linear systems, Time-varying systems
Abstract: We model two systems of two conservation laws defined on complementary spatial intervals and coupled by a moving interface as a single non-autonomous port-Hamiltonian system, and provide sufficient conditions for its Kato-stability. An example shows that these conditions are quite restrictive. The more general question under which conditions an evolution family is generated remains open.
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17:00-17:20, Paper WeC26.4 | |
>Sub-Predictors for Finite-Dimensional Observer-Based Control of Stochastic Semilinear Parabolic PDEs |
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Wang, Pengfei | Tel Aviv University |
Fridman, Emilia | Tel-Aviv Univ |
Keywords: Distributed parameter systems, Stochastic systems, Delay systems
Abstract: We study output-feedback control of 1D stochastic semilinear heat equation with constant input delay and nonlinear multiplicative noise where the nonlinearities satisfy globally Lipschitz condition. We consider the Neumann actuation and nonlocal measurement. To compensate delay r, we construct a chain of M+1 sub-predictors in the form of ODEs that correspond to the delay fraction r/M. Differently from the deterministic case, we add an additional sub-predictor to the chain that leads to the closed-loop system with the stochastic infinite-dimensional tail and the finite-dimensional part that consists of non-delayed stochastic equations and delayed deterministic ones. The latter essentially simplifies the Lyapunov-based mean-square L^2 exponential stability analysis of the full-order closed-loop system. We employ corresponding It^{o}'s formulas for stochastic ODEs and PDEs, respectively. Our stability analysis leads to LMIs which are shown to be feasible for any input delay provided M and the observer dimension are large enough and Lipschitz constants are small enough. A numerical example demonstrates the efficiency of the proposed approach.
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17:20-17:40, Paper WeC26.5 | |
>A PIE Representation of Scalar Quadratic PDEs and Global Stability Analysis Using SDP (I) |
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Jagt, Declan S. | Arizona State University |
Seiler, Peter | University of Michigan, Ann Arbor |
Peet, Matthew M. | Arizona State University |
Keywords: Distributed parameter systems, Stability of nonlinear systems, LMIs
Abstract: It has recently been shown that the evolution of a linear Partial Differential Equation (PDE) can be more conveniently represented in terms of the evolution of a higher spatial derivative of the state. This higher spatial derivative (termed the 'fundamental state') lies in L_2 - requiring no auxiliary boundary conditions or continuity constraints. Such a representation (termed a Partial Integral Equation or PIE) is then defined in terms of an algebra of bounded integral operators (termed Partial Integral (PI) operators) and is constructed by identifying a unitary map from the fundamental state to the state of the original PDE. Unfortunately, when the PDE is nonlinear, the dynamics of the associated fundamental state are no longer parameterized in terms of partial integral operators. However, in this paper we show that such dynamics can be compactly represented using a new tensor algebra of Partial Integral operators acting on the tensor product of the fundamental state. We further show that this tensor product of the fundamental state forms a natural distributed equivalent of the monomial basis used in representation of polynomials on a finite-dimensional space. This new representation is then used to provide a simple SDP-based Lyapunov test of stability of quadratic PDEs. The test is applied to three illustrative examples of quadratic PDEs with various types of boundary conditions.
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17:40-18:00, Paper WeC26.6 | |
>Imitation Learning Control for Thermoacoustic Stabilization of a Rijke Tube |
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de Andrade, Gustavo Artur | Universidade Federal De Santa Catarina |
Fiacchini, Mirko | CNRS, Univ. Grenoble Alpes |
Prieur, Christophe | CNRS |
Keywords: Backstepping, Distributed parameter systems, Machine learning
Abstract: This work studies the use of Neural Network (NN) boundary controllers to stabilize thermoacoustic instabilities in a Rijke tube. The dynamics of this phenomenon are governed by a system of 4x4 hyperbolic linear partial differential equations (PDEs) for the acoustic wave propagation, plus a linear ordinary differential equation (ODE) for the heat release. The control action is applied in one of the left boundary conditions, characterizing this system as underactuated. Previous results in the literature showed that this control problem can be solved by the backstepping methodology with stability guarantees in the L2 sense. However, the stabilization and closed-loop system performance are usually affected by uncertainties. To tackle this issue, we rewrite this PDE-ODE boundary control problem as an imitation learning problem for stabilizing the system by observing the state values of a numerical simulator of the Rijke tube system under different operating conditions. Additionally, we present a Lyapunov-based method with local sector quadratic constraints to analyze the stability of the closed-loop system with the NN controllers. We demonstrate by simulations that the NN controller is able to stabilize the system under uncertain conditions, with the potential to overcome the performance of the backstepping.
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WeC27 |
Roselle & Simpor Bayview Foyer |
Benchmark Competitions on Control of Electric Vehicles and Autonomous
Inspection |
Poster Session |
Chair: Nguyen, Thien-Minh | Nanyang Technological University |
Co-Chair: Shen, Tielong | Sophia Univ |
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16:00-18:00, Paper WeC27.1 | |
>Reinforcement Learning Based Motion Control of 4-In-Wheel Motor Actuated Electric Vehicles |
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Essuman, Jones | Louisiana State University |
Meng, Xiangyu | Louisiana State University |
Tang, Xun | Louisiana State University |
Keywords: Machine learning, PID control, Autonomous vehicles
Abstract: The automotive industry has witnessed a remarkable transition towards Electric Vehicles in recent years. This shift has been primarily driven by the need to reduce carbon dioxide emissions and the advancements in battery and electric drive technologies. Among the various electric vehicle variants, 4-in-Wheel Motor-Actuated Electric Vehicles have emerged as a notable option. This variant possesses a distinctive feature of independently controlling all four motors, which leads to improved maneuverability and efficiency. To fully leverage these advantages, an optimal control strategy is required to ensure both precise motion control and energy efficiency. Achieving this objective presents a significant challenge. To address this challenge, two reinforcement learning based strategies are proposed: Proportional-Integral-Derivative (PID) control and Direct Torque control. The first strategy involves implementing four independent PID controllers, one for each motor. An adaption mechanism is employed to handle changing operating conditions and disturbances. This mechanism enables the controller to continuously update its parameters. The second strategy employs a Direct Torque control approach, where the reinforcement learning agents directly learn the optimal torque to each wheel using an actor-critic framework. Both approaches leverage recent advancements in reinforcement learning application for continuous control to achieve energy efficiency and precise control over each wheel, taking advantage of the ability of deep neural networks to handle large action and observation spaces. To evaluate the performance of the PID and Direct Torque controllers for 4-In-Wheel Motor-Actuated Electric Vehicles, benchmark driving scenarios such as velocity profile tracking and a lane change maneuver at a constant speed are employed. The results demonstrate that the reinforcement learning based controllers can smoothly track reference velocity and execute lane changes while consuming less energy. These findings highlight the potential of the reinforcement learning based controllers to enhance the efficiency and maneuvering capabilities of 4-In-Wheel Motor-Actuated Electric Vehicles.
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16:00-18:00, Paper WeC27.2 | |
>A Hierarchical Motion Control Framework for Constrained Electric Vehicles with Four In-Wheel Motors |
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Zhang, Chuntao | Beijing Institute of Technology |
Han, Jinheng | Tsinghua University |
Hu, Bin-Bin | Nanyang Technological University |
Wei, Henglai | Nanyang Technological University |
Lv, Chen | Nanyang Technological University |
Keywords: Automotive control, Automotive systems, Autonomous vehicles
Abstract: Ensuring motion comfort and optimizing economy performance are pivotal benchmarks for vehicle chassis dynamics control, presenting considerable challenges for automotive engineers. This paper introduces a hierarchical comfort constraints control framework to enhance the body motion control and energy efficiency of Electric Vehicles (EVs) equipped with 4 In-Wheel Motors (IWM). Given the stringent constraints on vehicle body motion states for optimal passenger comfort, a dynamic comfort filter is employed. This filter dynamically adjusts tracking reference signals, striking a balance between comfort constraints and velocity tracking performance. Once these signals are recalibrated, an adaptive gain-scheduling PID controller is implemented to boost the velocity tracking performance, even in the face of uncertain road conditions and vehicle dynamics parameters—and this without necessitating a detailed vehicle dynamics model. Further, in acknowledgment of the EV's over-actuated nature, the overall driving torque is divided into four distinct wheel-driving torques. This division is based on optimizing tracking performance, energy consumption, and wheel vertical loading. MATLAB-Simulink simulation results validate the effectiveness of our proposed method, demonstrating its capability in addressing high-performance constraints tracking issues for EVs.
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16:00-18:00, Paper WeC27.3 | |
>Strategies for Cooperative Aerial Robots Inspection |
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Manvi, Bharat | Tata Consultancy Services |
Gupte, Sumedh Sunil | TCS Research |
Keywords: Autonomous robots, Cooperative control, Robotics
Abstract: In this work, we explore the solutions to the cooperative aerial robot inspection problem in the three given environments. The goal is to come up with strategies that maximize the quality of the inspection measured by a scoring function. The unmanned aerial vehicles (UAVs) of different types and capabilities need to cooperate to maximize this score. We aim to solve the problem modeling it as a Partially observable Markov game (POMG) with cooperation. Here, the POMG is the generalization of the POMDP to the multi agent system. In particular, the focus is on the cooperative actions of the agents (drones) involved in the POMG. In the POMG, the explorer drones are made into one group and photographic drones are made into another group. The explorer group's objective is to map the environment as early as possible, for this we aim to come up with an appropriate reward function. On the other hand, the photographer group's objective is to increase the score of the interesting points by getting higher resolution images. Once the explorer group covers whole map the state becomes (almost) fully observable. Now the game becomes a Markov game (MG) with complete information and all drones (explorer and photographic) will cooperate to get better score of the interesting points. Here, to maximize the score all drones cooperate to cover the interesting points in an intelligent manner.
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16:00-18:00, Paper WeC27.4 | |
>Enhancing Vehicle Stabilization in Harsh Driving Conditions Using Model Predictive Control with Neural Network Integration |
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Choi, Jung Hyun | ETRI |
Jin, Yongsik | Electronics and Telecommunications Research Institute |
Kang, Dongyeop | Electronics and Telecommunications Research Institute |
Kim, Chung-geun | Electronics and Telecommunications Research Institute |
Keywords: Cooperative control, Autonomous systems, Control applications
Abstract: Motion stabilization and energy-efficient driving algorithms are crucial in autonomous driving for four-independent drive wheel-based electric vehicles. Nonetheless, a significant challenge arises for AI within autonomous vehicles: generating an optimal driving path while accounting for the intricate interplay of vehicle performance and status inheritance. This poster introduces an innovative approach to address these challenges within specific driving scenarios. Notably, it focuses on scenarios involving driving under low friction load conditions and executing a double lane change maneuver. In these scenarios, predetermined speed profiles and driving routes are provided. The primary objective is to drive the vehicle along the predefined path while prioritizing stability, overall performance, and energy efficiency. To achieve this, a model predictive control algorithm is proposed, incorporating slip ratio control. This approach manages inputs, including steering angle and yaw moment, and outputs, like yaw rate, side slip angle, and speed. The system operates under diverse constraints reflective of the vehicle's dynamic behavior. Moreover, an acceptable yaw moment update rule based on a neural network using motion sensor data is proposed. The effectiveness and accomplishments of the proposed algorithm are demonstrated through simulations using Modelica, a vehicle motion analysis simulator integrated with Matlab/Simulink.
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16:00-18:00, Paper WeC27.5 | |
>Benchmark Problem for Motion Control of Four In-Wheel Motor |
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Lee, Jihyeong | Kyungpook National University |
Kim, Junghyo | Kyungpook National University |
Nam, Sanghyeon | Kyungpook National University |
Han, Kyoungseok | Kyungpook National University |
Keywords: Automotive control, Autonomous vehicles, Optimization
Abstract: In this study, we presents a comprehensive control strategy for in-wheel motor independent drive electric vehicles (full 4-IWM EV). The primary objectives of our control strategy encompass three key aspects: accurate tracking of desired speed, precise following of reference paths, and enhanced energy efficiency. The control architecture consists of upper and lower controllers. The upper controller focuses on determining longitudinal forces and yaw moments using model predictive control (MPC). Specifically, it calculates the desired slip angle and yaw rate based on the bicycle model, and derives the optimum longitudinal force and yaw moment decision process. The lower controller is responsible for individual wheel torque allocation and can exactly follow the commands of the upper controller. To achieve these goals, we develop a cost function that addresses both reduced engine power consumption and improved wheel stability. By carefully balancing these factors, we aim to achieve the optimal trade-off between energy efficiency and vehicle performance. Additionally, We will formulate a control strategy that aims to optimize energy by minimizing rolling resistances associated with wheel slip angle and carry out our mission of performing stable driving on rough roads. Respond to road undulation pattern, analysis of the suspension model was carried out in order to fulfill the specified constraints. Through simulation and analysis. We verify the effectiveness of control strategies to achieve the proposed goals. This result indicates successful coordination between the upper and lower controllers, leading to better tracking accuracy and better energy-saving capabilities. This study will contribute to an efficient torque distribution method for full 4-IWM EV.
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16:00-18:00, Paper WeC27.6 | |
>MPC Based Four-Wheel Hub Motor Vehicle Linear Driving and Steering Stability Control |
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Sun, Chaoyang | Tianjin University |
Chen, Tao | National Key Laboratory of Advanced Internal Combustion, Tianjin |
Chen, Liujun | Tianjin University |
Zhang, Guoli | Tianjin University |
Li, Shuo | Tianjin University |
Chen, Daxin | National Key Laboratory of Advanced Internal Combustion, Tianjin |
Qin, Tang | National Key Laboratory of Advanced Internal Combustion, Tianjin |
Gao, Yonghan | National Key Laboratory of Advanced Internal Combustion, Tianjin |
Keywords: Optimal control, Uncertain systems, Grey-box modeling
Abstract: Body stability control is an important research problem in vehicle control because it involves many aspects of vehicle comfort, operability and economy. Based on the simulation and research platform provided by CDC benchmark Challenge, this study carried out optimization control research on the control problems in acceleration and deceleration and lane change of passenger cars driven by four-wheel hub motors. In this study, the 8-dimensional transverse and 8-dimensional longitudinal dynamics models of the target vehicle were first built, and the key parameters of the target vehicle model were identified as the basis of model-based optimization control. The relationship between the vehicle active control torque and its distribution ratio and the pitch Angle, roll Angle and vertical acceleration is established, and the cost function and constraint conditions for optimization are constructed. The vehicle speed and path following control architecture based on model iterative optimization is designed, which meets the requirements of CDC benchmark Challenge
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16:00-18:00, Paper WeC27.7 | |
>Robust Torque Distribution Control with Energy Optimization for Four-Wheel Electric Vehicles |
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Kubota, Yuya | Sophia University |
Cao, Wenjing | Sophia University |
Keywords: Optimal control, Robust control, Autonomous vehicles
Abstract: In this study, we propose an optimal torque distribution control strategy with robustness for electric vehicles equipped with four in-wheel motor, aiming at vehicle motion and energy optimization. The control input of the steering angle is governed by a default controller designed solely for path tracking. This research focuses on designing a controller that optimizes the torque distribution among each wheel while using the steering angle as an external input. Based on a nonlinear 7-degree-of-freedom(7-DOF) vehicle model incorporating uncertain disturbances, the proposed approach is designed. The control architecture consists of two layers: vehicle motion control and torque distribution. The first layer, vehicle motion control, aims to achieve robustness against disturbances and model uncertainties through Direct Yaw Moment Control (DYC) and Direct Longitudinal force Control (DLC). DYC contributes an additional yaw moment to track the desired yaw rate derived from a linear 2-DOF model. DLC, inspired by DYC, generates additional longitudinal force to track a desired speed. Both DYC and DLC employ Sliding Mode Control (SMC) known for constructing robust control systems. Hyperplanes are designed based on the deviations from desired states, and Lyapunov function and proportional reaching law are utilized to reach these hyperplanes within a finite time. To mitigate chattering inherent in sliding mode control, a nonlinear disturbance observer is introduced, and the gain of the sign function is made adaptable. The second layer, torque distribution, aims to minimize power consumption while satisfying the desired yaw moment and longitudinal force obtained from the first layer. Sequential Quadratic Programming (SQP) is employed to optimize this torque distribution. Through the combined two-layer control logic, the torque allocation for each wheel is determined with the steering angle as an external input. By comparing the proposed approach with torque distribution methods based on disturbance-agnostic vehicle control and conventional equal torque distribution, this study demonstrates the effectiveness of the proposed method in achieving both robustness against uncertain disturbances and energy optimization.
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16:00-18:00, Paper WeC27.8 | |
>A Hierarchical Controller Design for the Motion Stability of Four In-Wheel Motor Actuated Electric Vehicles |
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Zhou, Yunfei | Dalian University of Technology |
Ta, La | Dalian University of Technology |
Ren, Libin | Dalian Minzu University |
Kang, Mingxin | Ningbo University of Technology |
Zhang, Jiangyan | Dalian Minzu University |
Wu, Yuhu | Dalian University of Technology |
Keywords: Automotive control, Predictive control for nonlinear systems, Optimization
Abstract: Popularization of electrified and intelligent vehicles makes new challenges and opportunities to the traditional vehicle control technologies. The motion stability control of four in-wheel motor actuated electric vehicle is one of the significant problems, hence it is proposed as a benchmark problem at the 62nd IEEE Conference on Decision and Control. In this paper, a hierarchical control scheme is proposed to deal with the associated problems in terms of longitudinal and lateral stability control, respectively. This hierarchical scheme control proposed consists of two levels: the primary control based on nonlinear model predictive control (NMPC) and PID algorithm ensures the accuracy of speed tracking or trajectory tracking; the secondary control optimizes the vehicle's motion stability by tire torque allocation. In order to deal with the longitudinal motion control problem, the longitudinal kinematics model and four-wheel rotation dynamic model are constructed, and an online estimation algorithm is proposed for the wheel ration rate. Then, a longitudinal dynamics controller is built by using NMPC algorithms, in which the optimal performance indexes comprehensively consider the energy consumption, comfort, and longitudinal stability. Finally, the four wheels' torque outputs are optimized in real time by an online optimization algorithm. Furthermore, for the lateral stability control, a hierarchical control scheme is developed. At the high level, a PID controller is used to achieve the tracking control of lateral displacement first, meanwhile, a simplified two-degree-of freedom bicycle model is used to represent the system dynamics in terms of the yaw rate and the sideslip angle, and by deducing a linear reference model in the stability domain, and the reference states are generated. Then model predictive controller is proposed to adjust the additional yaw moment torque that realizes the real-time tracking control of reference yaw rate and sideslip angle, and finally, guarantees the lateral stability. The above proposed controller is validated in the official simulation platform of the Benchmark and the simulation results demonstrate the effectiveness of the proposed control scheme.
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16:00-18:00, Paper WeC27.9 | |
>An Optimal Control and Reinforcement Learning Approach with Multi-Fidelity Simulation Models for Motion Control of Four In-Wheel Motor Vehicles |
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Nguyen, Huu Thien | University of Porto |
Vinha, Sergio | University of Porto |
Fernandes, Manuel C. R .M. | Universidade Do Porto |
Ahmed, Afaq | COMSATS University Islamabad |
Paiva, Luis Tiago | Universidade Do Porto |
Uppal, Ali Arshad | COMSATS University Islamabad |
Fontes, Fernando A. C. C. | Universidade Do Porto |
Keywords: Automotive control, Optimal control, Learning
Abstract: We address the motion control of an electric vehicle with four in-wheel motors, which comprises two main tasks: the first is a velocity tracking problem and the second is a trajectory tracking problem through a double lane change maneuver, while satisfying constraints and minimizing energy objective functions in both cases. Our approach to this problem consists of solving an open-loop optimal control problem to obtain the initial trajectory planning and utilizing reinforcement learning to devise the final policy. Simulation models with different degrees of complexity and fidelity, including unknown disturbances from the road surface, are used to train the reinforcement learning algorithm.
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16:00-18:00, Paper WeC27.10 | |
>Robust Learning-Based Predictive Motion Control for Four In-Wheel Motor Drive Electric Vehicles |
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Tian, Cheng | The Hong Kong Polytechnic University |
Su, Jiangcheng | The Hong Kong Polytechnic University |
Hu, Dong | Hong Kong Polytechnic University |
Yang, Xiaoyu | The Hong Kong Polytechnic University |
Huang, Chao | The Hong Kong Polytechnic University (PolyU) |
Huang, Hailong | Hong Kong Polytechnic University |
Keywords: Automotive control, Learning, Autonomous vehicles
Abstract: This poster proposed a novel predictive motion control method for in-wheel motor drive electric vehicles, encompassing vehicle stability, ride comfort, and power consumption. The control structure comprises two levels: two upper-level controllers and a lower-level torque allocation coordinated controller. For the upper-level, a longitudinal motion controller based on active disturbance rejection control (ADRC) is designed considering vehicle pitch motion. Moreover, an integrated lateral controller based on Model Predictive Control (MPC) is constructed considering vehicle lateral stability and rollover stability. For the lower-level, a torque allocation coordinated controller to distribute four-wheel torques, which can coordinate tracking performance, vehicle stability and energy consumption. Subsequently, curriculum learning (CL) is applied to adjust torque distribution coefficient to obtain the optimal vehicle handling control strategy. Ultimately, the efficacy of the proposed control method is thoroughly validated via simulation experiments using high-fidelity Modelon vehicle models across various driving scenarios.
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16:00-18:00, Paper WeC27.11 | |
>Vehicle Motion Control and Energy Saving Optimization Based on Q Learning for a Four-Wheel Independently Driven Electric Vehicle |
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Hou, Shengyan | Jilin University |
Liu, Xuan | JiLin University |
Li, Kai | Jilin University |
Liu, Jinfa | JiLin University |
Wang, Yilin | Jilin University |
Xu, Zhenhui | Sophia University |
Gao, Jinwu | Jilin University |
Keywords: Automotive control, Optimal control, Autonomous vehicles
Abstract: With the rapid development of vehicle autonomous and electrification, vehicle motion control is the basis for vehicle intelligence. This study presents an optimization control strategy for the powertrain system of a four-wheel independently driven electric vehicle to improve the dynamic stability and energy saving performance of a four-wheel independently driven electric vehicle. Firstly, vehicle parameters are identified according to actual vehicle data. The vehicle traction torque is calculated according to the vehicle dynamics equation. Then, with the goal of reducing the body vertical motion, vehicle energy consumption and deviation from the reference speed, the vehicle traction torque is split based on a Q learning algorithm to achieve vehicle stability control and improve vehicle economy.
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16:00-18:00, Paper WeC27.12 | |
>Predictive Motion Control Considering Body Attitude Constraints for Four In-Wheel Motor Vehicles |
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Chu, Hongqing | Tongji University |
Zongxuan, Li | Tongji University |
Kang, Qiao | Tongji University |
Li, Zhenghao | Tongji University |
Gao, Bingzhao | Jilin Univ.; Yokohama National Univ |
Chen, Hong | Tongji University |
Keywords: Optimization algorithms, Predictive control for nonlinear systems
Abstract: The utilization of in-wheel motors in electric cars is a typical method for providing power, allowing for strategic power distribution. These motors are integrally linked to the suspension system, and the resultant output torque engenders a substantial vertical force due to the presence of anti-pitch geometry. The coupling between driving torque and vertical force precipitates body attitude oscillations during driving or braking, thus impacting the ride comfort significantly. A promising avenue for modulating the body attitude in in-wheel motor-driven vehicles involves a rational distribution of driving torque between the wheels. Considering the constraints of body attitude, this study introduces an innovative control scheme employing a learning model predictive control (MPC) framework. The objective of this technique is to determine the total driving torque, the additional roll moment and pitch moment, and the additional vertical force. Then, a transfer matrix is used to calculate the required wheel moment to satisfy the desired additional moment and vertical force. Finally, a Simulink/Modelon co-simulation test is conducted to validate the effectiveness of the proposed control scheme. The results show that the performance of the proposed controller is improved compared with the default controller. Notably, the proposed scheme successfully maintains vertical acceleration, roll angle, and pitch angle within the specified limits, affirming its effectiveness.
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16:00-18:00, Paper WeC27.13 | |
>Control Strategy and Path-Following in Electric Vehicles with 4 In-Wheel Motors Using a Linear Equivalent Two-Wheel Model |
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Nakano, Yoshihisa | Sophia University |
Cao, Wenjing | Sophia University |
Keywords: Modeling, Linear systems, Simulation
Abstract: In recent years, electric vehicles with four in-wheel motors have become a topic of interest in automotive research due to their potential in improving driving control and energy efficiency. One of the significant advantages of this configuration is the ability to independently control the torque of each wheel, which can offer better safety and path-following capabilities. This research primarily addresses the challenges in motor coordination and steering angle adjustments. The study utilizes a linear equivalent two-wheel model to demonstrate vehicle dynamics. This model was employed to simplify and then linearize the dynamics. Using Model Predictive Control (MPC), we aimed to drive the vehicle based on a set trajectory determined by target body position velocities. This helped in identifying an optimal steering angle for the front wheels. Further, using a mechanical model for the steering system we obtain the reference handle angles that derives the optimal steering angles. Important elements such as the inertia of the front wheel around the kingpin and the characteristics of the entire steering system were considered. Controls were then designed using a PID controller to ensure stability and precision. One of the study's notable features is the incorporation of real-time data. By combining the two-wheel model with MPC, we adjust the steering angle based on real-time information. The system also monitors vehicle roll, pitch, and z-coordinates to estimate the cornering power for each tire and update the model accordingly. The torque control strategy was developed with several objectives in mind: maintaining a speed of 60 km/h, aligning with the slip angles from the model, reducing vibrations, and conserving energy. The vibration control aspect was designed to resemble the inverse skyhook damper principle, targeting energy conservation in the z-direction.
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16:00-18:00, Paper WeC27.14 | |
>A Multi-Objective Robust Model Predictive Control Strategy for Trajectory Tracking with Variable Constraints |
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Kong, Aijing | Tongji University |
Yan, Zhoudong | Tongji University |
Hang, Peng | Tongji University |
Chen, Xinbo | Tongji University |
Wu, Xian | Tongji University |
Keywords: Autonomous vehicles, Optimal control, Fuzzy systems
Abstract: This poster aims to solve the benchmark motion control problem of a 4-wheel IWM vehicle. The longitudinal driving/braking force and lateral steering angle should be controlled smoothly with minimum energy cost. Besides, the control of body attitude through wheel vertical force is also considered. The difficulty of the problem lies in establishing a model between the control input and control target and combating unknown disturbances. To solve this problem, we presented a Multi-objective Robust Model Predictive Control (MRMPC) algorithm to optimize the steering wheel angle and allocate wheel torque. Firstly, a 7-degree-of-freedom vehicle model considering external unknown disturbance is established to complete the target construction. Then, the objective problem is designed. The objective function contains the deviation of the vehicle speed from the target, the deviation of the vehicle trajectory from the target, and energy consumption. These objectives have different weight values, generated by a fuzzy logic controller. The constraints of the MPC problem include the limitation of longitudinal and lateral location, speed, acceleration, and their increments. Moreover, the vehicle will drive on a rough road and the maximum height of the bump is 5mm. According to the simulation results, the vertical body acceleration, pitch angle, and roll angle are affected sharply by the jitter of the speed curve. Hence, the range of vertical body acceleration, pitch angle, and roll angle should also be restricted. We converted those quantities to variable constraints as a feedback compensator. When vertical body acceleration, pitch angle, and roll angle become larger, the constraints should be restricted more seriously. The MRMPC algorithm is conducted through MATLAB/Simulink. We compared our MRMPC algorithm with the PID method and the simulation results show that the maximum tracking error of lateral location and speed has reduced to a much lower level and the value of objective index became smaller.
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16:00-18:00, Paper WeC27.15 | |
>Advanced Motion Control of Four In-Wheel Motor Actuated Vehicles |
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Huanning, Yang | Jilin |
Wang, Jieshu | Jilin |
Yang, Boxiong | The Department of Control Science and Engineering, Jilin Univers |
Hu, Xiao | Jilin University |
Wang, Ping | Jilin University |
Hu, Yunfeng | Jilin University |
Chen, Hong | Tongji University |
Keywords: Autonomous systems, Autonomous vehicles, Learning
Abstract: Advanced motion controllers combining model-based and model-free methods are proposed to solve two problems of the benchmark challenge organized by IEEE CDC 2023. The proposed controllers allow the vehicle to track the target speed and trajectory while effectively suppressing its vertical acceleration on rough roads. First, the vehicle dynamics model is established, and its unknown parameters are identified via the nonlinear least squares method. Second, a longitudinal motion controller is proposed based on nonlinear control methods to track the target speed. Finally, the vehicle states, including vertical acceleration, body roll angle, and body pitch angle, are suppressed by torque allocation based on model-free reinforcement learning. Co-simulations of Modelon Impact and MATLAB/Simulink have been performed, and the results show that our methods are initially effective and promising.
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16:00-18:00, Paper WeC27.16 | |
>Cooperative Aerial Robots Inspection Challenge Based on Hierarchical Reinforcement Learning |
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Hu, Jinwen | Northwestern Polytechnical University |
Lei, Yifei | Northwestern Polytechnical University |
Zhang, Deteng | Northwestern Polytechnical University |
Xu, Zhao | Northwestern Polytechnical University |
Guo, Kexin | Beihang University |
Zhao, Chunhui | Northwestern Polytechnical University |
Lyu, Yang | Northwestern Polytechnical University |
Hou, Xiaolei | Northwestern Polytechnical University |
Keywords: Learning, Sensor networks
Abstract: The poster proposes a multi-UAV reinforcement learning strategy to train UAVs to get more points of interest scores. A reinforcement learning-based approach to a manoeuvre strategy for multi-drone hierarchical training is designed, where the exploration area is divided into multiple parts by the number of drones and explored separately in each area. The reward function of each intelligence is designed based on its total score and whether it collides with obstacles or not. The final goal is to get more scores.
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16:00-18:00, Paper WeC27.17 | |
>Model Predictive Planing and Control for the Benchmark Problem of Four In-Wheel Motor Actuated Vehicles |
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Li, Xingchen | Tsinghua University |
Hou, Zhinan | Tsinghua University |
Li, Tianxun | Beihang University |
You, Keyou | Tsinghua University |
Keywords: Autonomous vehicles, Predictive control for nonlinear systems, Hierarchical control
Abstract: The benchmark problem requires controlling the four in-wheel motor actuated vehicle by steering and wheel torques to minimize tracking error and energy consumption with given constraints. To this end, we first design a motion planner to generate total torque commands and achievable steering trajectories based on the slow mechanical dynamics of the 6-DOF vehicle body. Then, we distribute the torque to each wheel minimizing the tire slip energy loss by quadratic programming, and track the reference steering by model predictive control. Finally, the simulation results on the benchmark vehicle model validate the safety, tracking performance, and energy efficiency of the proposed method.
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16:00-18:00, Paper WeC27.18 | |
>Multi-Agent Cooperative Inspection in Unknown Aera with Temporal Logic Specifications |
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Zhao, Bangwei | Xiamen University |
Huang, Zhiyuan | Xiamen University |
Guo, Jiarui | Xiamen University |
Chen, Xianglin | Xiamen University |
Zheng, Yiwei | Xiamen University |
Lan, Weiyao | Xiamen University |
Yu, Xiao | Xiamen University |
Keywords: Autonomous robots, Cooperative control, Formal Verification/Synthesis
Abstract: In this benchmark challenge, we focus on the problem of multi-agent cooperative inspection problem in an unknown environment. A multi-agent system with 5 unmanned aerial vehicles is deployed in the environments without priori information. The primary goal for these agents is to capture images and point cloud data of the surface of the structures within the environments at the best possible quality. We first abstract the specifications for the inspection to a signal temporal logic formula. Then, the performance index and safety constraints are given in a cost function. With our designed algorithm, the optimal trajectories will be synthesized correct-by-construction based on the different system models of each agent. Finally, our algorithm has been tested with the provided simulation environment, and the result is of satisfactory.
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16:00-18:00, Paper WeC27.19 | |
>Optimal Control for Motion Control of Four In-Wheel Motor Actuated Vehicles |
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Chen, Lei | Yanshan University |
Zhu, Guanyu | Yanshan University |
Wang, Yuepeng | Yanshan University |
Jiao, Xiaohong | Yanshan University |
Zhang, Yahui | Yanshan University |
Keywords: Optimal control, Automotive control, Automotive systems
Abstract: 4轮毂电机的电动汽车(EV) (IWM),具有独立分布的优势 扭矩大,动力传输效率高,已显示出极大的 降低车辆能耗的潜力,提高 车辆稳定性和安全性。扭矩优化 分布算法,作为研究的核心内容 四轮毂电机 (IWM) 驱动的电动汽车 (EV), 是实现扭矩优化的挑战性问题 在未知的情况下,经济性和安全性的分布 测试条件。为了解决这些问题,本文 旨在探索电气领域基准问题的解决方案 基于四轮毂电机的车辆运动控制 构建 (IWM) 驱动电动汽车 (EV) 模型 使用模型。它建立了扭矩优化 同时考虑车辆经济性的分配算法 和稳定性。在直线行驶条件下, 论文侧重于通过优化 纵向驱动力分布。然后,通过 动态条件下的实时传动系统打滑控制, 它确保车轮
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16:00-18:00, Paper WeC27.20 | |
>Optimization-Based Hierarchical Robust Motion Control for In-Wheeled Motor Vehicles against Road Disturbance |
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Park, WonYoung | University of Seoul |
Kim, InGyeom | University of Seoul |
Kim, Sewon | University of Seoul |
Back, Juhoon | Kwangwoon University |
Park, Gyunghoon | University of Seoul |
Keywords: Autonomous vehicles, Optimization, Hierarchical control
Abstract: In this benchmark challenge, we propose a motion control strategy for in-wheeled motor vehicles to achieve multiple control objectives, such as improving maneuverability, minimizing energy loss, and tracking position and/or velocity references under uncertain road condition. In order to deal with a variety of control purposes as well as constraints at the same time, a vehicle controller in two-layered hierarchical structure is presented. The upper-layer controller in the hierarchy is constructed based on the finite-time optimal control problem formulated as an optimization problem, serving as a coordinator by computing optimal values for the torque distributed to each in-wheeled motors. The aim of the upper-layer controller is to minimize energy consumption and to generate a trackable motion by modifying the given reference. Then we employ a lower-layer controller to follow the refined reference generated by the upper-layer controller, in the presence of disturbance caused by uncertain road condition. For this, robust control schemes are utilized in design of the lower-layer controller. In doing so, the proposed hierarchical controller achieves both robustness and energy efficiency at once. To verify the validity of the proposed controller, simulations are conducted in MATLAB/Simulink environment with a sophisticated model of a vehicle offered by Modelon. In the simulation, two main scenarios introduced in the technical paper on Autonomous Driving Control Benchmark Challenge are dealt with: one aims to address a velocity tracking problem, while the other pursues a reliable lane change on a slippery road.
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16:00-18:00, Paper WeC27.21 | |
>Integrated Motion Control of Four In-Wheel Motor Actuated Vehicles Considering Path Tracking, Ride Comfort, and Energy Efficiency |
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Ryu, Myeongseok | Gwangju Institute of Science and Technology |
Shin, Yuhwan | Gwangju Institute of Science and Technology |
Jang, Seunghoon | GIST |
Choi, Kyunghwan | GIST |
Keywords: Automotive control, Predictive control for nonlinear systems, Optimal control
Abstract: Many efforts have been made to design motion control methods for the path tracking of autonomous vehicles while satisfying vehicle stability. However, considering ride comfort and energy efficiency in motion control methods is still challenging. This poster presents a motion control method for an autonomous electric vehicle, which can consider path tracking, energy efficiency, and ride comfort in an integrated framework. The proposed method consists of a model predictive controller for path tracking, a vertical body motion stabilizer for enhancing ride comfort, and a torque vectoring controller for minimizing energy consumption. The vertical body motion stabilizer determines the longitudinal and lateral acceleration ranges that stabilize the pitch and roll dynamics. These ranges are used as constraints in the model predictive controller that determines optimal values of the steering angle and longitudinal tire forces for minimizing the tracking error. The torque vectoring controller distributes the longitudinal tire forces to each wheel torque and determines the optimal distribution for minimizing energy consumption. The proposed control method is validated using a four-in-wheel motor-actuated vehicle under two challenging scenarios. The validation results demonstrate that the proposed control method provides satisfactory performance in path tracking, ride comfort, and energy efficiency, even under harsh operating conditions with many road bumps.
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16:00-18:00, Paper WeC27.22 | |
>Efficient Hierarchical Robust Predictive Control Strategy for Motion Control of Four In-Wheel Motor Actuated Vehicles |
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Zhang, Yuhang | Beijing Institute of Technology |
Yang, Chao | Beijing Institute of Technology |
Wang, Weida | Beijing Institute of Technology |
Sun, Renfei | Beijing Institute of Technology |
Yuan, Shilong | Beijing Institute of Technology |
Qie, Tianqi | Beijing Institute of Technology |
Keywords: Automotive control, Predictive control for linear systems, Robust control
Abstract: The application of in-wheel motors makes the motion control of electric vehicles more flexible and enables the possibility of vehicle attitude control without active suspension systems. However, the obvious symmetry of the model of four in-wheel motor-driven vehicles (4IWMDVs) leads to the issue of homogeneous cost, resulting in oscillations in control output. Moreover, the substantial computational burden due to the high-dimensional vehicle dynamics system, along with the uncertainties stemming from road conditions and actuator dynamics, also deteriorates the performance of vehicle motion control. To solve the above problems, an efficient hierarchical robust predictive control strategy is proposed for 4IWMDVs. The hierarchical structure is adopted to reduce the dimensions of the individual solving problems. At the upper layer, a robust predictive control method based on the invariant set theory is applied to generate the generalized force and torque for motion control. The maximum robust positive invariant set of predictive errors is calculated, and the feedback compensating law is design to reduce uncertainty influence. Then, at the lower layer, a dimensionality-reduction-aware torque allocation algorithm is developed, leveraged the model symmetry fully. The devised torque allocation algorithm achieves dimension-reduced solution under homogeneous cost condition by the self-adjusting mapping matrix, solving the control oscillation caused by multiple optimal solutions. Besides, the algorithm considers the generalized force and torque constraints while minimizing overall energy consumption and ensuring the reasonable vehicle attitude. To sum up, the proposed robust hierarchical strategy can achieve balance motion control demand and energy consumption for 4IWMDVs. The performance of the proposed strategy is verified to meet the requirements of the benchmark problem for motion control of 4IWMDVs through the Matlab/Simulink-Modelica co-simulation.
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