Keywords:Distributed control, Agents-based systems, Optimization algorithms Abstract: In this paper, we study the optimization problems for a group of agents whose individual objective functions and constraints may depend on the variables of neighboring agents. Several algorithms are proposed based on operator splitting techniques that can iteratively converge to an optimal primal (or dual) solution of the optimization problems. Then, via random coordinate updates, asynchronous implementations of the algorithms are developed with low computation and communication complexity and guaranteed almost sure convergence to an optimal solution. Numerical results are presented to illustrate the proposed algorithms.

Keywords:Hybrid systems, Robust control, Computer-aided control design Abstract: In order to control a system with complex physical dynamics against a temporal specification, we can compute a discrete abstraction of the system dynamics and then solve a game built from the abstraction and the specification. A strategy in this game is then a controller that enforces the satisfaction of the specification. Such games are typically huge, which implies the need to solve them symbolically, i.e., without considering every position in the game separately. Binary decision diagrams (BDDs) are the most commonly used data structure for this purpose, but the BDD of a system's transition relation is typically huge, which limits the scalability of the approach.

In this paper, we present a new approach to implement the enforceable predecessor operator for games represented in BDD form. Solving a game is typically performed by repetitive application of this operator. Our new approach targets system dynamics for which some dimensions are translation invariant, as common in robotics and vehicle control. We avoid the construction of the overall transition relation in the game and instead base the computation on local substitutions of coordinate values in the translation invariant dimensions, which keeps the intermediate result BDDs small.

We perform a comprehensive experimental comparison of the classical enforceable predecessor implementation and our new operator implementation. The results show that our approach reduces game solving times and hence increases the scalability of controller synthesis when employing a physical system abstraction.

Keywords:Linear systems, Optimization, Output regulation Abstract: In this paper the problem of optimizing the output regulation of a weakly dual redundant plant with multiple actuators is addressed from a control theoretic viewpoint. When a system is underactuated, only subsets of the outputs can be independently controlled, while the remaining ones are constrained. With a specific focus on the asymptotic output tracking problem for MIMO systems with periodic references, we investigate the connection between the overall optimal input and the individually optimal controllers that lead to a perfect tracking of each output component. In particular the design of the optimal closed-loop controllers using a dynamic compensator is proposed.

Keywords:Optimization, Optimization algorithms, Uncertain systems Abstract: This paper proposes a novel transformation-proximal bundle algorithmic framework to solve multistage adaptive robust optimization (ARO) problems. Different from existing solution methods, the proposed algorithmic framework partitions recourse decisions into state decisions and local decisions. It applies affine decision rule only to state decision variables and allows local decision variables to be fully adjustable. In this way, the original multistage ARO problem is proved to be transformed into a two-stage ARO problem. The proximal bundle algorithm with the Moreau-Yosida regularization is further developed for the exact solution of the resulting two-stage ARO problem. The transformation-proximal bundle algorithmic framework could generate less conservative solutions compared with the decision rule based approach, while enjoying a high computational efficiency. An application on multiperiod inventory control problem under demand uncertainty is presented to demonstrate the effectiveness and superiority of the proposed algorithm.

Keywords:Stochastic systems, Optimization, LMIs Abstract: In this paper, we address the risk estimation problem where one aims at estimating the probability of violation of safety constraints for a robot in the presence of bounded uncertainties with arbitrary probability distributions. In this problem, an unsafe set is described by level sets of polynomials that is, in general, a nonconvex set. Uncertainty arises due to the probabilistic parameters of the unsafe set and probabilistic states of the robot. To solve this problem, we use a moment-based representation of probability distributions. We describe upper and lower bounds of the risk in terms of a linear weighted sum of the moments. Weights are coefficients of a univariate Chebyshev polynomial obtained by solving a sum-of-squares optimization problem in the offline step. Hence, given a finite number of moments of probability distributions, risk can be estimated in real-time. We demonstrate the performance of the provided approach by solving probabilistic collision checking problems where we aim to find the probability of collision of a robot with a non-convex obstacle in the presence of probabilistic uncertainties in the location of the robot and size, location, and geometry of the obstacle.

Keywords:Networked control systems, Identification, Optimization Abstract: In this paper, we propose a technique for the estimation of the influence matrix in a sparse social network, in which n individual communicate in a gossip way. At each step, a random subset of the social actors is active and interacts with randomly chosen neighbors. The opinions evolve according to a Friedkin and Johnsen mechanism, in which the individuals updates their belief to a convex combination of their current belief, the belief of the agents they interact with, and their initial belief, or prejudice. Leveraging recent results of estimation of vector autoregressive processes, we reconstruct the social network topology and the strength of the interconnections starting from partial observations of the interactions, thus removing one of the main drawbacks of finite horizon techniques. The effectiveness of the proposed method is shown on randomly generation networks.

Keywords:Predictive control for linear systems, Optimal control Abstract: This paper proposes a feedback model predictive control (MPC) strategy for linear time invariant discrete-time systems subject to predictable, persistent and bounded disturbances, and constraints on inputs and states. It is shown that with a sufficiently long prediction horizon, an infinite prediction horizon MPC with an indefinite index function and preview information of bounded disturbances can be approximated by a numerically tractable finite prediction horizon linear state feedback MPC. The proposed control strategy is essentially a non-causal economic MPC and can find its applications in a wide area, where the preview information of disturbance is available and conventional tracking control and regulation control strategies are not suitable, e.g. the energy maximization problem for sea wave energy converters. A numerical simulation is given to demonstrate the efficacy of the proposed control approach.

Keywords:Optimal control, Decentralized control, Power systems Abstract: This paper discusses the optimal output feedback control problem of linear time-invariant systems with additional restrictions on the structure of the optimal feedback control gain. These restrictions include setting individual elements of the optimal gain matrix to zero and making the sum of certain rows of the gain matrix equal to desired values. The paper proposes a method that modifies the standard quadratic cost function to include soft constraints ensuring the satisfaction of these restrictions on the structure of the optimal gain. Necessary conditions for optimality with these soft constraints are derived, and an algorithm to solve the resulting optimal output feedback control problem is given. Finally, a power systems example is presented to illustrate the usefulness of proposed approach.

Keywords:Optimal control, Predictive control for nonlinear systems, Linear parameter-varying systems Abstract: An optimal Restricted Structure Generalized Predictive Control (RS-GPC) control algorithm is introduced for the control of q-LPV discrete-time state-space multivariable systems. The controller may have a one, two or three degree of freedom structure. The feedback, tracking and feedforward controller terms are specified in a restricted structure form. These controller sub-systems are parameterized in terms of a set of pre-specified linear functions and a set of optimal gains, and computed to minimize a predictive control cost-function. The cost-function involves weighted error and control signal costing terms, but also includes novel terms to ensure the magnitude or rate of change of controller gains is not excessive. A valuable feature is that the controller has the performance benefits and advantages of model based control designs, but can be retuned as in classical control structures.

Keywords:Optimal control, Optimization, Optimization algorithms Abstract: The efficacy of the so-called sensitivity function in developing desensitized optimal control schemes is studied. A sensitivity function provides information about the first order variation of the state under parameter variations at a given time instant along a trajectory. It is demonstrated that the sensitivity function can be employed to effectively desensitize either an optimal trajectory or the state at a particular time instant (for example, the final state) along the optimal trajectory. Zermelo’s path optimization problem is chosen to test the theory. Monte- Carlo simulations are carried out, validating the key idea. The limitations of the proposed approach are identified and the possibilities for future work are discussed.

Keywords:Optimal control, Numerical algorithms, Distributed parameter systems Abstract: The sufficient approximate-optimality conditions for optimal control problem governed by Navier-Stokes system of partial differential equations with Navier boundary condition that models the evolution of viscous, incompressible flows is invstigated. An approximate dual dynamic programming approach is proposed and approximate-sufficient optimality conditions in terms of the approximate verification theorem are proved. Essential novelty of the paper is that all inequalities in the approximate dual dynamic programming are treated in a weak form. A numerical algorithm for approximate minimum is proposed.

Keywords:Optimal control, Numerical algorithms Abstract: A Gauss collocation method is developed for solving optimal control problems with convex control constraints. The method has a local exponential convergence rate when the solution of the continuous problem is smooth and the Hamiltonian possesses a convexity property.

Keywords:Agents-based systems, Distributed control, Optimization Abstract: This paper considers the design of a distributed dual-mode extremum seeking control (PIESC) technique for addressing equality constrained resource allocation problems of multi-agent systems in real-time. We address problems where the structure of each agent's resource allocation function is unknown but depends on the entire resource allocation vector. We incorporate dynamics and tackle this problem for a dynamic system. A cooperative approach that permits communication between neighbouring agents to minimize the unknown overall resource allocation function subject to the resource requirement is utilized. A simulation example is included to show the effectiveness of the proposed technique.

Keywords:Agents-based systems, Cooperative control, Distributed control Abstract: Output containment is achieved among linear heterogeneous multi-agent systems (MAS) thanks to the collaborative efforts of all agents, expressed by a communication digraph with nonnegative weights. Generally, state-feedback or output-feedback designs are used in the distributed containment control of MAS, which require the absolute value of state/output of each agent. This paper investigates the output containment of heterogeneous non-introspective MAS on signed digraphs, in the presence of uncertain parameter variations. Nonintrospective agent only has knowledge of relative information with respect to its neighbors, rather than the explicit knowledge about its own state/output. Agents on signed digraphs can have antagonistic interactions, modeled as negative weights on the communication network. To this end, we first formulate a new control problem called the robust bipartite output containment problem (RBOC), which aims at making each follower's output converge to the dynamic convex hull spanned by the outputs and the negative outputs of the leaders. It is proved that the RBOC problem can be solved by making certain signed output containment errors go to zero asymptotically. Then, a dynamic output-feedback control protocol is designed based on internal model principles. Finally, local sufficient conditions are obtained and explicit local design procedures are provided. Numerical simulations are performed to illustrate the proposed RBOC performances on signed communication digraphs.

Keywords:Agents-based systems, Cooperative control, Lyapunov methods Abstract: This paper studies H inf almost state and output synchronizations of homogeneous multi-agent systems (MAS) with partial-state coupling with general linear agents affected by external disturbances. We will characterize when static linear protocols can be designed for state or output synchronization for a MAS such that the impact of disturbances on the network disagreement dynamics, expressed in terms of the H inf norms of the corresponding closed-loop transfer function is reduced to any arbitrarily small value. Meanwhile, the static protocol only needs rough information on the network graph, that is a lower bound for the real part and an upper bound for the modulus of the non-zero eigenvalues of the Laplacian matrix associated with the network graph. Our study focuses on three classes of agents which are squared-down passive, squared-down passifiable via output feedback and squared-down minimum phase with relative degree 1.

Keywords:Agents-based systems Abstract: Game with second-order dynamic agents is explored for the case where the payoff function of each agent is concave and continuously differentiable. Several control laws that stabilize the Nash equilibrium by utilizing only the knowledge of each agent's payoff function are proposed. We use the results from convex optimization to derive our control laws. We illustrate our approach with a numerical example.

Keywords:Automata, Agents-based systems Abstract: This paper proposes a new optimal control synthesis algorithm for multi-robot systems with Linear Temporal Logic (LTL) specifications. Existing planning approaches with LTL specifications rely on graph search techniques applied to a product automaton constructed among the robots. In our previous work, we have proposed a more tractable sampling-based algorithm that builds incrementally trees that approximate the state-space and transitions of the synchronous product automaton and does not require sophisticated graph search techniques. Here, we extend our previous work by introducing bias in the sampling process which is guided by transitions in the Buchi automaton that belong to the shortest path to the accepting states. This allows us to synthesize optimal motion plans from product automata with hundreds of orders more states than those that state-of-the-art methods can manipulate. We also show that the proposed algorithm is probabilistically complete and asymptotically optimal.

Keywords:Agents-based systems, Stability of nonlinear systems, Network analysis and control Abstract: In this paper we propose a novel method to establish stability and convergence to a consensus state for a class of nonlinear discrete-time Multi-Agent System (MAS) which is not based on Lyapunov function arguments. In particular, we focus on a class of discrete-time multi-agent systems whose global dynamics can be represented by sub-homogeneous and order-preserving nonlinear maps. The preliminary results of this paper directly generalize results for sub-homogeneous and order-preserving linear maps which are shown to be the counterpart to stochastic matrices thanks to nonlinear Perron-Frobenius theory. We provide sufficient conditions on local interaction rules among agents to establish convergence to a fixed point and study the consensus problem in this generalized framework as a particular case. Examples to show the effectiveness of the method are provided to corroborate the theoretical analysis. In these examples, some nonlinear interaction protocols are proved to converge to the consensus state without the use of Lyapunov functions.

Keywords:Information technology systems, Quantized systems, Optimization Abstract: We study the problem of maximizing privacy of quantized sensor measurements by adding random variables. In particular, we consider the setting where information about the state of a process is obtained using noisy sensor measurements. This information is quantized and sent to a remote station through an unsecured communication network. It is desired to keep the state of the process private; however, because the network is not secure, adversaries might have access to sensor information, which could be used to estimate the process state. To avoid an accurate state estimation, we add random numbers to the quantized sensor measurements and send the sum to the remote station instead. The distribution of these random variables is designed to minimize the mutual information between the sum and the quantized sensor measurements for a desired level of distortion -- how different the sum and the quantized sensor measurements are allowed to be. Simulations are presented to illustrate our results.

Keywords:Information theory and control, Fault detection, Machine learning Abstract: Data-driven approaches are becoming increasingly crucial for modeling and performance monitoring of complex dynamical systems. Such necessity stems from complex interactions among sub-systems and high dimensionality that render majority of first-principle based methods insufficient. This paper explores the capability of a recently proposed probabilistic graphical modeling technique called spatiotemporal pattern network (STPN) in capturing Granger causality among observations in a dynamical system. In this context, we introduce the notion of Granger-STPN (G-STPN) that leverages the concept of transfer entropy computed in a symbolic domain that can capture Granger causality. However, G-STPN can become significantly more computationally expensive compared to STPN while considering larger memory for a dynamical system. We numerically compare the two frameworks for a real-life anomaly detection problem involving an industrial robot platform.

Keywords:Information theory and control, Network analysis and control, Biological systems Abstract: Reliable information processing is a hallmark of many physical and biological networked systems. In this paper, we propose a novel framework for modelling information transmission within a linear dynamical network. Information propagation is modelled by means of a digital communication protocol that takes into account the realistic phenomenon of inter-symbol interference. Building on this framework, we adopt Shannon information rate to quantify the amount of information that can be reliably sent over the network within a fixed time window. We investigate how the latter information metric is affected by the connectivity structure of the network. Here, we focus in particular on networks characterized by a normal adjacency matrix. We show that for such networks the maximum achievable information rate depends only on the spectrum of the adjacency matrix. We then provide numerical results that suggest that matrix non-normality could benefit information transmission in dynamical networks.

Keywords:Information theory and control, Control over communications, Stochastic systems Abstract: Bode integrals of sensitivity and sensitivity-like functions along with complementary sensitivity and complementary sensitivity-like functions are conventionally used for describing performance limitations of a feedback control system. In this paper, we show that in the case when the disturbance is a wide sense stationary process the (complementary) sensitivity Bode integral and the (complementary) sensitivity-like Bode integral are identical. A lower bound of the continuous-time complementary sensitivity-like Bode integral is also derived and examined with the linearized flight-path angle tracking control problem of an F-16 aircraft.

Keywords:Information theory and control, Statistical learning, Control system architecture Abstract: Target localization is a critical task for mobile sensors and has many applications. However, generating informative trajectories for these sensors is a challenging research problem. A common method uses information maps that estimate the value of taking measurements from any point in the sensor state space. These information maps are used to generate trajectories; for example, a trajectory might be designed so its distribution of measurements matches the distribution of the information map. Regardless of the trajectory generation method, generating information maps as new observations is made is critical. However, it can be challenging to compute these maps in real-time. We propose using convolutional neural networks to generate information maps from a target estimate and motion model in real-time. Simulations show that maps are accurately rendered while offering orders of magnitude reduction in computation time.

Keywords:Emerging control applications, Information theory and control, Control over communications Abstract: It is known that the conventional second law of thermodynamics is not applicable to thermodynamic systems when feedback control is applied to such systems. A generalized form of the second law should be introduced in this case, which contains an additive term that describes the correlation between the microstates and the measurement outcomes. In this study, we consider a situation where a linear stochastic thermodynamic system, which is in contact with a heat bath, is controlled over a noiseless digital channel to evaluate how channel capacity and control performance are interrelated considering the second law of thermodynamics. We show that in this case, the second law of thermodynamics is inclusive of a term that represents channel capacity. We then show that given a fixed value of free energy difference, we can extract a larger amount of work from the system and obtain higher control performance if more channel capacity is used, in the case where an optimal controller and a proper encoder are used in the control system.

Keywords:Distributed control, Autonomous systems, Control of networks Abstract: In this paper we consider the problem of a multi-agent system achieving a formation in the presence of misbehaving or adversarial agents. We introduce a novel continuous time resilient controller to guarantee that normally behaving agents can converge to a formation with respect to a set of leaders. The controller employs a norm-based filtering mechanism, and unlike most prior algorithms, also incorporates input bounds. In addition, the controller is shown to guarantee convergence in finite time. A sufficient condition for the controller to guarantee convergence is shown to be a graph theoretical structure which we denote as Resilient Directed Acyclic Graph (RDAG). Further, we employ our filtering mechanism on a discrete time system which is shown to have exponential convergence. Our results are demonstrated through simulations.

Keywords:Cooperative control, Stability of nonlinear systems, Networked control systems Abstract: Control laws for a multi-agent system to follow level curves of a spatially distributed scalar field generally require sharing field measurements among the agents for gradient estimation. This paper presents a distributed control law that does not rely on the communication of the field measurements nor the estimation of the gradient. Each agent only modulates its speed according to local measurements of the field and relative positions of its neighbors. The distributed control law scales to large swarms with connected undirected visibility graph. Stability is justified in a singular perturbation framework. The efficiency of the control law is validated through simulations demonstrating level curve tracking behaviors of 2-dimensional scalar fields.

Keywords:Optimization algorithms, Agents-based systems, Boolean control networks and logic networks Abstract: Convex Mixed-Integer Program (MIP) has received extensive attention due to its wide applications. This paper proposes a distributed optimization algorithm based on Projected Subgradient Algorithm (PSA) to solve general convex MIPs. We first decouple the feasible region as the intersection of multiple local convex constraints and the relaxed integrality constraints. Then an auxiliary variable vector is assigned to each decoupled constraint with a consensus constraint to keep equivalence. A Distributed Projected Subgradient Algorithm (DPSA) is proposed to solve the reformulated problem. The updates of the auxiliary variables associated with the convex local constraints as well as the integrality constraint are implemented in a parallel way, followed by the gossip step to drive all auxiliary variable sets into consensus. While this algorithm applies to general convex MIPs, special attention is paid to quadratic and linear constraints in order to obtain a closed-form solution for each subproblem. While convergence of such DPSA for convex problems has been studied, the presence of the integrality constraint makes it inapplicable. Consequently, convergence of the proposed DPSA and properties at the converging point under certain assumptions is presented. Numerical results on maximum clique problem are provided to sustain the effectiveness of the proposed algorithm.

Keywords:Distributed control, Power systems, Predictive control for linear systems Abstract: This paper proposes a centralized and a distributed sub-optimal control strategy to maintain in safe regions the real-time transient frequencies of a given collection of buses, and simultaneously preserve asymptotic stability of the entire network. In a receding horizon fashion, the centralized control input is obtained by iteratively solving an open-loop optimization aiming to minimize the aggregate control effort over controllers regulated on individual buses with transient frequency and stability constraints. Due to the non-convexity of the optimization, we propose a convexification technique by identifying a reference control input trajectory. We then extend the centralized control to a distributed scheme, where each subcontroller can only access the state information within a local region. Simulations on a IEEE-39 network illustrate our results.

Keywords:Distributed control, Agents-based systems, Adaptive control Abstract: The problem of time-constrained multi-agent task scheduling and control synthesis is addressed. We assume the existence of a high level plan which consists of a sequence of cooperative tasks, each of which is associated with a deadline and several Quality-of-Service levels. By taking into account the reward and cost of satisfying each task, a novel scheduling problem is formulated and a path synthesis algorithm is proposed. Based on the obtained plan, a distributed hybrid control law is further designed for each agent. Under the condition that only a subset of the agents are aware of the high level plan, it is shown that the proposed controller guarantees the satisfaction of time constraints for each task. A simulation example is given to verify the theoretical results.

Keywords:Chemical process control, Process Control, Optimization Abstract: The efficiency of irrigation systems is critically important for reducing water consumption in agricultural production process, especially with water scarcity nowadays being more and more severe all over the world. Empirical irrigation that often leads to over-watering and results in low yield and water waste should be prevented and substituted by advanced automatic irrigation systems. In this work, we focus on the data-driven real-time irrigation control and propose a model predictive control (MPC)-based approach to achieve desired plant root-zone deficit level given variable precipitation and evapotranspiration as disturbance. To take future weather into irrigation decision making, specialized local weather prediction is realized for local irrigation spots where regional weather forecast is less reliable, and the formulation of a dynamic uncertainty set is introduced to account for prediction errors and used in robust MPC design. The proposed approach is evaluated through a real-world case study in which we demonstrate that the implementation of the data-driven real time irrigation control system effectively facilitates the control of plant root-zone deficit level for local irrigation spots.

Keywords:Chemical process control, Process Control, Optimization Abstract: Model predictive control (MPC) under chance constraints has been a promising solution to complicated control problems subject to uncertain disturbance. However, traditional approaches either require exact knowledge of probabilistic distributions, or rely on massive multi-scenarios that are generated to represent uncertainties. In this paper, a novel approach is proposed based on actively learning a compact high-density region from available data in form of a polytope. This is achieved by adopting the support vector clustering, which has been recently utilized in data-driven robust optimization. A new strategy is developed to calibrate the size of the polytope, which provides appropriate probabilistic guarantee. Finally the optimal control problem is cast as a robust optimization problem, which can be efficiently handled by existing numerical solvers. The proposed method commonly requires less data samples than traditional approaches, and can help reducing the conservatism, thereby enhancing the practicability of model predictive control. The efficacy of the proposed method is verified based on a simulated example.

Keywords:Chemical process control, Robust control, Predictive control for linear systems Abstract: The paper addresses a problem of LMI-based robust MPC design for a neutralization plant. In a laboratory continuous stirred tank reactor (CSTR) ran the neutralization reaction of acetic acid and sodium hydroxide. The controlled output was pH value of the reaction mixture and the manipulated variable was the volumetric flow rate of acid. The integral action was designed to remove a steady-state error in set-point tracking. An uncertain mathematical model of the controlled process was identified from data measured in multiple step responses. Extensive laboratory experimental analysis was performed to tune the weighting matrices of an objective function to optimize the control performance of robust MPC for a laboratory plant. Control performance of the reactor was evaluated using analytical quality criteria.

Keywords:Control applications, Adaptive control, Process Control Abstract: The complicated physical and chemical reactions in the smelting process and the blast furnace (BF) internal complex operating environment have led to the difficulty of establishing the model-based controllers. Therefore, model free control methods meet the actual needs of the engineering projects. However, due to the sparse characteristic of the molten iron quality (MIQ) data in BF ironmaking, traditional model free adaptive control based MIQ control methods cannot control such a complex industrial system with strong nonlinear time-varying dynamics. In this paper, an extended compact form dynamic linearization (CFDL) based model free adaptive predictive control (MFAPC) scheme (CFDL-MFAPC) is proposed for multivariate MIQ indices by generalizing the CFDL-MFAPC method only for SISO system to MIMO system. Two groups of verified experiments are performed to evaluate the performance of the controller. The results show that the proposed method not only has better control performance than the compared traditional CFDL based model free adaptive control method and data-driven model predictive control (MPC) method, but also can guarantee the bounded-input bounded- output stability of the MIQ output control system for BF ironmaking process.

Keywords:Distributed parameter systems, Estimation, Process Control Abstract: In this paper, we present a model of reservoir pressure dynamics in view of estimating influx during drilling. The distributed nature of the model is shown to have an important impact on the transient behaviour of pressure and flow rate when a liquid influx is present. Then, two observers, designed using a backstepping approach, are used to estimate the distributed reservoir pressure as well as wellbore states. The relevance of the approach is illustrated in industry-relevant simulations.

Keywords:Manufacturing systems and automation, Process Control, Machine learning Abstract: In the manufacturing industry, it is crucial to identify process variables that strongly affect product quality so that high product quality is maintained. Conventional methods based on variable importance have not necessarily shown good results. In the present work, we propose a new method to estimate variable importance. First, we construct a regression model for predicting product quality from process variables by using support vector regression or gaussian process regression, then we compute variable importance from the sensitivity of the model. It is demonstrated through a numerical example and an industrial case study that the proposed method outperforms conventional methods such as partial least squares and random forest.

Keywords:Predictive control for nonlinear systems, Large-scale systems, Numerical algorithms Abstract: Large-scale nonlinear model predictive control (NMPC) often relies on real-time solution of optimization problems that are constrained by partial differential equations (PDEs). However, the size and complexity of the underlying PDEs present significant computational challenges. In this regard, the development of fast, efficient and scalable PDE-constrained optimization solvers remains central to large-scale NMPC. As a contribution in this direction, this paper proposes a new efficient preconditioned iterative scheme for optimal control of large-scale time-dependent diffusion-reaction problems with nonlinear reaction kinetics. The scheme combines a custom-made high-order spectral Petrov-Galerkin (SPG) method with a new preconditioner tailored for the linear-quadratic control problems that underly Sequential Quadratic Programming (SQP) methods. The preconditioner is matrix-free and amenable to parallelization. To demonstrate efficiency, a case study applies the SPG scheme to control solid fuel ignition (SFI) processes. In the absence of control, such processes lead to unstable systems that naturally exhibit finite-time blow-up phenomena. Open-loop simulations demonstrate the ability of the SPG scheme to efficiently control SFI processes, independently of the problem size and the model parameters.

Keywords:Predictive control for nonlinear systems, Optimization, Automotive control Abstract: In this paper we present a convex formulation of the Model Predictive Control (MPC) optimisation for energy management in hybrid electric vehicles, and an Alternating Direction Method of Multipliers (ADMM) algorithm for its solution. We develop a new proof of convexity for the problem that allows the nonlinear dynamics to be modelled as a linear system, then demonstrate the performance of ADMM in comparison with Dynamic Programming (DP) through simulation. The results demonstrate up to two orders of magnitude improvement in solution time for comparable accuracy against DP.

Keywords:Predictive control for nonlinear systems, Robust control Abstract: Within this paper we consider time optimal robust model predictive control of a robot arm that carries a glass plate. To this end, we propose a respective model and constraints on the strains in the extremal fibers of the glass plate based on the section modulus and tensile strength to avoid breakages. In order to synthesize a control strategy, we propose to use a tailored ellipsoidal tube based model predictive control scheme, which can deal with the highly nonlinear constraints of the glass plate. The necessity of modeling the strains in the fibers as well as the properties of the proposed robust control method are illustrated in a realistic case study for a KUKA youBot model, which is simulated in the presence of process noise.

Keywords:Predictive control for nonlinear systems, Optimization, Uncertain systems Abstract: This paper proposes a computationally efficient algorithm for robust multistage model predictive control (MPC). In multistage scenario MPC, the evolution of uncertainty in the prediction horizon is represented via a scenario tree. The resulting large-scale optimization problem can be decomposed into several smaller subproblems where, for example, each subproblem solves a single scenario. Since the different scenarios differ only in the uncertain parameters, the distributed scenario MPC problem can be cast as a parametric nonlinear programming (NLP) problem. By using the NLP sensitivity, we do not need to solve all the subproblems as full NLPs. Instead they can be solved exploiting the parametric nature by a path-following predictor-corrector algorithm that approximates the NLP. This results in a computationally efficient multistage scenario MPC framework. Simulation results show that the sensitivity-based distributed multistage MPC provides a very good approximation of the fully centralized scenario MPC.

Keywords:Predictive control for nonlinear systems, Robust control, Uncertain systems Abstract: This paper presents a robust model predictive controller for discrete-time nonlinear systems, subject to state and input constraints and unknown but bounded input disturbances. The prediction model uses a linearized time-varying version of the original discrete-time system. The proposed optimization problem includes the initial state of the current nominal model of the system as an optimization variable, which allows to guarantee robust exponential stability of a disturbance invariant set for the discrete-time nonlinear system. From simulations, it is possible to verify the proposed algorithm is real-time capable, since the problem is convex and posed as a quadratic program.

Keywords:Predictive control for nonlinear systems, Optimization algorithms, Markov processes Abstract: This paper proposes an algorithm to maximize the power extraction in wind turbine arrays given a varying external wind. Wind turbine arrays, or wind farms, can be viewed as large coupled networks, for which the application of traditional optimization techniques are impractical. In this paper we present an extension to a dynamic programming algorithm previously developed under the condition of uniform wind and extend it to higher-fidelity wind models. We then update our algorithm for under dynamically evolving wind conditions. Using a Markov chain derived from real-world data, the underlying optimization problem is reformulated in a Model Predictive Control framework. Simulation results are discussed, which demonstrate our algorithm provides improved performance compared to prior results.

Keywords:Systems biology, Machine learning, Uncertain systems Abstract: A key objective of systems biology is to understand how the uncertainty in parameter values affects the responses of biochemical networks. Variance-based sensitivity analysis is a powerful approach to address this question. However, commonly used implementations based on (Quasi-) Monte Carlo require a very large number of model evaluations, and are thus impractical for computationally expensive models. Here, we present an alternative method for variance-based sensitivity analysis that uses Gaussian process regression. Thanks to the appealing mathematical properties of Gaussian processes, we are able to derive exact analytic formulas for the required sensitivity indices. In this way our approach yields more accurate estimates with significantly less computational cost compared to conventional methods, as we demonstrate for a nonlinear model of a bacterial signaling system.

Keywords:Systems biology, Metabolic systems, Simulation Abstract: Size control is usually exerted in living cells by properly sensing the external inputs (like nutrients) and, accordingly, by activating the metabolic pathways in order to set and adjust their own growth rate. In this framework, experimental results have recently highlighted the role of metabolic noise, usually neglected because of its averaging over the great deal of reactions involved in metabolic networks. In this note, a basic model of the interplay among metabolic enzymes activity, resource allocation and growth rate is introduced. A noise source is supposed to affect the enzymatic activity. The model includes a feedforward action of the resource on the enzyme dynamics (modulated by growth), as well as a feedback of the enzyme on the resource production rate. A Stochastic Hybrid System formulation is exploited to investigate how the noise propagates through the metabolic pathway. Model-based results support the hypothesis that fluctuations in the enzyme production perturb cellular growth, and not vice versa, because of an apparent delay in the cross-correlation function. This result is coherent with single-cell recent experimental results.

Keywords:Systems biology, Cellular dynamics, Biological systems Abstract: How living cells employ counting mechanisms to regulate their numbers or density is a long-standing problem in developmental biology that ties directly with organism or tissue size. Diverse cells types have been shown to regulate their numbers via secretion of factors in the extracellular space. These factors act as a proxy for the number of cells and function to reduce cellular proliferation rates creating a negative feedback. It is desirable that the production rate of such factors be kept as low as possible to minimize energy costs and detection by predators. Here we formulate a stochastic model of cell proliferation with feedback control via a secreted extracellular factor. Our results show that while low levels of feedback minimizes random fluctuations in cell numbers around a given set point, high levels of feedback amplify Poisson fluctuations in secreted-factor copy numbers. This trade-off results in an optimal feedback strength, and sets a fundamental limit to noise suppression in cell numbers with short-lived factors providing more efficient noise buffering. We further expand the model to consider external disturbances in key physiological parameters, such as, proliferation and factor synthesis rates. Intriguingly, while negative feedback effectively mitigates disturbances in the proliferation rate, it amplifies disturbances in the synthesis rate. In summary, these results provide unique insights into the functioning of feedback-based counting mechanisms, and apply to organisms ranging from unicellular prokaryotes and eukaryotes to human cells.

Keywords:Systems biology, Biological systems Abstract: Engineering microbial consortia is an important new frontier for synthetic biology given its efficiency in performing complex tasks and endurance to environmental uncertainty. Most synthetic circuits regulate populational behaviors via cell-to-cell interactions, which are affected by spatially heterogeneous environments. Therefore, it is important to understand the limits on controlling system dynamics and provide a control strategy for engineering consortia under spatial structures. Here, we build a network model for a fractional population control circuit in two-strain consortia, and characterize the cell-to-cell interaction network by topological properties, such as symmetry, locality and connectivity. Using linear network control theory, we relate the network topology to system output's tracking performance. We analytically and numerically demonstrate that the minimum network control cost for good tracking depends on locality difference between two cell population's spatial distributions and how strongly the controller node contributes to interaction strength. To realize a robust consortia, we can manipulate the environment to form a strongly connected network. Our results ground the expected cell population dynamics in its spatially organized interaction network, and inspire directions in cooperative control in microbial consortia.

Keywords:Systems biology, Cellular dynamics, Metabolic systems Abstract: Recent advances in modeling bacterial cell functioning have deeply renewed questions about bioprocess design and opens the way towards the development of computer aided design (CAD) for strains. This article aims at explaining and exploring the consequences opened by the new cell models, investigating the questions related to the biological implementation of optimal strategies and in conclusion the possible role of the complex regulatory network in the retuning of the strain.

Keywords:Control of networks, Systems biology, Algebraic/geometric methods Abstract: Recent advances in the study of artiﬁcial and biological neural networks support the power of dynamic representations–computing with information stored as nontrivial limit-sets rather than ﬁxed-point attractors. Understanding and manipulating these computations in nonlinear networks requires a theory of control for abstract objective functions. Towards this end, we consider two properties of limit-sets: their topological dimension and orientation (covariance) in phase space and combine these abstract properties into a single well-deﬁned objective: conic control-invariant sets in the derivative space (i.e., the vector ﬁeld). Real-world applications, such as neural-medicine, constrain which control laws are feasible with less-invasive controllers being preferable. To this end, we derive a feedback control-law for conic invariance which corresponds to constrained restructuring of the network connections as might occur with pharmacological intervention (as opposed to a physically separate control unit). We demonstrate the ease and efﬁcacy of the technique in controlling the orientation and dimension of limit sets in high-dimensional neural networks.

Keywords:Sensor networks, Estimation, Game theory Abstract: In this paper, we consider a nonzero-sum dynamic game that arises in a remote sensing system with a sensor, an encoder, a decoder, and adversarial intervention. At each time step, the sensor makes a measurement on the state of a stochastic process, and then it decides whether to transmit the measurement or not. If the sensor decides to transmit the measurement, it sends the measurement to the encoder, which then transmits an encoded message to the decoder over an additive noise channel. The decoder generates a real-time estimate on the state of the stochastic process. In this scenario, the cost associated with the remote sensing system consists of a charge for the transmissions made by the sensor, a charge for the encoding power consumed by the encoder, and a charge for the estimation error caused by the decoder. The components of the remote sensing system have the common objective of minimizing this cost. On the other hand, the additive channel noise is generated by an adversary, which is charged the power of the noise and is rewarded the error of the estimated state. Under some technical assumptions, we obtain a Nash equilibrium solution to this nonzero-sum dynamic game.

Keywords:Game theory, Markov processes, Stochastic optimal control Abstract: We consider an environment where many players need to decide whether to buy a certain product (or adopt a trend) or not. The product is either good or bad, but its true value is not known to the players. Instead, each player has his own private information on the quality of the product. Each player can observe the previous actions of other players and deduce the quality of the product. A player can only buy the product once. In contrast to the existing literature on informational cascades, in this work players get more than one opportunity to act. In each turn, a player is chosen uniformly at random from all players and can decide to buy or not to buy. His utility is the total expected discounted reward, and thus myopic strategies may not be best responses. We provide a characterization of structured perfect Bayesian equilibria (PBE) with non-myopic strategies through a fixed-point equation of dimensionality that grows only polynomially with the number of players. Based on this characterization we study informational cascades and show that they happen with high probability for a large number of players. Furthermore, only a small portion of the total information in the system is revealed before a cascade occurs.

Keywords:Optimization algorithms, Game theory, Optimization Abstract: Submodular maximization is an important problem with many applications in engineering, computer science, economics and social sciences. Since the problem is NP-Hard, a greedy algorithm has been developed, which gives an approximation within 1/2 of the optimal solution. This algorithm can be distributed among agents, each making local decisions and sharing that decision with other agents. Recent work has explored how the performance of the distributed algorithm is affected by a degradation in this information sharing. This work introduces the idea of strategy in these networks of agents and shows the value of such an approach in terms of the performance guarantees that it provides. In addition, an optimal strategy that gives such guarantees is identified.

Keywords:Transportation networks, Autonomous systems, Fault detection Abstract: Vehicle-to-Infrastructure (V2I) communications are increasingly supporting highway operations such as electronic toll collection, carpooling, and vehicle platooning. In this paper we study the incentives of strategic misbehavior by individual vehicles who can exploit the security vulnerabilities in V2I communications and negatively impact the highway operations. We consider a V2I-enabled highway segment facing two classes of vehicles (agent populations), each with an authorized access to one server (subset of lanes). Vehicles are strategic in that they can misreport their class (type) to the system operator and get an unauthorized access to the server dedicated to the other class. This misbehavior causes additional congestion externality on the compliant vehicles, and thus, needs to be deterred. We focus on an environment where the operator is able to inspect the vehicles for misbehavior. The inspection is costly and successful detection incurs a fine on the misbehaving vehicle. We formulate a signaling game to study the strategic interaction between the vehicle classes and the operator. Our equilibrium analysis provides conditions on the cost parameters that govern the vehicles' incentive to misbehave or not. We also determine the operator's equilibrium inspection strategy.

Keywords:Traffic control, Game theory, Transportation networks Abstract: It is known that in traffic systems, less information can lead to better social welfare. This paper studies how to sequentially reveal traffic information to drivers to minimize social cost. We model this game as a multi-stage Stackelberg game between a designer, who sends public messages about traffic situation to drivers, and drivers, who can help improve the designer's observations. This paper studies the belief systems and the optimal strategies of both players, shows that drivers have a stationary optimal strategy, and provides a recursive formula to compute the designer's optimal strategy. Our simulation results indicate that feedback information from drivers help reduce total social cost and refine their own belief. In some cases, the designer broadcasts confusing information such that more drivers choose the congested path, which leads to more accurate future observation of the designer. In this way, the designer gains better future social welfare by sacrificing a little current social welfare.

Keywords:Optimal control, Cooperative control, Game theory Abstract: The context of graphical games is employed to solve the cooperative control problem for multi-agent systems interacting on graphs. Together with the need to have faster solution mechanisms urged for new approaches that employ the Dual Heuristic and Action Dependent Dual Heuristic Programming. This class of gradient-based solutions undergoes two main challenges. First, they have to use complex update expressions for the solving gradient-based structures. Second, they may overlook the local neighborhood information, if simpler costate expressions are enforced. A novel approach based on Action Dependent Dual Heuristic Programming is developed to solve the dynamic graphical games and to handle the aforementioned concerns. This adaptive learning approach is implemented online using means of value iteration and neural networks. The approximation of the optimal policy does not have priori knowledge about the agents' dynamics, while the value function gradient approximation is shown to depend only on the drift dynamics of the agents. The convergence results of the adaptive learning approach are highlighted by simulation example.

Keywords:Optimization algorithms, Networked control systems, Machine learning Abstract: This paper extends our recently proposed distributed optimization algorithm to the time-varying graphs. The striking feature of the algorithm is that each node only uses binary relative state information from its neighbors. Different from the stochastically time-varying case, the powerful tool of the stochastic approximation theory is no longer applicable here. We show that if the time-varying graphs are uniformly jointly connected, each node of the algorithm asymptotically converges to some common optimal solution of the optimization problem. We also include simulation examples to validate our results.

Keywords:Stochastic optimal control, Robust control, Learning Abstract: In stochastic control applications, typically only an ideal model (controlled transition kernel) is assumed and the control design is based on the given model, raising the problem of performance loss due to the mismatch between the assumed model and the actual model. Toward this end, we study continuity properties of discrete-time stochastic control problems with respect to system models (i.e., controlled transition kernels) and robustness of optimal control policies designed for incorrect models applied to the true system. We study both fully observed and partially observed setups under an infinite horizon discounted expected cost criterion. We show that continuity and robustness cannot be established the under weak convergence of transition kernels in general, but that the expected induced cost is robust under total variation in that it is continuous in the mismatch of transition kernels under convergence in total variation. By imposing further assumptions on the measurement models and on the kernel itself, we show that the optimal cost can be made continuous under weak convergence of transition kernels as well. Using these continuity properties, we establish convergence results and error bounds due to mismatch that occurs by the application of a control policy which is designed for an incorrectly estimated system model to a true model, thus establishing positive and negative results on robustness. Compared to the existing literature, we obtain refined robustness results that are applicable even when the incorrect models can be investigated under weak convergence and setwise convergence criteria (with respect to a true model), in addition to the total variation criteria. These lead to practically important results on empirical learning in (data- driven) stochastic control since often, in many applications, system models are learned through training data.

Keywords:Machine learning, Statistical learning, Learning Abstract: We study the finite-sample performance of batch actor-critic algorithm for reinforcement learning with nonlinear function approximations. Specifically, in the critic step, we estimate the action value function corresponding to the policy of the actor within some parametrized function class, while in the actor step, the policy is updated using the policy gradient estimated based on the critic, so as to minimize the objective function defined as the expected value of discounted cumulative rewards. Under this setting, for the parameter sequence created by the actor steps, we show that the gradient norm of the objective function at any limit point is close to zero up to some fundamental error. In particular, we show that the error corresponds to the statistical rate of policy evaluation with nonlinear function approximations. For the special class of linear functions and when the number of samples goes to infinity, our result recovers the classical convergence results for the online actor-critic algorithm, which is based on the asymptotic behavior of two-time-scale stochastic approximation.

Keywords:Optimization algorithms, Computational methods, Learning Abstract: Delaunay-based derivative-free optimization (∆-DOGS) is an efficient and provably-convergent global optimiza-tion algorithm for problems with computationally-expensivefunction evaluations, including cases for which analytical expressions for the objective function may not be available.∆-DOGS belongs to the family of response surface methods(RSMs), and suffers from the typical “curse of dimensionality”, with the computational cost increasing quickly as the numberof design parameters increases. As a result, the number of design parameters n in ∆-DOGS is typically limited to n less than 10. To improve performance for higher-dimensional problems, thispaper proposes a combination of derivative-free optimization, seeking the global minimizer of a successively-refined surrogate model of the objective function, and an active subspace method,detecting and exploring preferentially the directions of mostvariability of the objective function. The contribution of otherdirections to the objective function is bounded by a smallconstant. This new algorithm iteratively applies ∆-DOGS to seek the minimizer on the d-dimensional active subspace that has most function variation. Inverse mapping is used to project data from the active subspace back to full-model for evaluating function values. This task is accomplished by solving a related inequality constrained problem. Test results indicate that the resulting strategy is highly effective on a handful of model optimization problems.

Keywords:Machine learning, Learning, Iterative learning control Abstract: Many real-world tasks on practical control systems involve the learning and decision-making of multiple agents, under limited communications and observations. In this paper, we study the problem of networked multi-agent reinforcement learning (MARL), where multiple agents perform reinforcement learning in a common environment, and are able to exchange information via a possibly time-varying communication network. In particular, we focus on a collaborative MARL setting where each agent has individual reward functions, and the objective of all the agents is to maximize the network-wide averaged long-term return. To this end, we propose a fully decentralized actor-critic algorithm that only relies on neighbor-to-neighbor communications among agents. To promote the use of the algorithm on practical control systems, we focus on the setting with continuous state and action spaces, and adopt the newly proposed expected policy gradient to reduce the variance of the gradient estimate. We provide convergence guarantees for the algorithm when linear function approximation is employed, and corroborate our theoretical results via simulations.

Keywords:Agents-based systems, Machine learning, Cooperative control Abstract: In this paper, we study a problem of learning a linear regression model distributively with a network of N interconnected agents in which each agent can deploy an online learning algorithm to adaptively learn the regression model using its private data. The goal of the problem is to devise a distributed algorithm, under the constraint that each agent can communicate only with its neighbors depicted by a connected communication graph, which enables all N agents converge to the true model, with a performance comparable to that of conventional centralized algorithms. We propose a differentially private distributed algorithm, called emph{private gossip gradient descent}, and establish epsilon-differential privacy and OBigl (sqrt{frac{log^2 t }{epsilon (1-lambda_2)N t}};Bigr) convergence, where lambda_2 is the second largest eigenvalue of the expected gossip matrix corresponding to the communication graph.

Keywords:Autonomous vehicles, Cooperative control, Automotive control Abstract: The problem of coordinating automated vehicles at intersections can be formulated as an optimal control problem which is inherently difficult to solve, due to its combinatorial nature. In this paper, we propose a two-stage approximation algorithm based on a previously presented decomposition. The procedure (a) first solves a Mixed Integer Quadratic Program (MIQP) to compute an approximate solution to the combinatorial part of the problem, i.e. the order in which the vehicles cross the intersection; then (b), solves a Nonlinear Program (NLP) for the optimal state and control trajectories. We demonstrate the performance of the algorithm through extensive simulation, and show that it greatly outperforms the natural First-Come-First-Served heuristic.

Consejo Superior De Investigaciones Científicas (CSIC)

Keywords:Variational methods, Algebraic/geometric methods, Autonomous vehicles Abstract: In this article we introduce a variational approach to collision avoidance of multiple agents evolving on a Riemannian manifold and derive necessary conditions for extremals. The problem consists of finding non-intersecting trajectories of a given number of agents, among a set of admissible curves, to reach a specified configuration, based on minimizing an energy functional that depends on the velocity, covariant acceleration and an artificial potential function used to prevent collision among the agents.

Keywords:Autonomous vehicles, Biologically-inspired methods, Robust adaptive control Abstract: Synchronization is a fundamental function of swarm systems in nature and can be understood as a model of coupled oscillators. Even for manmade complex systems, such as an automated guided vehicles (AGVs) system in factories, synchronization is also important to enable temporal coordination of AGVs. In the present papter, we propose a new control law for synchronization of coupled relaxation oscillators and apply it to AGV dispatch control. Our law modulates the threshold of each oscillator, which is a model of a cellular production system. We analyze the stability of the system controlled by the proposed law. It is shown that the phase dynamics of the controlled system can be reduced to those of the Winfree-Kuramoto model. In addition, on the basis of a stability analysis, we produce a design procedure of the controller and verify the procedure by numerical simulation.

Keywords:Autonomous vehicles, Predictive control for linear systems, Distributed control Abstract: Heavy duty vehicle (HDV) platooning has been widely accepted as a solution to reduce fuel consumption and traffic congestion. However, the control strategy for HDV platoons interacting with other vehicles is not yet well established. This work presents a new framework for handling the requests of passenger vehicles (PV) plugging in or out of an HDV platoon. It consists of three main steps. First, the basic cruising control of the platoon is achieved by a distributed model predictive control (DMPC) scheme. Second, redesign of controllers ensures the stability of closed loop Plug and Play (P&P) operation. Finally, a transition phase to steady-states guarantees the feasibility of the newly synthesized controllers. Additionally for the plug-in case, we propose a novel approach of Formation Coordinator that determines the optimal location at which the redesigned controller has the best initial feasibility. The performance of the proposed control framework is illustrated on a multi-vehicle platooning system.

Keywords:Autonomous vehicles, Adaptive control, Fault tolerant systems Abstract: In this paper, we develop an adaptive control algorithm for addressing security for a class of networked vehicles that comprise n human-driven vehicles sharing kinematic data and an autonomous vehicle in the aft of the vehicle formation receiving data from the preceding vehicles by wireless vehicle-to-vehicle communication devices. Specifically, we develop an adaptive controller for mitigating time-invariant, state-dependent adversarial sensor and actuator attacks while guaranteeing uniform ultimate boundedness of the closed-loop networked system. The effectiveness of the proposed approach is demonstrated by an illustrative numerical example involving a platoon of connected vehicles.

Keywords:Autonomous vehicles, Robust adaptive control, Lyapunov methods Abstract: This paper presents a geometric adaptive control scheme for a quadrotor unmanned aerial vehicle, where the effects of unknown, unstructured disturbances are mitigated by a multilayer neural network that is adjusted online. The stability of the proposed controller is analyzed with Lyapunov stability theory on the special Euclidean group, and it is shown that the tracking errors are uniformly ultimately bounded with an ultimate bound that can be abridged arbitrarily. A mathematical model of wind disturbance on the quadrotor dynamics is presented, and it is shown that the proposed adaptive controller is capable of rejecting the effects of wind disturbances successfully. These are illustrated by numerical examples.

Keywords:Networked control systems, Cooperative control Abstract: In this letter, we establish a connection between cooperative control of passivity-short systems, and the regularization of a pair of dual network optimization problems. We build upon existing works that established, under a passivity requirement, an equivalence between the steady-state behavior of diffusively-coupled network system and the solutions to a pair of convex-dual optimization problems. We show that when the agents are passivity-short, the resulting optimization problems are no-longer convex. By introducing a regularization term to the problem, we then establish that this corresponds to a feedback passivation of each system via an appropriately chosen linear output-feedback gain. We also obtain conditions on the regularization term such that the resultant closed system possess the so-called maximally equilibrium-independent passivity property and exhibits a solution to their network-level interactions. Finally, we illustrate theoretical results with two case studies.

Keywords:Networked control systems, Estimation Abstract: Consider that a remote estimator seeks to estimate the state of a non-collocated discrete-time finite-dimensional linear time-invariant plant that is persistently excited by process noise. A communication link attempts to relay the state of the plant to the estimator whenever it receives a transmission request. The link experiences packet-drops and has an (action-dependent) state that is influenced by the history of current and past requests. A controlled Markov chain models this dependence and a given function of the link's state governs the packet-drop probability. Every randomized stationary transmission policy is specified by a function that determines the probability of a transmission request in terms of the link's state. The article focuses on the design of these policies. Two theorems provide necessary and sufficient conditions for the existence of a randomized stationary policy that stabilizes the estimation error, in the second-moment sense. They also show that it suffices to search for deterministic stabilizing policies and identify an important case in which the search can be further narrowed to threshold policies.

Keywords:Networked control systems, Stability of hybrid systems, Observers for nonlinear systems Abstract: We study the design of state observers for non-linear networked control systems (NCSs) that are implemented over WirelessHART (WH). WH is a wireless communication protocol for process automation applications. It is characterised by its multi-hop structure, slotted communication cycles, and simultaneous transmission over different frequencies. We present a solution based on the emulation approach. That is, given an observer designed with a specific stability property in the absence of communication constraints, we implement it over a WH network and we provide sufficient conditions on the latter, to preserve the stability property of the observer. In particular, we provide explicit bounds on the maximum allowable transmission interval. We assume that the plant dynamics and measurements are affected by noise and we guarantee an input-to-state stability property for the corresponding estimation error system.

Keywords:Networked control systems, Lyapunov methods, Stability of hybrid systems Abstract: This paper employs the hybrid-systems-with-memory formalism to investigate transmission intervals and delays that provably stabilize Networked Control Systems (NCSs). We consider nonlinear time-varying plants and controllers with variable discrete and distributed input, output and state delays along with nonconstant discrete and distributed network delays. Nominal system L2-stability, Uniformly Globally Exponentially Stable (UGES) scheduling protocols and upper bounds of network-induced output error dynamics are brought together to infer Uniform Global pre-Asymptotic Stability (UGpAS) of the closed-loop system via Lyapunov-Krasovskii arguments. In other words, we supplant the Lyapunov-Razumikhin conditions and trajectory-based small-gain theorem with linear L2-gains arguments, featured in our previous works, by Lyapunov-Krasovskii functionals to prove UGpAS of interconnected hybrid systems with memory. The selected methodology allows for more general delays (e.g., input/output/state discrete and distributed delays) and output error dynamics (e.g., multiple discrete and distributed delays) as well as less conservative estimates of Maximally Allowable Transfer Intervals (MATIs). Our results are applicable to control problems with output feedback and the so-called large delays. In addition, model-based estimators between two consecutive transmissions, rather than merely the Zero-Order Hold (ZOH) strategy, are allowed for in order to prolong MATIs. Lastly, a numerical example involving an observer-predictor-based Linear Time-Invariant (LTI) control system is provided.

Keywords:Networked control systems, Hybrid systems, Sensor networks Abstract: Network systems are one of the most active research areas in the engineering community as they feature a paradigm shift from centralized to distributed control and computation. When dealing with network systems, a fundamental challenge is to ensure their functioning even when some of the network nodes do not operate as intended due to faults or attacks. The objective of this paper is to address the problem of resilient consensus in a context where the nodes have their own clocks, possibly operating in an asynchronous way, and can make updates at arbitrary time instants. The results represent a first step towards the development of resilient event-triggered and self-triggered coordination protocols.

Keywords:Networked control systems, Distributed control, Optimal control Abstract: In this paper we consider a finite-horizon optimization problem with a distributed control policy. The local outputs are sent to a local controller in an intermittent fashion. As a consequence the controller has access to sensor information only if it is sent by the associated local scheduler or by neighboring controllers. We consider generalized event-triggered schedulers (which includes time-triggered schedulers as a special case, where time-instants define the events). This leads to an event-dependent information structure available at each local controller. As a result, the information structure changes, which potentially leads to a non-convex control design problem. For any event-triggered sensing topology, we give a necessary and sufficient condition for convexity of the optimal control problem, by using the quadratic invariance (QI) property. Furthermore, we provide an online algorithm that adapts the communication topology among the local controllers and guarantees a step-by-step QI, which translates to a global QI.

Keywords:Linear systems, Robust control Abstract: Bruce Francis’s research in the 1980’s was focused on H-inifinity theory, especially on the synthesis of optimal controllers in this norm. He realised that the problem could be addressed using interpolation theory from within the general area of mathematics of operator theory. His lecture notes and books were central to the development of the area and collaboration between operator theorists and the control community. In due course this led to the development of the state-space approach and the two Riccati equation solution presented by Bruce and the present authors. This joint presentation will outline these developments from an historical and mathematical perspective.

Keywords:Linear systems, Sampled-data control Abstract: Bruce Francis pioneered the extension of H^infty type control to sampled data systems. The idea was to apply a lifting technique to solve two very important optimal control problems. This gives a complete solution to the problem of controller design that meets constraints on the L^2 induced norm of the sampled-data system to be less than some prespecified level. Francis and collaborators also showed that the lifting technique is applicable in fact to all norm-based optimization problems, in particular to sampled-data quadratic regulation and optimal filtering problems as well as to certain types of structured uncertainty problems including gain margin.

Keywords:Stochastic systems, Autonomous systems Abstract: Besides the technical content behind the title, Bruce Francis left a legacy of strong collaborations and cooperation at various levels with a number of colleagues and friends. On the technical side, the idea of interacting agents became increasingly important at the turn of the century, and Bruce's ideas and work created an important niche. Closely related, is the body of work of Bruce Francis on cyclic pursuit problems that have strong connections to the curve shortening problem in geometric curve evolution theory. In the talk, we will attempt to highlight important ideas and subsequent developments, as well as reminisce on the impact of Bruce' thought and influence to some of us who were his contemporaries.

Keywords:Linear systems, Sampled-data control Abstract: Bruce Francis made a first impact on sampled-data systems by initiating the modern approach to sampled-data systems. He further proceeded to apply the modern method to signal processing. This talk summarizes the crucial difference between the modern and classical designs in terms of some design examples, and also review some basic ideas he pursued in applying the method to signal processing.

Keywords:Linear systems, Robust control Abstract: In his Ph.D. thesis, Bruce Francis proved the well-known "internal model principle," showing that in order to track an unstable reference signal in the face of plant variations, the controller must incorporate an internal model of the unstable signal. This formulation was in state space, and thus did not accommodate order uncertainty. In a later paper published in 1977. he expanded this idea to cover order uncertainty, but with perfect knowledge of the unstable part of the plant. Later, in 1981, Bruce and the speaker derived the internal model in full generality, namely, the case where the plant is perturbed in the graph topology. This talk will cover the historical evolution of this fundamental result in feedback control theory.

Keywords:Distributed control, Agents-based systems Abstract: Based on a combination of consensus and conservation, the paper develops a distributed update for solving linear equations by multi-agent networks, in which each agent only knows just a small part of the overall equation and can only communicate with its nearby neighbors. In the proposed distributed update, each agent knows only two scalar entries of the defining matrix of the overall equation and controls just two scalar states. Given the underlying networks to be connected and undirected, the proposed distributed update enables agents to collaboratively achieve a solution to the overall equation. Analytical proof is provided for the exponential convergence of the proposed update, which is also validated by numerical simulations.

Keywords:Distributed control, Sensor networks Abstract: Monitoring the state of communications in a distributed multilayer network with differing node capabilities requires the maintenance of a backbone which is a connected edge dominating set. In this paper, we present distributed algorithms that can efficiently create such multilayer resilient connected edge-dominating sets. After establishing the complexity of the problem and our proposed heuristics, we experimentally compare their performance while varying multiple characteristics of the underlying networks.

Keywords:Distributed control, Optimal control, Neural networks Abstract: In this paper, continuous and event-sampled approximate optimal distributed control schemes for an interconnected system, with nonlinear subsystem dynamics and strong interconnections, are presented. The control design problem for the interconnected system is reformulated as an N-player cooperative nonzero-sum differential game wherein the control policy of each subsystem is treated as a player in the game. The Nash solution of this game is used to design the control policy for each subsystem to optimize the performance of the interconnected system. Approximate dynamic programming (ADP), with critic neural networks, is utilized to approximate the solutions of the coupled Hamilton-Jacobi equations, for continuous and event-sampled control implementation. Event-sampling conditions are designed to asynchronously orchestrate the sampling and transmission at each subsystem. Finally, simulation results are included to substantiate the theoretical claims.

Keywords:Distributed control, Cooperative control, Agents-based systems Abstract: This paper addresses a formation control problem of multi-agent systems over generalized relative measurement. First, a general form of a class of obtainable measurement data is given, with which we can describe any combinations of relative/absolute bearing, with/without distance and reflection errors in the measurement of each agent. Next, we derive a strict class of formation task achievable over the generalized class of measurement data. Then, for a given network graph, an optimal gradient-based distributed and relative controller is designed. Finally, the effectiveness of the designed controller is illustrated through simulation results.

Keywords:Distributed control, Sensor networks, Communication networks Abstract: When a group of agents such as unmanned aerial vehicles are operating in 3-dimensional space, their coordinated action in pursuit of some group objective generally requires all agents to share a common coordinate frame or orientations of the coordinate axes of agents up to an unknown coordinate rotation common to all agents, which are simply referred to as common coordinate axis orientations. Given coordinate axes that are initially unaligned, this paper considers the process of using direction measurements between agent pairs (obtained in their own coordinate frames) to achieve orientation localization, i.e. determination of common coordinate axis orientations, the calculations all being distributed. The process builds on the initial determination of relative orientations of agent pairs in a common coordinate basis. Distributed differential equations then allow determination of a common set of coordinate axis orientations, uniquely up to a common rotation transformation, which can itself be determined if and only if one or more agents have access to global coordinates.

Keywords:Distributed control, Adaptive systems, Filtering Abstract: We study the problem of distributed state estimation in a network of sensing units that can exchange their measurements but the communication between the units is constrained. The units collect noisy, possibly only partial observations of the unknown state; they are assisted by a scheduler which organizes the exchange of measurements between the units. We consider the task of minimizing the total mean-square estimation error of the network while promoting balance between the individual units' performances. This problem is formulated as the maximization of a monotone objective function subject to a cardinality constraint. By leveraging the notion of weak submodularity, we develop an efficient greedy algorithm for the proposed formulation and show that the greedy algorithm achieves a constant factor approximation of the optimal objective. Our extensive simulation studies illustrate the efficacy of the proposed formulation and the greedy algorithm.

Keywords:Distributed parameter systems, Sensor networks, Fault detection Abstract: The work considers the effects of communication on the performance of multiple inexpensive actuating and sensing devices when used in place of single high capacity actuator and sensor. By opting for a large number of inexpensive actuating and sensing devices, one relies on their interconnection to emulate the performance of a controller based on single high capacity actuator and sensor. The communication effects become more prominent when the networked actuators and sensors are used to control spatially distributed systems. When the control units are viewed as the nodes of a communication topology, then accidental or deliberate actions on the connectivity of the networked actuator/sensor nodes may severely degrade the controller performance, or yet, destabilize the system. Viewing attacks on the actuator/sensor pairs as faults, which may be accidental or deliberate, a monitoring scheme based on detection and diagnostic observers is proposed for a class of partial differential equations with multiple interconnected actuator/sensor pairs. Two different types of network attacks are considered, accidental and deliberate, and both are modelled by a single attack function. The adaptive-based detection observer provides an alarm when an attack occurs in the system and via the diagnostic part of the observer, provides an indication of the node location within the communication graph that has been attacked. An attack accommodation scheme which takes the form of resetting the communication links of the affected node, is provided as a means to minimize the effects of the attack. Numerical results on a diffusion partial differential equation with five actuator sensor pairs is provided to highlight the detrimental effects of a network attack and the beneficial effects of a swift detection and accommodation.

Keywords:Distributed parameter systems, Fault detection Abstract: Unlike its Ordinary Differential Equation (ODE) counterpart, fault diagnosis of Partial Differential Equations (PDE) has received limited attention in existing literature. The main difficulty in PDE fault diagnosis arises from the spatiotemporal evolution of the faults, as opposed to temporal-only fault dynamics in ODE systems. In this work, we develop a fault diagnosis scheme for one-dimensional wave equations. A key aspect of this fault diagnosis scheme is to distinguish the effect of uncertainties from faults. The scheme consists of a PDE observer whose output error is treated as a fault indicating residual signal. Furthermore, a threshold on the residual signal is utilized to infer fault occurrence. The convergence properties of the PDE observer and residual signal are analyzed via Lyapunov stability theory. The threshold is designed based on the uncertain residual dynamics and the upper bound of the uncertainties. Simulation studies are performed to illustrate the effectiveness of the proposed fault diagnosis scheme.

Keywords:Distributed parameter systems, Distributed control, Predictive control for nonlinear systems Abstract: This work considers the problem of achieving model-based plant-wide control of a prototypical process network comprising interconnected lumped and distributed parameter systems. A community detection algorithm is used to obtain an optimal decomposition of this network for distributed control. The community detection is performed on a novel graph representation of the dynamics of the network, which accounts systematically for the interconnections among the variables of the process systems, including the different types of variables of the distributed parameter systems. The resulting distributed model predictive control implementation is shown to be computationally tractable, with performance close to that of centralized model predictive control.

Keywords:Distributed parameter systems, Stability of nonlinear systems, Process Control Abstract: This paper presents the control design of the two-phase Stefan problem via a single boundary heat input. The two-phase Stefan problem is a representative model of liquid-solid phase transition by describing the time evolutions of the temperature profile which is divided by subdomains of liquid and solid phases as the liquid-solid moving interface position. The mathematical formulation is given by two diffusion partial differential equations (PDEs) defined on a time-varying spatial domain described by an ordinary differential equation (ODE) driven by the Neumann boundary values of both PDE states, resulting in a nonlinear coupled PDE-ODE-PDE system. As an extension from our previous study on the one-phase Stefan problem, we design a state feedback control law to stabilize the interface position to a desired setpoint by employing the backstepping method. We prove that the closed-loop system under the control law ensures some conditions for model validity and the global exponential stability estimate is shown in L_2 norm. Numerical simulation is provided to illustrate the good performance of the proposed control law.

Keywords:Distributed control, Decentralized control, Networked control systems Abstract: In this paper, the optimal distributed linear time varying H2 control problem for cone causal spatially invariant linear time varying (SILTV) systems is considered. This class of systems was initially defined in the work of Voulgaris et al. for cone causal spatially invariant (SI) linear time invariant (LTI) systems. First, the optimal time varying H2 problem is posed using a version of the Youla parameterization. This allows to transform the problem into an affine form which results in a convex but infinite dimensional distributed optimization. Next, the problem is solved by computing an operator projection on a class of time varying Youla parameters with a cone causal distributed structure. The cone causal spatially invariant systems are viewed as input-output multiplicative operators with a mixed causal time varying structure with respect to time, and spatially invariant with respect to the space dimension.

Keywords:Adaptive systems, Distributed parameter systems, Lyapunov methods Abstract: This paper addresses the design and analysis of fast Newton-based extremum seeking feedback for scalar static maps in cascade with PDE dynamics in its actuation path. Although more general classes of PDE-based systems could be envisaged, we concentrate our efforts in handling diffusion PDEs. The proposed adaptive control scheme for real-time optimization follows two basic steps: first, it cancels out the effects of the actuation dynamics in the dither signals, and second, it applies a boundary control for the diffusion process via backstepping transformation. In particular, the diffusion compensator employs perturbation-based (averaging-based) estimates for the gradient and Hessian's inverse of the nonlinear-scalar static map to be optimized. The complete stability analysis of the closed-loop system is carried out using Lyapunov's method and applying averaging for infinite-dimensional systems in order to capture the infinite-dimensional state of the actuator model. Local exponential convergence to a small neighborhood of the unknown extremum is guaranteed and verified by means of a numerical example.

Keywords:Algebraic/geometric methods, Lyapunov methods, Stability of nonlinear systems Abstract: This paper presents a discrete-time stable tracking control scheme for an underactuated vehicle modeled as a rigid body. This energy-based control scheme guarantees discretetime stability of the feedback system. The underactuated vehicle is characterized by four control inputs for the six degrees of freedom of rigid body motion. These control inputs actuate the three degrees of freedom (DOF) of rotational motion and one degree of freedom of translational motion in a vehicle body-fixed coordinate frame. The actuated translational DOF corresponds to a body-fixed thrust direction. The stability analysis of translational and rotational motion of the vehicle are addressed separately, and it is shown that the total energylike quantity of the system is decreasing in discrete time. This leads to discrete-time control laws that achieve asymptotically stable tracking of desired position and attitude trajectories.

Keywords:Algebraic/geometric methods, Feedback linearization, Control software Abstract: Given a control-affine system and a controlled invariant submanifold, the local transverse feedback linearization problem is to determine whether or not the system is locally feedback equivalent to a system whose dynamics transversal to the submanifold are linear and controllable. In this paper we present necessary and sufficient conditions for a single-input system to be locally transversally feedback linearizable to a given submanifold that dualize, in an algebraic sense, previously published conditions. These dual conditions are of interest in their own right and represent a first step towards a Gardner-Shadwick like algorithm for local transverse feedback linearization.

Keywords:Algebraic/geometric methods, Computational methods, Optimal control Abstract: We propose an algebraic combinatoric approach to solve matrix Riccati differential equations. Functional series solutions for matrix Riccati differential equation are computed by formal power series method using Fliess operators. Finite escape time of the Riccati differential system is determined from such series solutions. Sufficient conditions for the nonexistence of finite escape time are also presented. Results are compared with solutions obtained by numerical integration and closed form solutions when they exist.

Keywords:Algebraic/geometric methods, Delay systems Abstract: Following the results recently obtained for nonlinear driftless systems affected by constant commensurate delays, a partial characterization of t − accessibility is provided for general nonlinear time-delay systems affected by constant commensurate delays. Conditions are given for this new property. The results are stated using the differential representation of time-delay systems

Keywords:Cooperative control, Algebraic/geometric methods, Stochastic systems Abstract: Attitude synchronization in the presence of noisy communications is an important problem in control, finding applications in the robotics and aerospace domains. The underlying Lie group geometry of SO(3) combined with the stochastic aspects pose fundamental difficulties in designing robust controllers. Even in Euclidean space, noise causes catastrophic problems for consensus algorithms. In this work we employ the Cayley representation of SO(3), to analyze some deterministic synchronizing controllers and show that they either become unweildy or fail in the presence of noise. Then we propose a new controller and show it is stable in the presence of noise and admits a principled design procedure.

Institute of Cybernetics, Tallinn University of Technology

Keywords:Delay systems, Algebraic/geometric methods Abstract: In this paper the problem of transforming a nonlinear multi-input multi-output time-delay control system, described by a set of higher order functional differential equations relating system inputs and outputs, into a set of first order functional differential equations, is studied. The globally linearized system equations are described in terms of polynomials in a delay operator and derivative operator. The Euclidean left division of polynomials is used to compute the basis of a certain free submodule of differential 1-forms. The integrability of the submodule is proved to be necessary and sufficient for the solvability of the problem.

Keywords:Robust control, Reduced order modeling, Modeling Abstract: This paper discusses active noise feedback control over a predefined frequency range for a cylindrical and closed three-dimensional cavity. An analytical 1D acoustic model is obtained by averaging the pressure on surfaces that are perpendicular to the sound propagation direction. Furthermore, a parametrized rational reduced order transfer function is proposed relying on the Cauchy method of residues. Based on this new model a Multi-objective H∞ control, aiming to attenuate the effect of an unknown noise in one or several points, is designed. Achieved performances are discussed in light of different design configurations using either a single or several measurement points.

Keywords:Robust control, Constrained control Abstract: The uncertainty and disturbance estimator (UDE)-based control is a robust control method, which is proposed as a replacement of the time-delay controller (TDC). With the filter design in the UDE-based controller, the challenging problem of designing a robust controller is converted into designing a filter. In this paper, a bounded UDE-based control is developed to deal with systems subject to uncertainties, disturbances and input constraints. The bounded controller output is achieved through nonlinear Lyapunov analysis, and an additional time-varying variable is introduced into the error dynamics to naturally avoid the integrator windup. The boundedness design is embedded into the existing UDE framework to form a bounded UDE-based controller without integrator windup via a simple structure and clear guidelines of parameter selections. Both theoretical analysis and simulation studies are provided to validate the proposed design.

Keywords:Robust control, Distributed control, Delay systems Abstract: This paper studies the delay margin and its bounds for second-order multi-agent systems to achieve robust consensus with respect to uncertain delays varying within a range. The issue under investigation dwells on the question: What is the largest delay range within which a distributed control protocol is able to achieve and maintain the consensus? We consider several second-order agents with different poles distributing on the complex plane communicating over an undirected network topology, and derive bounds on the delay margin. The results show that for a strictly unstable second-order multi-agent system, its consensuability robustness depends on the pole locations of the agents, as well as on the eigen-ratio of the network graph.

Univ. of New South Wales at the AustralianDefenceForceAcad

Keywords:Robust control, Uncertain systems, Linear systems Abstract: In this paper, we show that there exists an alternative transformation from the class of negative imaginary to the class of positive real systems. We use this to offer a solution to the problem of designing a controller such that the closed loop is strongly strictly negative imaginary and its associated linear fractional interconnection is internally stable.

Keywords:Robust control, Statistical learning, Identification for control Abstract: As the systems we control become more complex, first-principle modeling becomes either impossible or intractable, motivating the use of machine learning techniques for the control of systems with continuous action spaces. As impressive as the empirical successes of these methods have been, strong theoretical guarantees of performance, safety, or robustness are few and far between. This paper takes a step towards providing such guarantees by establishing finite-data performance guarantees for the robust output-feedback control of an unknown FIR SISO system. In particular, we introduce the “Coarse-ID control” pipeline, which is composed of a system identification step followed by a robust controller synthesis procedure, and analyze its end-to-end performance, providing quantitative bounds on the performance degradation suffered due to model uncertainty as a function of the number of experiments used to identify the system. We conclude with numerical examples demonstrating the effectiveness of our method.

Keywords:Robust control, Optimization, Numerical algorithms Abstract: We propose a new algorithm for designing low-order controllers for large-scale linear time-invariant (LTI) dynamical systems with input and output. While the high cost of working with large-scale systems can mostly be avoided by first applying model order reduction, this can often result in controllers which fail to stabilize the closed-loop plant of the original full-order system. By considering a modified version of the optimal H_{∞} controller problem that incorporates both full- and reduced-order model data, our new method ensures stability while remaining efficient. Using a publicly available test set, we find that the controllers obtained by our method outperform those computed by HIFOO (H-Infinity Fixed-Order Optimization) when applied to reduced-order models alone.

Keywords:Identification, Switched systems Abstract: This paper considers the problem of identifying error in variables switched affine models from experimental input/output data. Since this problem is generically NP hard, several relaxations have been proposed in the past. While these relaxations work well for low dimensional systems with few subsystems, they scale poorly with both the number of subsystems and their memory. As an alternative, in this paper we present a computationally efficient method based on embedding the data in the manifold of positive semidefinite matrices, and using a manifold metric to detect switches and identify subsystems. The main result of the paper shows that, under dwell-time assumptions, the method is guaranteed to identify the system, for suitably low noise scenarios. In the case of larger noise levels, experimental results are provided showing that the proposed method outperforms existing ones. These results are illustrated with a non-trivial practical example: action segmentation.

Keywords:Identification Abstract: Transmissibility operators are time-domain operators that model the relationship between outputs of an underlying system. Since real measurements are corrupted by noise, identification of transmissibilities is an errors-in-variables identification problem. This paper applies a bias-compensated recursive least-squares algorithm to errors-in-variables identification of transmissibilities. Noncausal FIR models are used to approximate transmissibility operators. To investigate the accuracy of this approach, we consider data from an acoustic experiment. The goal is to identify the transmissibility operator that models the relationship between measurements from two microphones.

Keywords:Automotive systems, Estimation, Linear parameter-varying systems Abstract: In this paper, a linear parameter varying (LPV) adaptive observer is designed for state estimation and tire cornering stiffness identification based on lateral motorcycle model. The estimation is based on a general Lipstchitz condition, Lyapunov function and is subjected to persistency of excitation conditions. Further, the LPV observer is transformed into Takagi-Sugeno (T-S) fuzzy observer and sufficient conditions, for the existence of the estimator, are given in terms of linear matrix inequalities (LMIs). This method is designed assuming that some of the states are not available, since parametric identification is generally developed assuming that all the system states are available (measured or estimated). Finally, the effectiveness of the proposed estimation method is illustrated through test scenarios performed with the well-known motorcycle simulator "BikeSim" and by field test using data measurement carried out on experimental motorcycle.

Keywords:Statistical learning, Nonlinear systems identification, Machine learning Abstract: This paper presents a method for nonlinear system identification with Gaussian process regression. The unsuper- vised method is able to generate an approximation of the system with correct extrapolation behaviour, that is refined with input/output-data in the typical working area and sampled online data. Therefore, an offline model is generated, which consists of a nominal model set up by the extrapolation behaviour and a detailed model for the refinement. The method is able to keep track of time-varying systems by using the confidence information to incorporate new measurements into the online model. The performance of the proposed method is tested on different numerical examples.

Keywords:Direct adaptive control, Adaptive control, Identification for control Abstract: The paper addresses the problem of performance improvement of direct model reference adaptive control (MRAC) for linear time-invariant (LTI) plants. Three new solutions to the problem are proposed and involve the recently introduced dynamic regressor extension and mixing (DREM) estimator modified and aggregated with standard gradient-based adaptation algorithm driven by augmented error. It is shown that dynamic extension of regressor dramatically improves tracking and parametric error convergence and generalizes existing results of MRAC. The performance of adaptive control with the proposed algorithms is demonstrated via comparable simulation.

Keywords:Systems biology, Biological systems, Nonlinear systems identification Abstract: Recently, system identification of biochemical circuits and systems has gained much research attention. Two key challenges for the identification of these systems are related to the types of available data from the experiments. Namely, the datasets that can be used for the identification are typically sparse, i.e. consist of intermittent measurements, and noisy. In this paper we show how the problem of identifying a biochemical circuit of interest can be recast as a minimax state estimation problem. Building upon this framework, we present an algorithmic procedure which not only estimates the biochemical parameters of a system/circuit of interest from noisy and intermittent data, but also the functions of the underlying dynamical model. The effectiveness of the approach is discussed by considering, as a testbed example, the genetic toggle switch

Korea Advanced Institute of Science and Technology

Keywords:Estimation, Identification, Uncertain systems Abstract: As complexity of models increases, one often encounters the case where the number of parameters to estimate outruns the available data. This is especially a problem when the available data are noisy and show strong correlations. To increase parameter estimability along with prediction accuracy, various methods for parameter subset selection (PSS) have been suggested to reduce the number of parameters to fit based on the mean squared error (MSE) of model predictions. This work proposes an alternative method where the original parameters are transformed to the directions of the principal components of the parameter covariance matrix, before a subset of parameters to estimate is identified. Although the transformed parameters lose their physical meanings, constraints on the original parameters can still be considered in the parameter estimation with the unselected transformed parameters fixed at their nominal values. A statistical analysis is performed to show that the proposed method can give smaller variances of the parameter estimates than the PSS method. This is also demonstrated through comparison of their performances for a case study involving a nonlinear bioreactor.

Keywords:Estimation, Optimization algorithms, Robust control Abstract: Set propagation through dynamic systems is a useful tool for reachability analysis, uncertainty analysis, optimal control, and global optimization. Several established methods for dynamic set propagation represent these sets using convex and concave relaxations. Implementing these methods typically requires evaluating relaxations at several domain points, which may be computationally costly. Subtangents of these relaxations typically provide weaker bounds, but are computationally favorable since they are readily minimized on polyhedral domains, and are fully described by a single relaxation evaluation and a single subgradient evaluation. This article provides results concerning the usefulness of subtangent relaxations in set propagation: first, two methods for computing subtangents for relaxations based on ordinary differential equations, and second, a theoretical guarantee that, under mild assumptions, subtangents are guaranteed to converge rapidly to the underlying system as the parametric domain shrinks.

Keywords:Estimation, Algebraic/geometric methods, Numerical algorithms Abstract: In this paper, we consider the problem of piecewise affine abstraction of nonlinear systems, i.e., the over-approximation of its nonlinear dynamics by a pair of piecewise affine functions that "includes'' the dynamical characteristics of the original system. As such, guarantees for controllers or estimators based on the affine abstraction also apply to the original nonlinear system. Our approach consists of solving a linear programming (LP) problem that over-approximates the nonlinear function at only the grid points of a mesh with a given resolution and then accounting for the entire domain via an appropriate correction term. To achieve a desired approximation accuracy, we also iteratively subdivide the domain into subregions. Our method applies to nonlinear functions with different degrees of smoothness, including Lipschitz continuous functions, and improves on existing approaches by enabling the use of tighter bounds. Finally, we compare the effectiveness of our approach with existing optimization-based methods in simulation and illustrate its applicability for estimator design.

University of Edinburgh and the Alan Turing Institute London

Keywords:Filtering, Estimation, Stochastic systems Abstract: A widely studied filtering algorithm in signal processing is the least mean square (LMS) method, due to B. Widrow and T. Hoff, 1960. A popular extension of the LMS algorithm, which is also important in deep learning, is the LMS method with momentum, originated by S. Roy and J.J. Shynk back in 1988. This is a fixed gain (or constant step-size) version of the LMS method modified by an additional momentum term, that is proportional to the last correction term. Recently a certain equivalence of the two methods has been rigorously established by K. Yuan, B. Ying and A.H. Sayed, assuming martingale difference gradient noise. The purpose of this paper is to present the outline of a significantly simpler and more transparent asymptotic analysis of the LMS algorithm with momentum under the assumption of stationary, ergodic and mixing signals.

Keywords:Identification, Machine learning, Hybrid systems Abstract: Gaussian regression combined with stochastic simulation schemes has proved to be an effective tool in hybrid systems estimation. In particular, recent works have shown that this approach can face effectively both the classification and estimation tasks jointly involved in this problem. In this paper, the combinatorial aspect arising in the choice between linear or nonlinear submodels is overcome with a new Gibbs sampling scheme. Numerical examples concerning the case of discontinuous (static) function estimation are provided to test this new approach.

Keywords:Kalman filtering, Uncertain systems, Estimation Abstract: This paper presents a mathematical framework for state estimation of dynamic systems for which only a simplified and rough model is available, using an approach that considers estimation variation itself as a possible source of uncertainty. The discrete-time case is studied and the filtering problem is solved, using a modified version of the Regularized Least Squares (RLS) and tools from the nonsmooth analysis. The solution points to a region in the innovation space in which no variation of estimation is optimal. An algorithm for real-time applications is presented and a numeric example is included to illustrate the benefits of this approach.

Keywords:Stability of nonlinear systems, Time-varying systems, Systems biology Abstract: Smillie (1984) proved an interesting result on the stability of nonlinear, time-invariant, strongly cooperative, and tridiagonal dynamical systems. This result has found many applications in models from various fields including biology, ecology, and chemistry. Smith (1991) has extended Smillie’s result and proved entrainment in the case where the vector field is time-varying and periodic. We use the theory of linear totally nonnegative differential systems developed by Schwarz (1970) to give a generalization of these two results. This is based on weakening the requirement for strong cooperativity to cooperativity, and adding an additional observability-type condition.

Keywords:Stability of nonlinear systems, Lyapunov methods, Uncertain systems Abstract: To establish input-to-state stability (ISS) of an interconnected nonlinear system, the small-gain framework makes use of nonlinear gain functions of components systems. Computing gain functions is usually hard without introducing Lyapunov functions to component systems. In the ISS formulation, Lyapunov functions of component systems naturally lead to a Lyapunov functions in the max-separable form for the interconnection. Since the maximization is not differentiable. technical modification or occurrence of artifical behavior is unavoidable in actual use of a max-separable Lyapunov function. This paper proposes a practical Lyapunov function by securing continuous differentiability and keeping it as simple and intuitive as the max-separable Lyapunov function.

Keywords:Stability of nonlinear systems, Delay systems Abstract: Graphical methods are a key tool to analyse Lur’e systems with time delay. In this paper we revisit clockwise properties of the Nyquist plot and extend results in the literature to critically stable systems and time-delayed systems. It is known that rational transfer functions with no resonant poles and no zeros satisfy the Kalman conjecture. We show that the same class of transfer functions in series with a time delay also satisfies the Kalman conjecture. Furthermore the same class of transfer functions in series with an integrator and delay (which may be zero) satisfies a suitably relaxed form of the Kalman conjecture. Useful results are also obtained where the delay is constant but unknown. Results in this paper can be used as benchmarks to test sufficient stability conditions for the Lur’e problem with time-delay systems.

Keywords:Stability of nonlinear systems, Lyapunov methods Abstract: A relation between finite-time stability and Rantzer's density function has been presented for both discrete- and continuous-time system. We show that the existence of an integrable Rantzer function (also called Lyapunov density or Lyapunov measure) implies the convergence of almost all trajectories to an invariant set in finite time. The proofs utilise the duality between Frobenious-Perron operator and Koopman operator, as well as Rantzer's lemma for the evolution of densities. To illustrate the theoretical results, some illustrative examples are presented. Additionally, a transformation that removes the integrability assumption has been addressed which makes the problem of the construction of a Rantzer function numerically tractable.

Keywords:Stability of nonlinear systems, Time-varying systems Abstract: Cooperative tridiagonal dynamical systems appear often in biological and engineering applications. The most important theorem for such systems was arguably one proved by Smillie in 1984, and subsequently refined by other authors. Smillie showed that--under mild technical assumptions--precompact trajectories always converge to equilibria. The key to his proof was the construction of an integer-valued Lyapunov function that certifies that the number of sign variations in the vector of derivatives of states eventually stabilizes.

This paper shows how to re-derive Smillie's theorem by appealing to results from Binyamin Schwarz, who analyzed the sign variations in solutions of linear systems whose flows are totally nonnegative or totally positive (meaning that all minors are nonnegative or positive, respectively). The connection is through the variational equation associated to the original system.

In addition to connecting two seemingly disparate areas of research, the connection allows one to both simplify proofs and extend the validity of Smillie's Theorem.

Keywords:Stability of nonlinear systems Abstract: This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary layer solutions converge to a bounded set, results on the closeness of solutions of the singularly perturbed system to the solutions of the reduced average and boundary layer systems over a finite time interval are presented. The closeness of solutions error is shown to be of order O(sqrt(ε)), where ε is the perturbation parameter.

Keywords:Identification, Hybrid systems, Optimization algorithms Abstract: In this paper we consider the problem of energy disaggregation, commonly referred in the literature as non-intrusive load monitoring. The problem is to estimate the end-use power consumption profiles of individual household appliance using only aggregated power measurements. We propose a two-stage supervised approach. At the first stage, dynamical models of individual appliances are estimated using disaggregated training data gathered over a short intrusive period. The consumption profiles of individual appliances are described by PieceWise Affine AutoRegressive (PWA-AR) models with multiple operating modes, which are estimated via a moving horizon PWA regression algorithm. Once the model of each appliance is identified, a binary quadratic programming problem is solved at the second stage to determine the set of active appliances which contribute to the instantaneous aggregated power, along with their operating modes. A benchmark dataset is used to assess the performance of the presented disaggregation approach.

Keywords:Hybrid systems, Linear systems, Estimation Abstract: This paper deals with the characterization of a particular structural property: strong observability, for a class of linear hybrid systems with periodic jumps. Such a property is given in terms of geometric and algebraic conditions over the matrices of the linear hybrid system. A characterization of the weakly unobservable subspace is also given for this class of hybrid systems as well as the relation it has with the strong observability. An example illustrates the proposed properties.

Keywords:Switched systems, Networked control systems, Estimation Abstract: One of the main issues related to the reliable operation of cyber-physical and networked control systems concerns how to handle network imperfections such as limited bandwidth, delay, and packet loss. In this paper, we address the issue of packet loss, and design a mechanism for packet-loss detection from process measurements. The proposed scheme, which is based on moving-horizon estimation, permits to detect when the packet-loss rate exceeds prescribed thresholds that are representative of closed-loop stability. A numerical example is discussed to substantiate the analysis.

Keywords:Switched systems, Stability of hybrid systems, Hybrid systems Abstract: We address the problem of deciding stability of a “black-box” dynamical system (i.e., a system whose model is not known) from a set of observations. The only assumption we make on the black-box system is that it can be described by a switched linear system. We show that, for a given (randomly generated) set of observations, one can give a stability guarantee, for some level of confidence, with a trade-off between the quality of the guarantee and the level of confidence. We provide an explicit way of computing the best stability guarantee, as a function of both the number of observations and the required level of confidence. Our results rely on geometrical analysis and combine chance-constrained optimization theory with stability analysis techniques for switched systems.

Keywords:Hybrid systems, Stability of hybrid systems, Observers for Linear systems Abstract: This paper proposes a general framework for the state estimation of plants given by hybrid systems with linear flow and jump maps, in the favorable case where their jump events can be detected instantaneously. A candidate observer consists of a copy of the plant's hybrid dynamics with continuous-time and/or discrete-time correction terms adjusted by two constant gains, and with jumps triggered by those of the plant. Assuming that the time between successive jumps is known to belong to a given closed set allows us to formulate an augmented system with a timer which keeps track of the time elapsed between successive jumps and facilitates the analysis. Then, since the jumps of the plant and of the observer are synchronized, the error system has time-invariant linear flow and jump maps, and a Lyapunov analysis leads to sufficient conditions on the design of the gains for uniform asymptotic stability in three different settings : continuous and discrete updates, only discrete updates, or only continuous updates. Those conditions take the form of matrix inequalities, which we solve in examples including cases where the time between successive jumps is unbounded or tends to zero (Zeno behavior).

Keywords:Time-varying systems, Optimization, Nonlinear systems identification Abstract: This paper investigates the minimization problem, under the practical setting where the scalar-valued loss function L_k is intrinsically time-varying, and the sequence of minimizers is time-varying too. We focus on the tracking capability of the recursive estimates generated by the constant-gain stochastic gradient algorithm. It is shown that the trajectory of a limiting nonautonomous ordinary differential equation can be associated with the iterates generated by the constant-gain stochastic gradient descent algorithm. The main tool in establishing the connection is the formula for variation of parameters. The established probabilistic bound is applicable in tracking a jump process. A synthetic example illustrates the accountability of the trajectory characterization depends on the magnitude of the noise, the drift magnitude, and the constant gain.

Keywords:Smart grid, Estimation, Optimization Abstract: The increasing amount of controllable generation and consumption in distribution grids poses a severe challenge in keeping voltage values within admissible ranges. Existing approaches have considered different optimal power flow formulations to regulate distributed generation and other controllable elements. Nevertheless, distribution grids are characterized by an insufficient number of sensors, and state estimation algorithms are required to monitor the grid status. We consider in this paper the combined problem of optimal power flow under state estimation, where the estimation uncertainty results into stochastic constraints for the voltage magnitude levels instead of deterministic ones. To solve the given problem efficiently and to bypass the lack of load measurements, we use a linear approximation of the power flow equations. Moreover, we derive a transformation of the stochastic constraints to make them tractable without being too conservative. A case study shows the success of our approach at keeping voltage within limits, and also shows how ignoring the uncertainty in the estimation can lead to voltage level violations.

Keywords:Smart grid, Optimization, Energy systems Abstract: In this paper, distributed energy management of interconnected microgrids, which is stated as a dynamic economic dispatch problem, is studied. Since the distributed approach requires cooperation of all local controllers, when some of them do not comply with the distributed algorithm that is applied to the system, the performance of the system might be compromised. Specifically, it is considered that adversarial agents (microgrids) might implement control inputs that are different than the ones obtained from the distributed algorithm. By performing such behavior, these agents might have better performance at the expense of deteriorating the performance of the regular agents. This paper proposes a methodology to deal with this type of adversarial agents such that we can still guarantee that the regular agents can still obtain feasible, though suboptimal, control inputs in the presence of adversarial behaviors. The methodology consists of two steps: (i) the robustification of the underlying optimization problem and (ii) the identification of adversarial agents, which uses hypothesis testing with Bayesian inference and requires to solve a local mixed-integer optimization problem. Furthermore, the proposed methodology also prevents the regular agents to be affected by the adversaries once the adversarial agents are identified.

Keywords:Smart grid, Neural networks, Estimation Abstract: In recent years, as the share of solar power in the electrical grid has been increasing, accurate methods for forecasting solar irradiance have become necessary to manage the electrical grid. More specifically, as solar generators are geographically dispersed, it is very important to have general models that can predict solar irradiance without the need of ground data. In this paper, we propose a novel technique that can accomplish that: using satellite images, the proposed model is able to forecast solar irradiance without the need of ground measurements. To illustrate the performance of the proposed model, we consider 15 locations in The Netherlands, and we show that the proposed model is as accurate as local models that are individually trained with ground data.

Keywords:Smart grid, Power systems, Control applications Abstract: We propose a parametrized Model Predictive Control (MPC) approach for optimal operation of microgrids. The parametrization expresses the control input as a function of the states, variables, and parameters. In this way, it is possible to apply an MPC approach by optimizing only the parameters and not the inputs. Moreover, the value of the binary control variables in the model is assigned according to parametrized heuristic rules, thus obtaining a formulation for the optimization problem that is more scalable compared to standard approaches in the literature. Furthermore, we propose a control scheme based on one single controller that uses two different sampling times and prediction models. By doing so, we can include both fast and slow dynamics of the system at the same level. This control approach is applied to an operational control problem of a microgrid, which includes local loads, local production systems, and energy storage systems and results show the effectiveness of the proposed approach.

Keywords:Smart grid, Smart cities/houses, Grey-box modeling Abstract: A model predictive control (MPC) framework is developed in the present study, with the final objective to improve the energy flexibility of building thermal loads through demand-side management. Three different configurations are tested and tuned, with the following objective functions: minimizing the delivered energy to the building, the electrical energy used by the HVAC system (heat pump) or the cost of this electricity use. To validate these MPC configurations, a Matlab-Trnsys co-simulator is also created, in order to run the MPC on a virtual plant composed of a detailed building model. The MPC strategy manages to run effectively on the chosen study case (a residential building with heat pump in Spain), and the differences between configurations are discussed.

Keywords:Energy systems, Decentralized control, Large-scale systems Abstract: Nowadays, large wind farms are expected to guarantee stability of the electrical grid contributing with ancillary services, such as frequency support. To this end, wind farm controllers must set the power generation of each turbine to compensate generation and demand imbalances. With the aim of optimizing primary frequency support, this paper proposes a partitioning approach to split large wind farms into several disjoint subsets of turbines according to the wake propagations through the wind farm. The partitioning problem is solved as a mixed-integer multi-objective optimization problem stated to maximize the strength of the coupling among the turbines due to the wake effect. Thus, no additional information sharing related to the wake propagations needs to be considered between the subsets. Different control tasks are assigned to the local controller of each subset, such that the total power generated meets the power demanded by the grid while the power reserve for enhancing primary frequency support is maximized. Finally, as an application of the proposed model, a decentralized wind farm control strategy is designed and compared with a centralized approach.

Keywords:Computational methods, Distributed control, Large-scale systems Abstract: We study the optimal distributed control (ODC) problem and propose a design method based on the approximation of the mathcal{H}_2 performance using the optimal centralized controller. The designed distributed controller obeys a prescribed sparsity pattern in the frequency domain. The proposed method enables a convex approximation of the distributed controller problem with optimality guarantees, which has a closed-form solution. After introducing the notion of rank-preserving weights, we give sufficient conditions for the controller to be proper, and furthermore characterize the set of controllers that can be obtained by the proposed technique via fine-tuning the algorithm parameters. The results are applied to the linear-quadratic regulator problem and the purely decentralized case with a diagonal sparsity pattern, where certain connections to the simple methods of thresholding and averaging are discovered. Numerical examples are provided to demonstrate the effectiveness of the developed method.

Keywords:Computational methods Abstract: The space of finite games can be decomposed into three orthogonal subspaces, which are the subspaces of pure potential games, nonstrategic games, and pure harmonic games as shown in a paper by Candogan et al. [2]. This decomposition provides a systematic characterization for the space of finite games. Explicit expressions for the orthogonal projections onto the subspaces are helpful in analyzing general properties of finite games in the subspaces and the relationships of finite games in different subspaces. In the work by Candogan et al., for the two-player case, explicit expressions for the orthogonal projections onto the subspaces are given. In the current paper, we give an algorithm for computing explicit expressions for the n-player case by developing our framework in the semitensor product of matrices and the group inverses of matrices. Specifically, using the algorithm, once we know the number of players, no matter whether we know their number of strategies or their payoff functions, we can obtain explicit expressions for the orthogonal projections. These projections can then be used to analyse the dynamical behaviors of games belonging to these subspaces.

Keywords:Computational methods, Optimization, Power systems Abstract: The optimal power flow (OPF) problem determines an optimal operating point of the power network that minimizes a certain objective function subject to physical and network constraints. There has been a great deal of attention in convex relaxation of the OPF problem in recent years, and it has been shown that a semidefinite programming (SDP) relaxation can solve different classes of the nonconvex OPF problem to global or near-global optimality. Although it is known that the SDP relaxation is exact for radial networks under various conditions, solving the OPF problem for cyclic networks needs further research. In this paper, we propose sufficient conditions under which the SDP relaxation is exact for special but important cyclic networks. More precisely, when the objective function is a linear function of active powers, we show that the SDP relaxation is exact for odd cycles under certain conditions. Also, the exactness of the SDP relaxation for simple cycles of size 3 and 4 is proved under different technical conditions. The existence of rank-1 or -2 SDP solutions for weakly-cyclic networks is also proved in both lossy and lossless cases. In addition, when the objective function is an increasing function of reactive powers, we prove that the SDP relaxation is exact under certain conditions. This result justifies why the sum of reactive powers acts as a low-rank-promoting term for OPF. The findings of this paper provide intuition into the behavior of SDPs for different building blocks of cyclic networks.

Keywords:Computational methods, Numerical algorithms, Switched systems Abstract: We describe an algorithm to compute a common Lyapunov function for a finite set of nonlinear discrete-time systems. In this algorithm a compact neighbourhood of a common equilibrium of the systems is subdivided into simplices and a linear programming problem is constructed. We prove that any feasible solution to this linear programming problem can be used to parameterize a common Lyapunov function for the systems that is continuous and affine on each of the simplices of the triangulation. We conclude the paper by applying our algorithm to two planar examples.

Keywords:Model/Controller reduction, Computational methods Abstract: A novel Krylov subspace method is proposed to substantially reduce the computational complexity of the special class of quadratic bilinear dynamical systems. Based on the first two generalized transfer functions of the system, a Petrov-Galerkin projection scheme is applied. It is shown that such a projection amounts to interpolating the transfer functions at specific points which, in fact, is equivalent to constructing the corresponding Krylov subspace. For single-input single-output systems, the relevant Krylov subspace can be readily constructed for the interpolation points. For multi-input multi-output systems, also user-specified directional information is required so that a tangential interpolation can be determined. The method is demonstrated by numerical examples.

Keywords:Computational methods, Stability of nonlinear systems, Optimal control Abstract: In this paper, we propose a data-driven approach for control of nonlinear dynamical systems. The proposed data-driven approach relies on transfer Koopman and Perron- Frobenius (P-F) operators for linear representation and control of such systems. Systematic model-based frameworks involving linear transfer P-F operator were proposed for almost everywhere stability analysis and control design of a nonlinear dynamical system in previous works. Lyapunov measure can be used as a tool to provide linear programming-based computational framework for stability analysis and optimal control design of a nonlinear system. In this paper, we show that the Lyapunov measure-based framework can extended to a data-driven setting, where the finite dimensional approximation of linear transfer P-F operator and optimal control can be obtained from time-series data. We exploit the positivity and Markov property of P-F operator to provide linear programming based approach for designing an optimally stabilizing feedback controller.

Keywords:Machine learning, Optimization algorithms, Control over communications Abstract: This paper considers a wireless network in which each node is charged with minimizing the global objective function, which is an average of sum of the statistical average loss function of each node (agent) in the network. Since agents are not assumed to observe data from identical distributions, the hypothesis that all agents seek a common action is violated, and thus the hypothesis upon which consensus constraints are formulated is violated. Thus, we consider nonlinear network proximity constraints which incentivize nearby nodes to make decisions which are close to one another but not necessarily coincide. Moreover, agents are not assumed to receive their sequentially arriving observations on a common time index, and thus seek to learn in an asynchronous manner. An asynchronous stochastic variant of the Arrow-Hurwicz saddle point method is proposed to solve this problem which operates by alternating primal stochastic descent steps and Lagrange multiplier updates which penalize the discrepancies between agents. Our main result establishes that the proposed method yields convergence in expectation both in terms of the primal sub-optimality and constraint violation to radii of sizes ccalO(sqrt{T}) and ccalO(T^{3/4}), respectively. Empirical evaluation on an asynchronously operating wireless network that manages user channel interference through an adaptive communications pricing mechanism demonstrates that our theoretical results translate well to practice.

Keywords:Computational methods, Optimization algorithms, Power systems Abstract: This paper develops an algorithmic framework for tracking fixed points of time-varying contraction mappings. Analytical results for the tracking error are established for the cases where: (i) the underlying contraction self-map changes at each step of the algorithm; (ii) only an imperfect information of the map is available; and, (iii) the algorithm is implemented in a distributed fashion, with communication delays and packet drops leading to asynchronous algorithmic updates. The analytical results are applicable to several classes of problems, including time-varying monotone mappings emerging from online and asynchronous implementations of gradient-based methods for time-varying convex programs. In this domain, the proposed framework can also capture the operating principles of feedback-based online algorithms, where the online gradient steps are suitably modified to accommodate actionable feedback from an underlying physical or logical network. Examples of applications and illustrative numerical results are provided.

Keywords:Optimization algorithms, Time-varying systems Abstract: This paper considers time-varying nonconvex optimization problems, utilized to model optimal operational trajectories of systems governed by possibly nonlinear physical or logical models. Algorithms for tracking a Karush-Kuhn-Tucker point are synthesized, based on a regularized primal-dual gradient method. In particular, the paper proposes a feedback-based primal-dual gradient algorithm, where analytical models for system state or constraints are replaced with actual measurements. When cost and constraint functions are twice continuously differentiable, conditions for the proposed algorithms to have bounded tracking error are derived, and a discussion of their practical implications is provided. Illustrative numerical simulations are presented for an application in power systems.

Keywords:Optimal control, Linear systems, Output regulation Abstract: We consider the problem of designing a feedback controller that guides the input and output of a linear time-invariant system to a minimizer of a convex optimization problem. The system is subject to an unknown disturbance that determines the feasible set defined by the system equilibrium constraints. Our proposed design enforces the Karush-Kuhn-Tucker optimality conditions in steady-state without incorporating dual variables into the controller. We prove that the input and output variables achieve optimality in equilibrium and outline two procedures for designing controllers that stabilize the closed-loop system. We explore key ideas through simple examples and simulations.

Swiss Federal Institute of Technology (ETH) Zurich

Keywords:Switched systems, Optimization, Power systems Abstract: This paper is concerned with the study of continuous-time, non-smooth dynamical systems which arise in the context of time-varying non-convex optimization problems, as for example the feedback-based optimization of power systems. We generalize the notion of projected dynamical systems to time-varying, possibly non-regular, domains and derive conditions for the existence of so-called Krasovskii solutions. The key insight is that for trajectories to exist, informally, the time-varying domain can only contract at a bounded rate whereas it may expand discontinuously. This condition is met, in particular, by feasible sets delimited via piecewise differentiable functions under appropriate constraint qualifications. To illustrate the necessity and usefulness of such a general framework, we consider a simple yet insightful power system example, and we discuss the implications of the proposed conditions for the design of feedback optimization schemes.

Keywords:Optimization, Optimization algorithms, Adaptive control Abstract: A novel class of derivative-free optimization algorithms is developed. The main idea is to utilize certain non-commutative maps in order to approximate the gradient of the objective function. Convergence properties of the novel algorithms are established and simulation examples are presented.

Keywords:Stochastic systems, Uncertain systems, Stability of linear systems Abstract: We consider the continuous-time setting of linear time-invariant (LTI) systems in feedback with multiplicative stochastic uncertainties. The objective of the paper is to characterize the conditions of Mean-Square Stability (MSS) using a purely input-output approach, i.e. without having to resort to state space realizations. This has the advantage of encompassing a wider range of models (such as infinite dimensional systems and systems with delays). This approach leads to uncovering new tools such as stochastic block diagrams that have an intimate connection with the more general stochastic integral equations (SIE), rather than stochastic differential equations (SDE). Various stochastic interpretations are considered, such as Ito and Stratonovich, and block diagram conversion schemes between different interpretations are devised. The MSS conditions are given in terms of the spectral radius of a matrix operator that takes different forms when different stochastic interpretations are considered.

Keywords:Stochastic optimal control, Predictive control for nonlinear systems, Markov processes Abstract: In this paper, we describe a stochastic model predictive control algorithm for finite-space partially observable Markov decision process problems with time-joint chance constraints. We discuss theoretical properties of the algorithm, including an approach to its recursive feasibility. An example representing path planning for an autonomous car is considered to illustrate the computational tractability of the algorithm.

Keywords:Stochastic optimal control, Machine learning, Predictive control for nonlinear systems Abstract: Stochastic Model Predictive Control (SMPC) can improve the system performance under probabilistic uncertainties by shaping the predicted probability distribution functions of system states. The scenario approach incorporates a large number of scenarios into an online optimization problem. It may cause substantial feedback delays, which in turns leads to system performance degradation.

In this paper, an advanced-step SMPC (asSMPC) is proposed to address this issue. During the background stage (the period between control implementation and the next sampling event) of each time step, it generates many predictions of the next-step state and solves parallel SMPC problems to form a data set. The machine learning algorithm -- Random Forests (RF) is adopted to construct an approximate control law for the next time step. Simulation studies have shown that the proposed asSMPC approach can achieve control performance similar to that of scenario-based SMPC without computational delays.

Keywords:Stochastic optimal control, Decentralized control, Networked control systems Abstract: In this paper, a decentralized stochastic control system consisting of one leader and many homogeneous followers is studied. The leader and followers are coupled in both dynamics and cost, where the dynamics are linear and the cost function is quadratic in the states and actions of the leader and followers. The objective of the leader and followers is to reach consensus while minimizing their communication and energy costs. The leader knows its local state and each follower knows its local state and the state of the leader. The number of required links to implement this decentralized information structure is equal to the number of followers, which is the minimum number of links for a communication graph to be connected. In the special case of a leaderless network, no link is required among followers, i.e., the communication graph is not even connected. We propose a near-optimal control strategy that converges to the optimal solution as the number of followers increases. One of the salient features of the proposed solution is that it provides a design scheme, where the convergence rate as well as the collective behavior of the followers can be designed by choosing appropriate cost functions. In addition, the computational complexity of the proposed solution does not depend on the number of followers. Furthermore, the proposed strategy can be computed in a distributed manner, where the leader solves one Riccati equation and each follower solves two Riccati equations to calculate their strategies. Two numerical examples are provided to demonstrate the effectiveness of the results in the control of multi-agent systems.

Keywords:Stochastic optimal control, Optimal control, Robust control Abstract: The policy of an optimal control problem for nonlinear stochastic systems can be characterized by a second-order partial differential equation for which solutions are not readily available. In this paper we provide a systematic method for obtaining approximate solutions for the infinite-horizon optimal control problem in the stochastic framework. The method is demonstrated on an illustrative numerical example in which the control effort is not weighted, showing that the technique is able to deal with one of the most striking features of stochastic optimal control.

Keywords:Stochastic optimal control Abstract: In this paper, we address a finite-horizon stochastic optimal control problem with covariance assignment and input energy constraints for discrete-time stochastic linear systems with partial state information. In our approach, we consider separation-based control policies that correspond to sequences of control laws that are affine functions of either the complete history of the output estimation errors, that is, the differences between the actual output measurements and their corresponding estimated outputs produced by a discrete-time Kalman filter, or a truncation of the same history. This particular feedback parametrization allows us to associate the stochastic optimal control problem with a tractable semi-definite (convex) program. We argue that the proposed procedure for the reduction of the stochastic optimal control problem to a convex program has significant advantages in terms of improved scalability and tractability over the approaches proposed in the relevant literature.

Keywords:Autonomous systems, Game theory, Optimization Abstract: In this paper we consider a robot patrolling scenario on a weighted graph where an intruder can observe the patrolling path and use the information gained by observation to attack the graph's vertices. We pose the problem of finding a patrolling strategy as a multi-stage two player game. The patroller commits to a strategy that is unknown to the intruder. The intruder observes the patroller's actions for a finite amount of time to learn the patroller's strategy and then decides to either attack or renege based on its confidence in the learned strategy. We characterize the expected payoffs for the players and show that finding a k-factor approximation to the optimal patrolling strategy is NP-hard even when the patroller's strategy set is constrained to time homogeneous Markov chains. We propose a search algorithm to find a patrolling policy in such scenarios and illustrate the trade off between hard to learn and hard to attack strategies through simulations.

Keywords:Autonomous systems, Optimization algorithms Abstract: Unmanned Aircraft Systems (UASs) have gained great popularity in land monitoring, 3-D mapping, search and rescue, among others. Existing studies on UAS path planning in these missions consider only a single region to be examined. However, it is frequently encountered that multiple regions need to be considered while performing a real life mission. How to design the optimal path for the UAS to cover multiple regions is then critical. From a strategical point of view, such a problem can be considered as a variant of the traveling salesman problem (TSP) combined and enhanced with the coverage path planning (CPP) problem. Although TSP and CPP have been studied extensively, its combination, which here is given the name TSP-CPP, hasn't received any attention. In this paper, a preliminary study on how to formulate and solve this problem is conducted. Two novel approaches including a grid-based approach and a dynamic programming based approach are introduced to find the (near) optimal solution. Both numerical analysis and simulation studies are conducted to prove and illustrate the optimality and efficiency of the proposed TSP-CPP approaches.

Keywords:Autonomous systems, Constrained control, Hybrid systems Abstract: The need for computationally-efficient control methods of dynamical systems under temporal logic tasks has recently become more apparent. Existing methods are computationally demanding and hence often not applicable in practice. Especially with respect to multi-robot systems, these methods do not scale computationally. In this work, we propose a framework that is based on control barrier functions and signal temporal logic. In particular, time-varying control barrier functions are considered where the temporal properties are used to satisfy signal temporal logic tasks. The resulting controller is given by a switching strategy between a computationally-efficient convex quadratic program and a local feedback control law.

Keywords:Autonomous systems, Decentralized control, Distributed control Abstract: This paper proposes a general framework for distributed coverage control of mobile robotic sensors. We pose the multiagent coverage problem as an optimization problem over the space of density functions. We show that the popular locational optimization framework for coverage can be viewed as a special case of optimizing the Kullbeck-Leibler divergence in the space of density functions. We also see that more general approaches to distributed coverage control can be formulated based on minimizing different notions of distances. In particular we consider the L2-distance as a possible metric to design distributed coverage control laws.

Keywords:Autonomous systems, Distributed control, Predictive control for linear systems Abstract: In this paper a distributed constrained control architecture is developed to address the obstacle avoidance problem for rotating wings unmanned aerial vehicles. The proposed strategy aims at achieving a flexible formation whose topology can be properly reorganized whenever narrowed corridors are accessible. This reasoning is translated into a computable procedure by resorting to model predictive control (MPC) ideas that allow to efficiently manage model uncertainties and physical constraints.

Keywords:Autonomous systems, Decentralized control Abstract: We study the problem of synthesizing strategies for a mobile sensor network to conduct surveillance in partnership with static alarm triggers. We formulate the problem as a multi-agent reactive synthesis problem with surveillance objectives specified as a temporal logic formula. In order to avoid the state space blow-up arising from a centralized strategy computation, we propose a method to decentralize the surveillance strategy synthesis by decomposing the multi-agent game into subgames that can be solved independently. We also decompose the global surveillance specification into local specifications for each mobile sensor and show that sensors satisfying their local surveillance specifications guarantees that the sensor network as a whole will satisfy the global surveillance objective. Thus, our method is able to guarantee global surveillance properties in a mobile sensor network while synthesizing completely decentralized strategies with no need for communication between the sensors. We also present a case study where we demonstrate an application of decentralized surveillance strategy synthesis.

Keywords:Control over communications, Cooperative control Abstract: The paper considers distributed control of human-in-the-loop multi-agent systems (MASs) using only relative input-output measurements. A human supervises the team through broadcasting a command signal to only one agent, called the leader, in response to any changes. To impose the human control signal, the leader needs to be a non-autonomous agent. All followers autonomously synchronize to the leader by locally interacting with each other over a communication graph and using only the relative input-output information. To decrease the communication burden, a novel distributed observer is presented for leader-follower MASs with non-autonomous leaders to approximate the relative state information of the agents. To obviate the requirement of knowing an upper bound on the human input, each agent adaptively estimates the human force by communicating its estimation with its neighbors. It is shown that the gain margin of the proposed distributed observer is infinity. The provided simulation results show effectiveness of the proposed method.

Keywords:Control over communications, Fault tolerant systems, Observers for Linear systems Abstract: Remote sensing is often a crucial part of cyber-physical and networked systems. Measurements taken at remote locations can both serve as monitoring tools as well as to inform control decisions. Over the past few years, a number of cyberattacks were mounted against such systems with severe socio-economic consequences. In this paper we explore how physical measurements can be used in combination with a consensus algorithm, to ensure secure state estimation for a class of tree-like networked systems.

Keywords:Control over communications, Lyapunov methods, Chaotic systems Abstract: In this paper, we develop a communication protocol for the observation of discrete time, possibly unstable, dynamical systems over communication channels with limited communication capacity. We develop an observer based on the upper box dimension for one-way communication channels that leads to a certain type of observability. This communication scheme preserves observability under communication losses which makes the communication scheme robust towards communication losses without feedback in the communication channel. Using Lyapunov-like techniques, we provide bounds on the minimum communication rate required to implement this observer. We also use the Lyapunov dimension to provide analytical upper bounds on the communication rate. We compute an analytical upper bound and an exact expression for the Lyapunov dimension of the smoothened Lozi map. This bound is then tested in simulations of the communication protocol for the observation problem of the smoothened Lozi map.

Keywords:Control over communications, Networked control systems, Robotics Abstract: We discuss a new reachability problem for networked controlled system where a master node ---the controller--- broadcasts commands to a set of slave nodes, which must take turn to relay back state measurements. This problem finds applications in some robotics and intelligent transportation systems setups. Constraints on communication demand a coupled design of the controller and the measurement schedule. We prove that the problem is formally equivalent to the Pinwheel Problem from scheduling theory, and building on this result we provide conditions for schedulability and reachability. The results are illustrated in three numerical examples.

Keywords:Distributed control, Computational methods Abstract: Two communication-efficient distributed algorithms are proposed to solve a system of linear equations Ax = b with Laplacian sparse A. A system of linear equations with Laplacian sparse A can be found in many applications, e.g., the power flow problems and other network flow problems. The first algorithm is based on the gradient descent method in optimization and the agents only share two parts of the system state instead of that of the whole system state, which saves significant communication. The two parts shared by every agent through a communication link are the state information of its own and its neighbors connected by the communication link. The second method is obtained from an approximation of the Newton method, which converges faster. It requires twice as much communication as the first one but is still communication-efficient due to the low dimension of each part shared between agents. The convergence at a linear rate of both methods is proved. A comprehensive comparison of the convergence rate, communication burden, and computation costs between the methods is made. Finally, a simulation is conducted to show the effectiveness of both methods.

Keywords:Large-scale systems, Control over communications, Estimation Abstract: In this paper, we propose a distributed quantized algorithm for solving the network linear equation z = Hy subject to digital node communications, where each node only knows a single row of the partitioned matrix [H z]. Each node holds a dynamic state and interacts with its neighbors through an undirected connected graph. Due to the datarate constraint, each node builds an encoder-decoder pair, with which it produces transmitted message with a zoomingin finite-level uniform quantizer and also generates estimates of its neighbors’ states from the received signals. When the equation admits a unique solution, the algorithm drives all nodes’ estimates to converge exponentially fast to that solution. When a unique least-squares solution exists, such a solution can be obtained with a suitably selected time-varying step size. In both cases, a minimal data rate with the three-level quantizers is shown to be enough for guaranteeing the desired convergence.

Keywords:Optimization, Optimization algorithms, Communication networks Abstract: In this paper we propose a distributed implementation of the relaxed Alternating Direction Method of Multipliers algorithm (R-ADMM) for optimization of a separable convex cost function, whose terms are stored by a set of interacting agents, one for each agent. Specifically the local cost stored by each node is in general a function of both the state of the node and the states of its neighbors, a framework that we refer to as `partition-based' optimization. This framework presents a great flexibility and can be adapted to a large number of different applications. By recasting the problem into an operator theoretical framework, the proposed algorithm is shown to be provably robust against random packet losses that might occur in the communication between neighboring nodes. Finally, the effectiveness of the proposed algorithm is confirmed by a set of compelling numerical simulations run over random geometric graphs subject to i.i.d. random packet losses.

Keywords:Optimization, Communication networks, Agents-based systems Abstract: In this paper, we focus on solving a distributed convex optimization problem in a network, where each agent has its own convex cost function and the goal is to minimize the sum of the agents’ cost functions while obeying the network connectivity structure. In order to minimize the sum of the cost functions, we consider a new distributed gradient-based method where each node maintains two estimates, namely, an estimate of the optimal decision variable and an estimate of the gradient for the average of the agents’ objective functions. From the viewpoint of an agent, the information about the decision variable is pushed to the neighbors, while the information about the gradients is pulled from the neighbors (hence giving the name “push-pull gradient method”). The method unifies the algorithms with different types of distributed architecture, including decentralized (peer-to-peer), centralized (master-slave), and semi-centralized (leader-follower) architecture. We show that the algorithm converges linearly for strongly convex and smooth objective functions over a directed static network. In our numerical test, the algorithm performs well even for time-varying directed networks.

Keywords:Optimization algorithms, Large-scale systems, Distributed control Abstract: In this paper we deal with a network of agents aiming at solving in a distributed way Mixed-Integer Linear Programs (MILPs) with a coupling constraint (modeling a limited resource to be shared among agents) and local constraints. MILPs are known to be NP-hard problems and several additional challenges arise in a distributed framework, so that looking for feasible solutions with suboptimality bounds is of interest. To achieve this goal, the presence of a linear coupling calls for tailored decomposition approaches. In particular, we propose a fully distributed algorithm based on a primal decomposition approach and a suitable tightening of the coupling constraints. Agents repeatedly update local allocation vectors, which converge to an optimal resource allocation of a problem with convexified local constraints and suitably tightened coupling. Based on such allocation vectors, agents are able to (locally) compute a mixed-integer solution, which is guaranteed to be feasible after a sufficiently large time. Asymptotic and finite-time suboptimality bounds are established for the computed solution. Numerical simulations highlight the efficacy of the proposed methodology.

Keywords:Optimization algorithms, Distributed control, Agents-based systems Abstract: In this paper, we propose a fully distributed algorithm for second-order continuous-time multi-agent systems to solve the distributed optimization problem. The global objective function is a sum of private cost functions associated with the individual agents and the interaction between agents is described by a weighted undirected graph. We show the exponential convergence of the proposed algorithm if the underlying graph is connected, each private cost function is locally gradient-Lipschitz-continuous, and the global objective function is restricted strongly convex with respect to the global minimizer. Moreover, to reduce the overall need of communication, we then propose a dynamic event-triggered communication mechanism that is free of Zeno behavior. It is shown that the exponential convergence is achieved if the private cost functions are also globally gradient-Lipschitz-continuous. Numerical simulations are provided to illustrate the effectiveness of the theoretical results.

Keywords:Optimization algorithms, Distributed control, Agents-based systems Abstract: We deal with decision making in a large-scale multi-agent system, where each agent aims at minimizing a local cost function subject to local constraints, and the local decision variables of all agents are coupled through a global constraint. We consider a cooperative framework where the multi-agent decision problem is formulated as a constrained optimization program with the sum of the local costs as global cost to be minimized with respect to the local decision variables of all agents, subject to both local and global constraints. We focus on a non-convex linear set-up where all costs and constraints are linear but local decision variables are discrete or include a discrete component, and propose a distributed iterative scheme based on dual decomposition and consensus to solve the resulting Mixed Integer Linear Program (MILP). Our approach extends recent results in the literature to a distributed set-up with a time-varying communication network and allows to: reduce the computational and communication effort, achieve resilience to communication failures, and also preserve privacy of local information. The approach is demonstrated on a numerical example of optimal charging of plug-in electric vehicles.

Keywords:Optimization algorithms Abstract: This paper studies the problem of optimization in multi-agent systems where each agent seeks to minimize the sum of all agents' objective functions without knowing others' functions. Under the requirement of security, each of them needs to keep its objective function private from other agents and potential eavesdroppers. We design a completely distributed algorithm, which achieves differential privacy by perturbing states and adjusting directions with decaying Laplace noise. The proposed algorithm ensures that an attacker who intercepts the messages cannot obtain the objective function of any agent even if it bribes all other agents. A constant stepsize is adopted to improve the convergence rate. It is shown that the algorithm converges almost surely and the convergence point is independent of the noise added to the states. The trade-off between differential privacy and convergence accuracy is characterized. Finally, simulations are conducted to validate the efficiency of the proposed algorithm.

Keywords:Control applications, Power electronics, Stability of nonlinear systems Abstract: Advanced control methods are nowadays increasing in interest for power electronics devices. This paper proposes a nonlinear control law for a DC/DC boost converter dedicated to extract the maximum power from a photovoltaic (PV) array, taking into account the constraints of the control action. System stability analysis is provided by a proper Lyapunov function. Simulations on SimPowerSystems validate how the developed control strategy is able to properly control the converter with good performances.

Keywords:Fault detection, Power electronics, Algebraic/geometric methods Abstract: This paper presents a nonlinear geometric approach to fault detection and isolation (FDI) in grid-connected inverters. Faults are considered in inverter switches as well as in grid voltage and source current sensors. The FDI system is not sensitive to load variations or grid transients. No assumptions on balanced, zero-sum or sinusoidal form of voltages or currents are made. The resulting residual converges to zero in no-fault condition such that no threshold adjustment is needed. Simulations demonstrate performance of the proposed FDI system in presence of unknown disturbance.

Keywords:Power electronics, Smart grid, Control system architecture Abstract: Microgrids have emerged as viable alternatives for supporting the utility grid, reducing feeder losses and improving power quality by enabling integration of growing deployments of distributed energy resources (DERs) with local loads. They can operate in both grid-tied as well as islanded modes. There are two primary objectives in the islanded mode - (a) ensuring system stability by regulating the voltage and frequency at the point-of-common-coupling (PCC), and (b) load power sharing among multiple DERs connected in parallel. While droop based schemes enjoy the advantages of fully decentralized implementation (no communication) and plug-and-play capabilities, such schemes often fail to address the issue of precise active and reactive power sharing, primarily due to unmatched impedances. In this paper, we overcome this limitation by proposing a novel, droopless control scheme for accurate active and reactive power sharing among DERs in an islanded microgrid, while simultaneously regulating output voltage and frequency at the PCC. Similar to droop based schemes, the proposed method too facilitates fully decentralized implementation. This is achieved by smart choice of control design enabled by - (a) disturbance rejection viewpoint, (b) decoupling of d-q control loops through appropriate feedforward blocks, and (c) extension of the network control scheme proposed in our prior work. A system consisting of three parallel inverters is simulated in MATLAB Simscape for various challenging scenarios and the results corroborate the effectiveness of the proposed approach.

Keywords:Power electronics, Switched systems, Sampled-data control Abstract: This paper deals with the design of new periodic switching control laws for high frequency DC-DC converters. The contributions are twofolds. On a first hand, the DC-DC converter model are rewritten as a periodic switched affine systems thanks to a delta-operator formulation, which represent an efficient framework for the numerical discretization at high frequencies. On a second hand, three different control laws are provided, the first one being the usual Lyapunov-based control law and the two others being relaxed versions of this first solution. The benefits of these two new control laws over the usual Lyapunov-based one are demonstrated on an simple example. More particularly, it is showed that the selection of sampling period and of the control law strongly influence the size of the region of attraction.

Keywords:Adaptive control, Power electronics Abstract: This paper studies output tracking control of three-phase grid-connected systems with parameter uncertainties. An output feedback model reference adaptive control (MRAC) scheme is employed to achieve three main goals: (i) the asymptotic output tracking of a time-varying reference signal, (ii) the asymptotic rejection of a practical class of unknown high-order harmonic signal disturbances, and (iii) a large reduction of signal measurements for control implementation. Control design conditions are verified for the PV system model, and the MRAC based disturbance rejection scheme is derived. Desired system performance is verified by simulation results. This study shows potential advantages of using adaptive control techniques for PV inverter systems.

Keywords:Power systems, Smart grid, Stability of nonlinear systems Abstract: Hybrid AC/DC networks are a key technology for future electrical power systems, due to the increasing number of converter-based loads and distributed energy resources. In this paper, we consider the design of control schemes for hybrid AC/DC networks, focusing especially on the control of the interlinking converters (ILC(s)). We present two control schemes: firstly a decentralized algorithm for primary control, and secondly, a distributed controller for secondary control. In the primary case, the stability of the controlled system is proven in a general hybrid AC/DC network which may include asynchronous AC subsystems. It is shown that power-sharing across the AC/DC network is significantly improved compared to previously proposed dual droop control. The distributed secondary control scheme guarantees the convergence of the AC system frequencies and the average DC voltage of each DC subsystem to their nominal values respectively. A prescribed power-sharing is also achieved. The proposed algorithms are verified by simulation on a test hybrid AC/DC network in MATLAB / Simulink.

Keywords:Predictive control for nonlinear systems, Constrained control, Optimal control Abstract: Dissipativity properties have become the tool to analyse economic model predictive control (MPC) schemes and optimal system operation. In this paper we establish equivalences between different characterizations of periodic dissipativity used in economic MPC. This allows us to unify various results and use a standard dissipativity condition instead of periodic dissipativity notions in order to characterize optimal periodic operation. As a corollary, we can formulate sufficient conditions that ensure practical asymptotic stability of the optimal periodic orbit when using an economic MPC scheme without terminal constraints.

Keywords:Predictive control for nonlinear systems, Networked control systems, Stability of nonlinear systems Abstract: In this paper, the stability for a class of nonlinear networked control systems with a model predictive controller (MPC) is investigated. Both the sensor-to-controller channel and the controller-to-actuator channel suffer from random packet losses. By constructing a novel cost function, and studying its deviation from the original MPC cost function, we establish the stochastic stability for the closed-loop system. To guarantee the stability, the relationship between the prediction horizon and the packet loss probabilities of two channels is also discussed. Finally, the effectiveness of our results is demonstrated by a numerical example.

Keywords:Predictive control for nonlinear systems, Robust control, Constrained control Abstract: The popularity of model predictive control (MPC) is mainly founded on its easy implementation and its ability to consider state and input constraints. For future applications in safety-critical systems, however, it is necessary to provide formal guarantees of safety despite disturbances and measurement noise. In this paper, we include reachability analysis in an MPC approach to obtain provably safe controllers which are easy to implement. We consider continuous-time, nonlinear systems affected by disturbances and measurement noise. In contrast to most existing techniques, we explicitly consider the computation time and guarantee the satisfaction of state and input constraints despite the previously-mentioned disturbances. We use a novel type of dual mode MPC, which does not require the computation of Lyapunov functions. We demonstrate the applicability of our approach with a numerical example of a chemical reactor, where we show the advantages of our approach compared to existing MPC.

Keywords:Predictive control for nonlinear systems, Delay systems, Lyapunov methods Abstract: This paper represents a first attempt toward an alternative way of computing reduction-based feedback à la Arstein for input-delayed systems. To this end, we first exhibit a new reduction state evolving as a new dynamics which is free of delays. Then, feedback design is carried out by enforcing passivity-based arguments in the reduction time-delay scenario. The case of strict-feedforward dynamics serves as a case study to discuss in details the computational advantages. A simulated exampled highlights performances.

Keywords:Predictive control for nonlinear systems, Observers for nonlinear systems, Estimation Abstract: In this paper, we consider optimization-based state estimation for general detectable nonlinear systems subject to unknown disturbances. The main contribution is a novel formulation of the cost function and a novel proof technique, which allows us (i) to ensure robust global exponential stability of the estimation error under a suitable exponential detectability condition and (ii) to overcome several of the drawbacks in the existing literature. In particular, we obtain improved estimates for the disturbance gains and the required minimal estimation horizon (which are independent of some maximum a priori disturbance bound), and provide a unified proof technique which can be used for both full information estimation and moving horizon estimation.

Keywords:Predictive control for nonlinear systems, Robust control, Aerospace Abstract: Powered descent (PD) is the final stage in Entry, Descent, and Landing where a spacecraft plans and executes a trajectory to a desired landing location. Increased demand for precise landing has driven the need for more robust and sophisticated guidance and control algorithms. While several advances have been made in optimization-based guidance, little progress has been made in developing robust nonlinear controllers. The main technical challenge for controller design is the nonlinear control dynamics in the standard PD model; making traditional methods not applicable. This work derives a robust, exponentially stable nonlinear controller using the Control Contraction Metric framework. The resulting controller takes the form of a nonlinear mass-scheduled proportional-derivative controller - an interesting result given no assumptions about the controller's structure are made. Theoretical guarantees for integrated control effort (i.e., fuel usage) and tracking performance are derived and verified via Monte Carlo simulation. Modifications that facilitate integrating the contraction-based controller into existing optimization-based guidance algorithms are also proposed and verified in simulation.

Keywords:Biological systems, Output regulation Abstract: Mitochondrial Dynamics (MD) has recently emerged as one of the most interesting topics in biology since the intricate connection between energy production and MD regulates cells development and function. On the other hand, the impairment of such mechanism is strictly related to the emergence of various diseases, among which neurodegenerative disorders. In this work, we provide a simple, yet self-consistent, and well-posed mathematical model to describe the MD and the related phenomena through a population-dynamics approach, together with the ATP-energy turnover, which is an important step to unravel the underlying dynamics of the whole cell system and has a key role in its quality control. With the tools of system theory, we highlight the positiveness of the system and the presence of non-zero equilibria and compute bounds for the involved system state quantities. Furthermore, we consider a situation of impairment in the MD and design a control law, based on input-output linearization and state-feedback control able to allow a damaged system to compensate for the defect and behave as a nominal one. In this scenario, we test two different protocols that could be suggestive for treatment strategies.

Keywords:Biological systems, Estimation, Distributed parameter systems Abstract: Multicellular systems play a key role in bioprocess and biomedical engineering. Cell ensembles encountered in these setups show phenotypic variability like size and biochemical composition. As this variability may result in undesired effects in bioreactors, close monitoring of the cell population heterogeneity is important for maximum production output, and accurate control. However, direct measurements are mostly restricted to a few cellular properties. This motivates the application of model-based online estimation techniques for the reconstruction of non-measurable cellular properties. Population balance modeling allows for a natural description of cell-to-cell variability. In this contribution, we present an estimation approach that, in contrast to existing ones, does not rely on a finite-dimensional approximation through grid based discretization of the underlying population balance model. Instead, our so-called characteristics based density estimator employs sample approximations. With two and three- dimensional benchmark examples we demonstrate that our approach is superior to the grid based designs in terms of accuracy and computational demand.

Keywords:Systems biology, Switched systems, Emerging control applications Abstract: Motivated by our prior work on a Triple Negative breast cancer cell line, the focus of this paper is controller synthesis for cancer treatment, through the use of drug scheduling and a switched dynamical system model. Here we study a cyclic schedule of d drugs with maximal waiting times between drug inputs, where each drug is applied once per cycle in any order. We suppose that some of the d drugs are highly toxic to normal cells and that these drugs can shrink the live cancer cell population. The remaining drugs are less toxic to normal cells and can only reduce the growth rate of the live cancer cell population. Also, we assume that waiting time bounds related to toxicity, or to the onset of resistance, are available for each drug. A cancer cell population is said to be stable if the number of live cells tends to zero, as time becomes sufficiently large. In the absence of modeling error, we derive conditions for exponential stability. In the presence of modeling error, we prove exponential stability and derive a settling time, under certain mathematical conditions on the error. We conclude the paper with a numerical example that uses models which were identified on Triple Negative breast cancer cell line data.

Keywords:Hybrid systems, Biological systems, Discrete event systems Abstract: In this paper, a class of stochastic hybrid systems comprising of multiple operation modes is studied. In each mode, the state evolves according to a linear stochastic differential equation. We allow for stochastic switching between operational modes with switching times controlled by an underlying renewal process such that the time spent in each mode is a random variable with an arbitrary given probability distribution. We present a novel method to derive exact analytical solutions for the statistical moments, and illustrate the applicability of the method on an example drawn from systems biology. More specifically, we study how random switching of a gene between transcriptionally active and inactive states drives stochastic variation in the level of the expressed protein. Our results show that while randomness in gene switching times has no effect on the mean protein level, it critically impacts the magnitude of fluctuations in the protein level. This effect is further amplified for proteins with high decay rate. We finally discuss how noise in protein levels can be used to infer the underlying gene expression mechanisms.

Keywords:Biological systems, Pattern recognition and classification, Optimization Abstract: Spatial-temporal patterning is an essential process indicating the cell and tissue types formed during synthetic and natural tissue development. Due to biological complexity within and among cells, most approaches to engineer cell cultures are limited in their ability to control the timing of spatial patterning. This paper presents a computational framework to control spatial-temporal pattern formation in a network of locally interacting agents. Given a parameterized model of patterning in stem cell colonies, we use a supervised machine learning algorithm combined with temporal logics to quantitatively describe and characterize spatial-temporal patterns. We utilize an optimization procedure to achieve optimal parameters that maximize the occurrence of desired spatial patterns at a specified time interval and demonstrate the ability of our algorithm to control transitioning in a sequence of patterns.

Keywords:Biological systems, Variational methods, Game theory Abstract: We investigate a variational problem on the probability simplex with a path cost expressed as a sum of two terms reminiscent of Lagrangian mechanics. This arose first in a 1972 paper of Y. M. Svirezhev on mathematical genetics, where it was demonstrated that solutions to certain equations governing evolutionary processes are extremals of the variational problem. In the present work, we show that this result holds generally for replicator dynamics, a natural class of dynamical systems on the probability simplex, of great interest in evolutionary game theory. The Lagrangian of Svirezhev respects time-translation symmetry and hence has a conserved quantity, the energy. In particular, solutions to replicator dynamics are extremals confined to the zero level set of energy. Solutions of the dual Hamiltonian system are also of interest. Here we investigate their properties in relation to 2 x 2 matrix games, and assert existence of periodic orbits under suitable hypotheses.

Keywords:Game theory, Variational methods, Network analysis and control Abstract: We consider distributed generalized Nash equilibrium (GNE) seeking over networks, in games with shared affine constraints. Existing methods require that each player has full access to opponents' decisions. Here we assume that players have only partial-decision information, and can communicate with their neighbours over an arbitrary undirected graph. We recast the problem as one of zero finding for a sum of monotone operators through primal-dual analysis. To distribute the problem, we doubly augment variables: each player has local decision estimates and local copies of Lagrangian multipliers. We propose a single-layer algorithm, fully distributed with respect to both primal and dual variables, based on a forward-backward splitting for doubly-augmented monotone operators. We show its convergence with fixed step-sizes, under cocoercivity of the extended pseudo-gradient.

Keywords:Game theory, Stability of nonlinear systems, Network analysis and control Abstract: We study the evolutionary dynamics of games under environmental feedback using replicator equations for two interacting populations. One key feature is to consider jointly the co-evolution of the dynamic payoff matrices and the state of the environment: the payoff matrix varies with the changing environment and at the same time, the state of the environment is affected indirectly by the changing payoff matrix through the evolving population profiles. For such co-evolutionary dynamics, we investigate whether convergence will take place, and if so, how. In particular, we identify the scenarios where oscillation offers the best predictions of long-run behavior by using reversible system theory. The obtained results are useful to describe the evolution of multi-community societies in which individuals’ payoffs and societal feedback interact.

Keywords:Game theory, Optimization algorithms, Distributed control Abstract: We address the generalized aggregative equilibrium seeking problem for noncooperative agents playing average aggregative games with affine coupling constraints. First, we use operator theory to characterize the generalized aggregative equilibria of the game as the zeros of a monotone set-valued operator. Then, we massage the Douglas–Rachford splitting to solve the monotone inclusion problem and derive a single layer, semi-decentralized algorithm whose global convergence is guaranteed under mild assumptions. The potential of the proposed Douglas–Rachford algorithm is shown on a simplified resource allocation game, where we observe faster convergence with respect to forward-backward algorithms.

Keywords:Optimization algorithms, Game theory, Optimization Abstract: This paper considers an N-player stochastic Nash game in which the ith player minimizes a composite objective f_i(x) + r_i(x_i), where f_i is expectation-valued and r_i has an efficient prox-evaluation. In this context, we make the following contributions. (i) Under a strong monotonicity assumption on the concatenated gradient map, we derive ({bf optimal}) rate statements and oracle complexity bounds for the proposed variable sample-size proximal stochastic gradient-response (VS-PGR) scheme; (ii) We overlay (VS-PGR) with a consensus phase with a view towards developing distributed protocols for aggregative stochastic Nash games. Notably, when the sample-size and the number of consensus steps at each iteration grow at a suitable rate, a linear rate of convergence can be achieved; (iii) Finally, under a suitable contractive property associated with the proximal best-response (BR) map, we design a variable sample-size proximal BR (VS-PBR) scheme, where the proximal BR is computed by solving a sample-average problem. If the batch-size for computing the sample-average is raised at a suitable rate, we show that the resulting iterates converge at a linear rate and derive the oracle complexity.

Keywords:Stability of nonlinear systems, Game theory Abstract: This paper investigates an energy conservation and dissipation – passivity – aspect of dynamic models in evolutionary game theory. We define a notion of passivity using the state-space representation of the models. Our main contributions include devising systematic methods to examine passivity and identifying properties of passive dynamic models. We explain how our main results can be used to establish a connection between passivity and stability of equilibrium in population games and provide numerical simulations to illustrate stability in population games.

Keywords:Variational methods, Agents-based systems, Control over communications Abstract: We study distributed algorithms for seeking a Nash equilibrium in a class of non-cooperative games with strongly monotone mappings. Each player has access to her own smooth local cost function and can communicate to her neighbors in some undirected graph. We first consider a distributed gradient play algorithm, which we call GRANE, for determining a Nash equilibrium. The algorithm involves every player performing a gradient step to minimize her own cost function while sharing and retrieving information locally among her neighbors in the network. We prove the convergence of this algorithm to a Nash equilibrium with a geometric rate. Further, we introduce the Nesterov type acceleration for the gradient play algorithm. We demonstrate that, similarly to the accelerated algorithms in centralized optimization and variational inequality problems, our accelerated algorithm outperforms GRANE in the convergence rate.

Keywords:Hybrid systems, Computational methods Abstract: The synthesis of correct-by-design control software is a promising direction to address the well known difficulties in formally verifying complex cyber-physical systems. Despite the promise of this approach, it is currently limited to small systems since it typically requires the computation of a finite-state abstraction whose size grows exponentially with the number of continuous states. In this paper we present a new way to tackle the lack of scalability of control software synthesis by adopting a lazy controller synthesis approach. Instead of synthesizing a controller using a precomputed abstraction of the full system, the abstraction is computed lazily as needed for safety and reachability specifications. We illustrate, through different examples, how this lazy approach significantly reduces the total time required for the synthesis of correct-by-design controllers.

Keywords:Automata, Discrete event systems, Optimization algorithms Abstract: This paper investigates the synthesis of edit functions for opacity enforcement using abstraction methods to reduce computational complexity. Edit functions are used to alter system outputs by erasing or inserting events in order to prevent violations of opacity. We introduce two abstraction methods, called opaque observation equivalence and opaque bisimulation, that are used to abstract the original system and its observer before calculating edit functions. We present a set of results on abstraction for opacity and its enforcement by edit functions that prove that edit functions synthesized from abstracted models are “equivalent” to ones synthesized from original ones. Our approach leverages the technique of edit function synthesis using the All Edit Structure from prior works.

Keywords:Game theory, Markov processes, Stochastic optimal control Abstract: The majority of work in pursuit-evasion games assumes perfectly rational players who are omnipotent and have complete knowledge of the environment and the capabilities of other agents and, consequently, are correct in their assumption of the game that is played. This is rarely the case in practice. Most often than not, the players have different knowledge about the environment either because of sensing limitations or because of prior experience. In this paper, we wish to relax this assumption and consider pursuit-evasion games in a stochastic setting, where the players involved in the game have different perspectives regarding the transition probabilities that govern the world dynamics. We show the existence of a (Nash) equilibrium in this setting and discuss the computational aspects obtaining such an equilibrium. We also investigate a relaxation of this problem employing the notion of correlated equilibria. Finally, we demonstrate the approach using a grid-world example with two players in the presence of obstacles.

Keywords:Optimization algorithms, Numerical algorithms, Autonomous systems Abstract: The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in guidance of systems. Unfortunately, those algorithms are still seen as new and obscure and are not considered as a viable option for safety critical roles. This paper deals with the formal verification of convex optimization algorithms. Additionally, we demonstrate how theoretical proofs of real-time convex optimization algorithms can be used to describe functional properties at the code level, thereby making it accessible for the formal methods community. In seeking zero-bug software, we use the Credible Autocoding framework. We focused our attention on the Ellipsoid Algorithm solving second-order cone programs (SOCP). The paper also considers floating-point errors and gives a framework to numerically validate the method.

Keywords:Predictive control for linear systems, Predictive control for nonlinear systems, Optimal control Abstract: Abstract--- This paper presents an online approach to safety critical control. The common approach for enforcing safety of a system requires the offline computation of a viable set, which is either hard and time consuming or very restrictive in terms of operational freedom for the system. The first part of this work shows how one can constrain a system to stay within reach of an appropriately chosen backup set in a minimally invasive way by performing online sensitivity analysis around a backup trajectory. For linear systems, we show how to use an optimal backup strategy in the form of a Model Predictive Controller (MPC) to maximize the operational freedom of the system. The second part of this work shows how to leverage this capability and factor in state constraints to enforce set invariance only based on online computations of sensitivities. For linear systems, the optimal strategy is again considered and we show how one can perform the sensitivity analysis based on a measure of feasibility of a state constrained MPC. This approach is illustrated in simulation on a linear inverted pendulum.

Keywords:Optimization algorithms, Numerical algorithms, Constrained control Abstract: Real-time optimization problems are ubiquitous in control and estimation, and are typically parameterized by incoming measurement data and/or operator commands. This paper proposes solving parameterized constrained nonlinear programs using a semismooth predictor-corrector (SSPC) method. Nonlinear complementarity functions are used to reformulate the first order necessary conditions of the optimization problem into a parameterized non-smooth root-finding problem. Starting from an approximate solution, a semismooth Euler-Newton algorithm is proposed for tracking the trajectory of the primal-dual solution as the parameter varies in time. Active set changes are naturally handled by the SSPC method, which only requires the solution of linear systems of equations. The paper establishes conditions under which the solution trajectories of the root-finding problem are well behaved and provides sufficient conditions for ensuring boundedness of the tracking error. Numerical case studies, featuring the application of the SSPC method to nonlinear model predictive control, are reported and demonstrate the advantages of the proposed method.

Keywords:Autonomous vehicles, Autonomous systems, Autonomous robots Abstract: In this paper, we address the problem of risk-aware conditional planning where the goal is generating risk bounded motion policies in the presence of uncertainty. The problem is modeled as a chance-constrained Partially Observable Markov Decision Process (CC-POMDP) with one controllable agent and multiple uncontrollable agents, each of which can choose from a set of maneuver actions. The risk is defined as the probability of the controllable agent violating safety constraints. Off-line computations include generating a library of probabilistic maneuvers for the controllable agent and planning an initial motion policy to execute. During runtime, the conditional planner can quickly look up maneuver sequences to ensure risk bounds as the world around our agent evolves. We introduce the iterative RAO* heuristic search algorithm, which iteratively generates risk bounded conditional plans over a finite horizon. We demonstrate the performance of the provided approach on two planning problems of autonomous vehicles.

Keywords:Autonomous vehicles, Pattern recognition and classification Abstract: This paper discusses a novel approach to model human driver behavior. A classification-based method is proposed to construct a reactive bound on possible human driving actions given the scenario description (such as the vehicle states and the behavior of surrounding vehicles). This approach captures the reactiveness and uncertainty of human drivers. Real human driving data is used as the positive training data, while dangerous actions sampled via a Hamilton Jacobi reachability computation constitute the negative training data. A classifier that separates the two groups is then trained via a customized pazocal{L}_1 Support Vector Machine (SVM), and an analytical bound function is derived from the classifier which maps the state and surrounding vehicles' actions to the bound on possible actions of the human driver. The credibility of the proposed approach is analyzed under the random convex optimization framework. Potential applications of this work include the computation of safe sets, synthesis of safety guaranteed controllers for systems interacting with humans such as autonomous vehicles, and evaluation of such systems.

Keywords:Autonomous vehicles, Automotive systems Abstract: This paper addresses the robust cooperative leader tracking problem for a platoon of connected autonomous vehicles in the presence of both multiple Vehicle-to-Vehicle (V2V) time-varying communication delays and external disturbances. To tackle this issue, a distributed adaptive protocol is proposed, that exploits shared information among connected vehicles to achieve leader synchronization. The robust stability of the closed-loop delayed network is proven via Lyapunov-Krasovskii theory. Delay-dependent linear matrix inequalities (LMIs) conditions are analytically derived for ensuring both robust synchronization to the leader dynamics and disturbances attenuation. An exemplar driving maneuver is considered for evaluating the robustness of the performance achieved by vehicles platoon and the numerical results confirm the effectiveness of the theoretical derivation.

Keywords:Autonomous vehicles, Adaptive control, Control applications Abstract: This paper presents the use of a quadratic band controller in an autonomous vehicle (AV) to regulate emergent traffic waves resulting from traffic congestion. The controller dampens the emergent traffic waves through modulating its velocity according to the relative distance and velocity of the immediately preceding vehicle in the flow. At the same time, it prevents any collision within the range specified by the design parameters. The approach is based on a configurable quadratic band that allows smooth transitions between (i) no modification to the desired velocity; (ii) braking to match the speed of the preceding vehicle; and (iii) braking to avoid collision with the lead vehicle. By assuming that the lead vehicle's velocity will be oscillatory, the controller's smooth transition between modes permits any vehicle following the AV to have a smoother reference velocity. The configurable quadratic band allows design parameters, such as actuator and computation delays as well as the dynamics of vehicle deceleration, to be taken into account when constructing the controller. Experimental data, software-in-the-loop distributed simulation, and results from physical platform performance in an experiment with 21 human-driven vehicles are presented. Analysis shows that the design parameters used in constructing the quadratic band controller are met, and assumptions regarding the oscillatory nature of emergent traffic waves are valid.

Keywords:Autonomous vehicles, Adaptive systems, Uncertain systems Abstract: This paper focuses on a rendezvous guidance method for vehicles taking account of unknown but bounded target maneuvers and uncertain vehicle dynamics including the uncertain system lag by using two estimators; one is an extended state high-gain-observer-based estimator for the estimation of an uncertainty and disturbance term treated as an unknown (extended) state that affects the line-of-sight rate dynamics, and the other is a novel filter to estimate the uncertain system lag. The novel filter is driven only when the filter system produces a difference between the filter's estimated state and the commanded value, which makes the system observable as long as the difference exists while the linearized system from this original system is usually unobservable. The potential of the proposed disturbance-compensated rendezvous guidance is demonstrated with some representative simulations.

Keywords:Autonomous vehicles, Human-in-the-loop control, Automotive control Abstract: In this paper, we use control improvisation to synthesize voluntary lane-change policy that meets human preferences under given traffic environments. We first train Markov models to describe traffic patterns and the motion of vehicles responding to such patterns using traffic data. The trained parameters are calibrated using control improvisation to ensure the traffic scenario assumptions are satisfied. Based on the traffic pattern, vehicle response models, and Bayesian switching rules, the lane-change environment for an automated vehicle is modeled as a Markov decision process. Based on human lane-change behaviors, we train a voluntary lane-change policy using explicit-duration Markov decision process. Parameters in the lane-change policy are calibrated through control improvisation to allow an automated car to pursue faster speed while maintaining desired frequency of lane-change maneuvers in various traffic environments.

Keywords:Network analysis and control, Agents-based systems, Algebraic/geometric methods Abstract: This paper is about a new model of opinion dynamics with opinion-dependent connectivity. We assume that agents update their opinions asynchronously and that each agent's new opinion depends on the opinions of the "k" agents that are closest to it. We show that the resulting dynamics is substantially different from comparable models in the literature, such as bounded-confidence models. We study the equilibria of the dynamics, observing that they are robust to perturbations caused by the introduction of new agents. We also prove that if the number of agents "n" is smaller than "2k", the dynamics converge to consensus. This condition is only sufficient.

Keywords:Network analysis and control, Sensor networks Abstract: In this paper, we consider the problem of assigning time-varying weights on the links of a time-invariant digraph, such that average consensus is reached in a finite number of steps. More specifically, we derive a finite set of weight matrices that are based on the Laplacian and the Laplacian eigenvalues of the given digraph, such that the product of these weight matrices (in any order) leads to a rank-one matrix. Using the weights associated with this sequence of weight matrices, the nodes run two linear iterations (each with its own initial conditions) and, after a finite number of steps, can calculate the average of the initial values by taking the ratio of the two values they possess at the end of the iteration process. As in the case of undirected graphs, we show that the set of matrices depends on the number of nonzero distinct eigenvalues of the Laplacian matrix. However, unlike the case for undirected graphs, the Laplacian matrix is no longer symmetric, and the number of steps depends not only on the number of distinct eigenvalues but also on their algebraic multiplicities. Illustrative examples demonstrate the validity of the derived results.

Keywords:Network analysis and control, Stability of nonlinear systems, Petri nets Abstract: In this note we consider consensus protocols where an agent would not be influenced by any of his neighbours singularly taken, but might be sensitive to the simultaneous and coherent influence of two or more of them. This may resemble several common behaviours in social, economic and opinion networks (i.e. conformity, risk aversion, social inertia, herding). We derive novel graph-theoretical concepts to describe and analyze the ability of general networks with joint-agent interactions to converge towards consensus. Interestingly, and for the first time, we borrow to this end the language of Petri Nets as a convenient way to describe bipartite directed graphs, showing how the notion of siphon is helpful in characterizing the flow of information across the network and its ability to induce attainment of consensus among agents in the considered set-up.

Keywords:Network analysis and control, Networked control systems, Communication networks Abstract: The behavior of a network of heterogeneous Van der Pol oscillators under output diffusive coupling is studied. By the intuition on strong coupling given by the series of `blended dynamics' research, we first show that under sufficiently strong coupling gain the network achieves practical synchronization among heterogeneous oscillators even when there is no common internal model. Then, a further analysis finds a necessary and sufficient condition for the network to achieve synchronous and oscillatory behavior. It should be noted that the condition is the existence of a stable limit cycle for an emergent Van der Pol oscillator we introduce in this paper. Since the stability of each oscillator is not asked, the individual can be any system having the same structure with the Van der Pol oscillator, for instance, double integrator, linear oscillator, and a Van der Pol oscillator with an unstable limit cycle. Finally, by applying a modified singular perturbation theory, we show that the individual agent oscillates near the stable limit cycle of the emergent Van der Pol oscillator.

Keywords:Network analysis and control, Identification, Networked control systems Abstract: This paper deals with identifiability of undirected dynamical networks with single-integrator node dynamics. We assume that the graph structure of such networks is known, and aim to find graph-theoretic conditions under which the state matrix of the network can be uniquely identified. As our main contribution, we present a graph coloring condition that ensures identifiability of the network’s state matrix. Additionally, we show how the framework can be used to assess identifiability of dynamical networks with general, higher-order node dynamics. As an interesting corollary of our results, we find that excitation and measurement of all network nodes is not required. In fact, for many network structures, identification is possible with only small fractions of measured and excited nodes.

Keywords:Network analysis and control, Control of networks, Control system architecture Abstract: The impacts of high and low gain controllers on remote channels in a linear diffusive network model are studied, from a topological perspective. Specifically, we study how a high or low gain controller deployed at one point in the network influences the finite and infinite zero structure of a second channel. The analysis shows how the network's graph topology, the positions of the control channels relative to the topology, and the specifics of the built controller influence the zero structure. The analysis yield conditions under which a deployed controller can induce nonminimum phase behaviors, and also conditions where minimum-phase dynamics are preserved.

Keywords:Compartmental and Positive systems, Large-scale systems, Stability of linear systems Abstract: In this tutorial paper we first present some foundational results regarding the theory of positive systems. In particular, we present fundamental results regarding stability, positive realization and positive stabilization by means of state-feedback. Special attention is also paid to the system performance in terms of disturbance attenuation. Under the asymptotic stability assumption, such performance can be measured in terms of Lp-gain of the positive system. In the second part of the paper we propose some recent results about control synthesis by linear programming and semidefinite programming, under the positivity requirement on the resulting controlled system. These results highlight the value of positivity when dealing with large scale systems. Indeed, stability properties for these systems can be verified by resorting to linear (copositive) or diagonal Lyapunov functions that scale linearly with the system dimension, and such linear functions can be used also to design stabilizing feedback control laws. In addition, stabilization problems with disturbance attenuation performance can be easily solved by imposing special structures on the state feedback matrices. This is extremely valuable when dealing with large scale systems for which state feedback matrices are typically sparse, and their structure is a priori imposed by practical requirements.

Keywords:Compartmental and Positive systems, Large-scale systems, Stability of linear systems Abstract: In the talk we will start by providing some real-world motivating examples that stimulated the research in this field. The talk will provide then an overview of the main theoretical tools adopted in the investigation of linear state-space models under the positivity constraint, e.g., Perron-Frobenius theory, linear copositive Lyapunov functions, diagonal Lyapunov functions, L1-induced norm. Stability and stabilizability of both positive systems and positive switched systems will be discussed, by pointing out known results and open problems.

Keywords:Compartmental and Positive systems, Large-scale systems, Stability of linear systems Abstract: Positive systems appear naturally in modeling of many large network problems. In this presentation, we will show how to exploit the positivity property to simplify analysis and synthesis of controllers for such networks. In particular, we will explain how synthesis of H-infinity optimal distributed controllers can achieve the same performance as centralized Riccati equation-based controllers, at much lower computational cost. For controllers with integral action, internal positivity of the closed loop system will be lost, but the crucial benefits can still be retained by exploiting external positivity. Motivated by transportation networks, we will also a take brief look at the effect of capacity constraints, where the notion of positivity needs to be replaced by its non- linear counterpart, monotonicity.

Keywords:Compartmental and Positive systems, Large-scale systems, Stability of linear systems Abstract: In this talk we start from the basics about linear copositive Lyapunov functions for positive systems, followed by the characterization of the L1-induced norm of positive systems by means of linear inequalities (linear programming problems). We show that, a slightly generalized version, weighted L1-induced norm, is useful for the stability analysis of large-scale interconnected systems constructed from positive subsystems. More precisely, we show that the interconnected system is stable if and only if there exists a set of weighting vectors that renders the weighted L1-induced norm of each positive subsystem smaller than one. We can readily apply this result to decentralized stabilizing state-feedback controller synthesis for large-scale interconnected systems, where we can design each local controller optimally and purely locally without knowing global information about the whole interconnected system.

Keywords:Switched systems, Compartmental and Positive systems, Optimal control Abstract: In the talk we briefly illustrate three application-oriented problems: 1) Therapy scheduling for HIV load mitigation, 2) Traffic light scheduling in road junctions, 3) AIMD based distributed car battery charging in public parking. The three problems are closely connected with the theory of optimal control of positive switched systems. It is shown that under some assumptions one can exploit the convexity of the cost function, thus paving the way to easy numerical solutions. Another fundamental tool is played by the so-called “arg-min” switching theory inherited by co-positive Lyapunov-Metzler inequalities. Such inequalities generate a switching rule capable to stabilize the system and provide an upper bound on the optimal cost. Finally the classical AIMD (additive increasing multiplicative decreasing) algorithm is presented and its effectiveness in distributed scheduling problems is illustrated via a simple resource allocation problem.

Keywords:Distributed control, Optimization algorithms, Power systems Abstract: The Primal-Dual (PD) algorithm is widely used in convex optimization to determine saddle points. While the stability of the PD algorithm can be easily guaranteed, strict contraction is nontrivial to establish in most cases. This work focuses on continuous, possibly non-autonomous PD dynamics arising in a network context, in distributed optimization, or in systems with multiple time-scales. We show that the PD algorithm is indeed strictly contracting in specific metrics and analyze its robustness establishing stability and performance guarantees for different approximate PD systems. We derive estimates for the performance of multiple time-scale multi-layer optimization systems, and illustrate our results on a primal-dual representation of the Automatic Generation Control of power systems.

Keywords:Distributed control, Predictive control for linear systems, Robust control Abstract: A tube-based distributed model predictive control (DMPC) scheme is proposed for dynamically coupled linear systems. The control scheme is designed to guarantee local performance even when neighboring controllers are not complying with the requirements of the algorithm (e.g., they are malicious or faulty). The resulting conservativeness is minimized, for controllers aim to minimize their state and input constraint sets to reduce mutual disturbances. Also, sufficient conditions for feasibility and exponential stability are given. Finally, these ideas are illustrated and assessed with respect to other robust DMPC via a simulated example.

Keywords:Distributed control, Networked control systems, Optimization algorithms Abstract: In this paper we present a distributed control approach for the multi-user multi-constrained waterfilling. This a specific category of distributed optimization for Networked Control Systems (NCSs), where agents aim at optimizing a non-separable global objective function while satisfying both local constraints and coupling constraints. Differently from the existing literature, in the considered setting we adopt a fully distributed mechanism where communication is allowed between neighbors only. First, we formulate a general multi-user waterfilling-structured optimization problem including coupling constraints, which may represent many engineering distributed control problems. Successively, we define a low-complexity iterative distributed algorithm based on duality, consensus and fixed point mapping theory. Finally, applying the technique to a simulated case referring to the electric vehicles optimal charging problem, we show its effectiveness.

Keywords:Distributed control, Networked control systems, Randomized algorithms Abstract: Many problems in distributed control reduce to the distributed computation of the average of initial values in a networked system of autonomous agents, known as the average consensus problem.

We present a randomized algorithm that solves this problem in networks with directed, time-varying communication topolo- gies, in linear time in the size of the network. This algorithm leverages properties of exponential random variables, which allows for approximating sums by computing minima. It is completely decentralized, in the sense that it does not rely on agent identifiers or global information of any kind. Besides, the agents do not need to know their out-degree; hence, our algorithm demonstrates how randomization can be used to circumvent the impossibility result established in [1].

Using a logarithmic rounding rule, we show that this algo- rithm can be used under the additional constraints of finite memory and channel capacity. We furthermore extend the al- gorithm with a termination test, by which the agents can decide irrevocably in finite time — rather than simply converge — on an estimate of the average.

Keywords:Distributed control, Cooperative control Abstract: Using relative measurements in agents’ neighborhoods, graph theoretic distributed algorithms have been widely investigated to achieve agreement in a group of individual dynamical systems. We consider a class of partially known multiagent systems with mixed first- and second-order agents whose nonlinear dynamics interact over two agent layers. We assume a constant reference command is sent to only a few agents and propose a cooperative reference tracking problem from a large-scale system viewpoint. We investigate the case that no local control implementation is permitted and, proposing a linear distributed protocol with two communication topologies as control layers, formulate the problem as two graph topology design tasks to be solved using an optimal control theoretic approach. We develop closed-form solutions for these control layers and prove the robustness of exponential reference tracking behavior with respect to the modeling uncertainties over agent layers. We also investigate the robust performance of closed-loop multiagent system based on a quadratic cost function. We verify the feasibility of these developments through a simulation study.

Keywords:Distributed control, Optimal control, Robust control Abstract: The problem of robust distributed control arises in several large-scale systems, such as transportation networks and power grid systems. In many practical scenarios controllers might not have enough information to make globally optimal decisions in a tractable way. We propose a novel class of tractable optimization problems whose solution is a controller complying with any specified information structure. The approach we suggest is based on decomposing intractable information constraints into two subspace constraints in the disturbance feedback domain. We discuss how to perform the decomposition in an optimized way. The resulting control policy is globally optimal when a condition known as Quadratic Invariance (QI) holds, whereas it is feasible and it provides a provable upper bound on the minimum cost when QI does not hold. Finally, we show that our method can lead to improved performance guarantees with respect to previous approaches, by applying the developed techniques to the platooning of autonomous vehicles.

Keywords:Distributed parameter systems, Time-varying systems, Linear systems Abstract: Time-variant fractional systems have many applications. For example, they can be used for system identification of lithium-ion batteries. However, the analytical solution of the time-variant fractional pseudo state space equation is missing so far. To overcome this limitation, this letter introduces a novel matrix approach, namely the generalized Peano–Baker series, which is comparable to the transition matrix in the case of ordinary systems. Using this matrix, the solution of the time-variant fractional pseudo state space equation is derived. The initialization process is taken into account, which has been proven to be a crucial part for fractional operator calculus. Following this initialization, a modified definition of a fractional pseudo state is presented.

Keywords:Distributed parameter systems, Fluid flow systems, Lyapunov methods Abstract: This paper considers the problem of finite-time stabilization of coupled reaction-diffusion partial differential equations by means of boundary time-varying feedbacks; moreover, the time of convergence can be prescribed in the design. The design of time-varying feedbacks is carried out based on the backstepping approach. Selecting a suitable target system with time varying-coefficients, the resulting kernel of the backstepping transformation is time-varying which provides the control feedback to be time-varying as well. The target system turns out to be fixed-time stable and two cases for the control design are pointed out in order to obtain either boundedness or fixed-time convergence of the original system. A simulation example is presented to illustrate the results.

Keywords:Distributed parameter systems, Algebraic/geometric methods, Mechatronics Abstract: In this paper, we consider nonlinear PDEs in a port-Hamiltonian setting based on an underlying jet bundle structure. We restrict ourselves to systems with 1-dimensional spatial domain and 2nd-order Hamiltonian including certain dissipation models that can be incorporated in the port-Hamiltonian framework by means of appropriate differential operators. For this system class, energy-based control by means of Casimir functionals as well as energy balancing is analysed and demonstrated using a nonlinear Euler-Bernoulli beam.

Keywords:Fluid flow systems, Optimal control, Distributed parameter systems Abstract: This paper is concerned with establishing a rigorous mathematical framework to address optimal control designs for heat transfer in unsteady Stokes flows. In particular, we focus on the problem of enhancing convection-cooling between two fluids via controlling the velocity of the cold fluid flow, where both internal and boundary controls will be investigated. This essentially leads to a bilinear control problem. We present a rigorous proof of the existence of an optimal control and derive the first-order necessary conditions for optimality by using a variational inequality. Finally, we show that the uniqueness of the optimal controller can be obtained if the control weight is sufficiently large.

Keywords:Distributed parameter systems, Lyapunov methods Abstract: In this paper, we establish the input-to-state stability (ISS) and the integral input-to-state stability (iISS) in L^q-norm for some qgeq 2 with respect to in-domain and boundary disturbances for a generalized Burgers' equation with higher-order nonlinearities. Two different boundary conditions corresponding to, respectively, linear and nonlinear boundary controls are considered in the investigation of the ISS properties of such a system. These results are achieved by using the method of Lyapunov functional combined with some Sobolev embedding-like inequalities, which allow dealing with the boundary conditions involving spatial derivatives of the solution.

Keywords:Control applications Abstract: In general, researchers use numerous methods to tune controllers for the given generalized plant structure. This structure deals with integer/fractional order plant plus dead time with real coefficient. However, controller tuning methods for complex coefficient plus fractional complex order plant with dead time are not reported in the existing literature. In this paper, a unified fractional and fractional complex order controller expressions are derived for the proposed universal structure. This structure comprises complex coefficient plus fractional complex order derivatives with dead time. To demonstrate the controller tuning for the defined structure, two different case studies are simulated to meet the desired specifications.

Keywords:Model/Controller reduction, Differential-algebraic systems, Linear systems Abstract: Differential-algebraic equations (DAEs) are a widespread dynamical model that describes continuously evolving quantities defined with differential equations, subject to constraints expressed through algebraic relationships. As such, DAEs arise in many fields ranging from physics, chemistry, and engineering. In this paper we focus on linear DAEs, and develop a theory for their minimization up to an equivalence relation. We present backward invariance, which relates DAE variables that have equal solutions at all time points (thus requiring them to start with equal initial conditions) and extends the line of research on backward-type bisimulations developed for Markov chains and ordinary differential equations. We apply our results to the electrical engineering domain, showing that backward invariance can explain symmetries in certain networks as well as analyze DAEs which could not be originally treated due to their size.

Keywords:Model/Controller reduction, Sampled-data control, Identification for control Abstract: This paper investigates the sampled-data driven modeling and controlling strategy for a class of high-order nonlinear systems. With discretization techniques and estimation methods, a novel characteristic model is constructed and then its corresponding adaptive control law is designed. The proposed approaches are proven to be effective in modeling and control via the studies on the fast stability problem of sun synchronous orbit satellite.

Keywords:Model/Controller reduction, Control of networks, Network analysis and control Abstract: In this work, we derive sufficient conditions under which compositional abstractions of interconnected systems evolving on Riemannian manifolds can be constructed using the interconnection topology and joint differential dissipativity-type properties of subsystems and their abstractions. This allows for a much broader variety of systems than the ones considered in the existing works defined over Euclidean spaces. In the proposed framework, the abstraction, itself a control system (possibly with a lower dimension), can be used as a substitute of the original system in the controller design process. We provide an example to illustrate the effectiveness of the proposed differential dissipativity-type compositional reasoning for interconnected control systems.

Keywords:Model/Controller reduction, Control of networks, Network analysis and control Abstract: In this work, we propose a compositional approach for the construction of approximations for interconnected systems evolving on Riemannian manifolds. This allows for larger classes of systems than the ones considered in existing works defined only over Euclidean spaces. In the proposed framework, the approximation, itself a control system (possibly with a lower dimension), can be used as a substitute of the original system in the controller design process. We employ a notion of so-called simulation function, constructed using a (pseudo) Riemannian metric defined over the tangent bundle of the state space, to quantify the error between concrete interconnected control systems and their approximations. We provide a small-gain type condition that enables the construction of an abstraction for the interconnected control system compositionally.

Keywords:Model/Controller reduction, Large-scale systems, Modeling Abstract: Nonlinear thermal simulations of distributed parameter systems with complex geometry can be performed using finite element analysis (FEA). In order to achieve accurate results, fine spatial and time discretization is required, which often leads to large computation times. However, many methods from system theory, such as parameter identification, real-time model-based control, and model-in-the-loop simulation, heavily rely on either multiple iterations or computation time limits. Hence, a direct model deviation from FEA is unfeasible for these approaches. Model order reduction (MOR) techniques have been proposed to improve computational performance. However, most of them are only applicable to linear systems, but linearization of nonlinear boundary conditions over a wide temperature range does not always fulfill accuracy requirements. Therefore, we propose a simplified nonlinear system description by decoupling nonlinear affected states, performing MOR of the remaining linear term and apply calculated projection to the nonlinear affected part. During simulation, the reduced linear system is frequently corrected by the nonlinear term with a specified execution trigger. As a result, computation performance is increased significantly, maintaining sufficient accuracy, which prospectively enables high-performance approximation of nonlinear system behavior.

Keywords:Model/Controller reduction, Estimation, Algebraic/geometric methods Abstract: From industry there is an increasing interest in applying model based control techniques to large-scale systems. Control designs like H_{2} and H_{∞} optimal control will typically contain a dynamic state observer in which the order will be equal to the model order. Consequently, real-time implementation of the controller may not be possible due to computational constraints. The problem of designing a constrained order observer for a large-scale system, with explicit guarantees on the output estimate is therefore a relevant problem in these applications.

This paper addresses the problem of constructing (if it exists) an observer with a constrained order that decouples the output estimation errors from the disturbances that are acting on the system. In addition, stability of the output estimate, a characterization of the orders for which the observer can achieve disturbance decoupled estimation and the explicit construction of the observer are discussed.

Univ. of New South Wales at the AustralianDefenceForceAcad

Keywords:Robust control, Stability of linear systems, Lyapunov methods Abstract: This paper presents a method for the synthesis of negative imaginary closed-loop systems with a prescribed degree of stability under the assumption of full state feedback. The approach extends existing work by using a perturbation method to ensure a closed-loop system that has both the negative imaginary property and a prescribed degree of stability. This approach involves the real Schur decomposition of a matrix followed by the solution to two Lyapunov equations which provides computational advantages over alternate state feedback synthesis techniques. Also, some counterexamples are presented which clarify the perturbation properties of strictly negative imaginary systems.

Keywords:Robust control, Optimal control, Robotics Abstract: Two important paradigms in control theory are the nonlinear H2 and H-infinity control approaches. Despite many advantages, such approaches present limitations in the sense to control the transient closed-loop response. An interesting approach to address these issues is the formulation of both controllers in the Sobolev space W_(m,p). However, the latter also presents drawbacks, now in sense of weighting the cost variable and its time derivatives component-wise. Therefore, aiming to deal with underactuated mechanical systems with input coupling, this work presents a new formulation of the nonlinear H2 and H-infinity control approaches in the Weighted Sobolev space W_(m,p,sigma). It is also shown that for the particular systems treated in this work the W2 and W-infinity optimal controllers are equivalent. In addition, a particular solution is proposed to the HJB and HJBI equations that arises from the problem formulation. The controller is corroborated by numerical experiments conducted with a quadrotor UAV.

Keywords:Robust control, Uncertain systems, Biomedical Abstract: This paper presents a new control method for the nonlinear human heart beat rate dynamics during treadmill exercise. The reference trajectory represents a desired heart rate profile suggested by the physician. The goal is to design the treadmill speed input for tracking control purposes. Using Lyapunov stability arguments, we propose a parsimonious static output feedback (SOF) scheme for real-time implementation where the system nonlinearity is incorporated in the control law to guarantee the control performance. In particular, the SOF controller is robust with respect to the convex polytopic uncertainty. The design procedure is recast as an LMI-based optimization and therefore can be easily solved with available numerical solvers. Moreover, it can be extended to handle other tracking and/or disturbance rejection objectives. The proposed control method can be applied to a wide class of polytopic uncertain systems subject to a cone-bounded nonlinearity. The effectiveness of our feedback design is demonstrated with both simulation and experimental results in training exercises.

Keywords:Robust control, Stability of nonlinear systems, LMIs Abstract: This paper proposes a new method for robust state-feedback control design for nonlinear systems. We introduce robust control contraction metrics (RCCM), extending the method of control contraction metrics from stabilization to disturbance attenuation and robust control. An RCCM is a Riemannian metric that verifies differential L2-gain bounds in closed-loop, and guarantees robust stability of arbitrary trajectories via small gain arguments. Numerical search for such a metric can be transformed to a convex optimization problem. We also show that the associated Riemannian energy can be used as a robust control Lyapaunov function. A simple computational example illustrates the approach.

Keywords:Robust control, Stability of nonlinear systems, Lyapunov methods Abstract: This paper presents a robust control approach for a class of nonlinear dynamic systems consisting of a linear plant connected in series with a hysteresis operator, and affected by control input saturation. Such a class of systems commonly appears in applications concerning smart materials, in particular thermal shape memory alloys wire actuators. The goal of this paper is to design a robust controller, in the form of an output PI law, which ensures set-point regulation with a desired decay rate and, at the same time, accounts for the effects of both hysteresis and input saturation. The resulting controller appears as attractive on the implementation standpoint, since no accurate hysteresis compensator is required. In order to deal with the proposed problem, the hysteretic plant is first reformulated as a linear parameter-varying system. Subsequently, a finite time stability approach is used to impose constraints on the control input. A new set of bilinear matrix inequalities is developed, in order to perform the design with reduced conservatism by properly exploiting some structural properties of the model. The effectiveness of the method is finally validated by means of a numerical case of study.

Keywords:Robust control, Cooperative control Abstract: This paper is concerned with robust output consensus for networks of homogeneous negative imaginary (NI) systems under L_{2} external disturbances and model uncertainty in a generalised framework. By removing certain assumptions which had been imposed in earlier studies, we derive generalised conditions that guarantee robust output consensus of the networked systems by means of recently published generalised internal stability results for NI systems. The proposed conditions are shown to reduce to earlier conditions in literature by imposing the same assumptions. A convergence analysis is also provided which is in agreement with the conclusions of previous literature. An example that demonstrates the effectiveness of the results is also provided.

Keywords:Nonlinear systems identification, Identification, Statistical learning Abstract: We consider a parameter estimation problem in a general class of stochastic multiple-inputs multiple-outputs Wiener models, where the likelihood function is, in general, analytically intractable. When the output signal is a scalar independent stochastic process, the likelihood function of the parameters is given by a product of scalar integrals. In this case, numerical integration may be efficiently used to approximately solve the maximum likelihood problem. Otherwise, the likelihood function is given by a challenging multidimensional integral. In this contribution, we argue that by ignoring the temporal and spatial dependence of the stochastic disturbances, a computationally attractive estimator based on a suboptimal predictor can be constructed by evaluating scalar integrals regardless of the number of outputs. Under some conditions, the convergence of the resulting estimators can be established and consistency is achieved under certain identifiability hypothesis. We highlight the relationship between the resulting estimators and a recently proposed prediction error method estimator. We also remark that the method can be used for a wider class of stochastic nonlinear models. The performance of the method is demonstrated by a numerical simulation example using a 2-inputs 2-outputs model with 9 parameters.

Keywords:Nonlinear systems identification, Identification, Stability of nonlinear systems Abstract: Equation error, a.k.a. one-step-ahead prediction error, is a common quality-of-fit metric in dynamical system identification and learning. In this paper, we use Lagrangian relaxation to construct a convex upper bound on equation error that can be optimized over a convex parametrization models with guaranteed stability. We provide theoretical results on the tightness of the relaxation, and show that the method compares favourably to established methods on a variety of case studies.

Team Sound Signals and Systems : Audio/Acoustics, instruMents (S

Keywords:Nonlinear systems identification Abstract: This article addresses the identification of nonlinear systems represented by Volterra series. To improve the robustness of state-of-the-art estimation methods, we introduce the notion of "homophase signals", for which a separation method is given. Those homophase signals are then used to derive a robust identification process. This prior step is similar to nonlinear homogeneous order separation, in which amplitude relations are used to separate the orders of a Volterra series, but offers a better conditioning by using phase deviations rather than amplitudes. First an academic phase-based method using complex-valued test signals is introduced for separating nonlinear orders. Second this notion of phase deviation is extended to real-valued signals, which leads to the design of the proposed homophase signals separation method. Finally, a new identification process is derived using the homophase signals. Simulations are used to highlight the benefits of the proposed identification process in comparison to the standard approach.

Keywords:Nonlinear systems identification, Neural networks, Predictive control for nonlinear systems Abstract: We introduce a new methodology for the identification of nonlinear state-space models using machine-learning techniques based on deep autoencoders for dimensionality reduction and neural networks. By learning a direct acyclic computational graph, our framework simultaneously identifies the nonlinear output and state-update maps, and optionally a neural state observer. After formulating the approach in detail and providing guidelines for tuning the related hyper-parameters and reducing the model order, we show its capability of fitting a nonlinear model from an input/output dataset generated by a benchmark nonlinear system. Performance is assessed in terms of the ability of filtering and predicting output signals ahead, and of controlling the system via nonlinear model predictive control (MPC) based on the identified model.

Keywords:Nonlinear systems identification, Identification, Uncertain systems Abstract: Abstract— In this paper, we present an extension of the class of uncertain-input models to handle cases of measurements with outliers. The general uncertain-input model framework allows us to treat system identification problems in which a linear system, represented by its impulse response, is subject to an input about which we have partial information. Both the impulse response and the input are modeled as Gaussian processes and the kernels are used to encode the information available. The whole model is then estimated using an approximate empirical Bayes approach. We extend the uncertain-input model framework to non-Gaussian measurement models by considering the noise precisions as realizations of a Gamma prior. We validate the approach on a dataset of linear systems and on a dataset of Hammerstein systems where the measurements are corrupted by outliers.

Keywords:Nonlinear systems identification, Identification Abstract: We present a technique for kernel-based identification of Wiener systems. We model the impulse response of the linear block with a Gaussian process. The static nonlinearity is modeled with a combination of basis functions. The coefficients of the static nonlinearity are estimated, together with the hyperparameters of the covariance function of the Gaussian process model, using an iterative algorithm based on the expectation-maximization method combined with elliptical slice sampling to sample from the posterior distribution of the impulse response given the data. The same sampling method is then used to find the posterior-mean estimate of the impulse response. We test the proposed algorithm on a benchmark of randomly generated Wiener systems.

Keywords:Hybrid systems, Identification, PID control Abstract: With the emergence of smart grids and the development of legislation related to the energy consumption of buildings, the need for accurate and reliable energy prediction models has increased in order to support decision making processes. In this work, we present a novel automated methodology for predicting the energy consumption of existing buildings based on real measurements. The methodology relies mainly on the modeling of the indoor air temperature using a hybrid switching system approach with a Piece Wise Auto-Regressive eXogeneous inputs (PWARX) technique. This technique is afterwards coupled with a classification technique, namely, Support Vector Machine (SVM), and integrated in a closed loop with PID controllers designed for each one of the continuous sub-models. The estimation of the energy consumption using the proposed approach based on measurements collected from a test building located in Angers, France is close to the one computed by physics-based methods.

Keywords:Linear systems, Estimation, Identification Abstract: Identification and control of systems with multiple time scales is in general known to be quite challenging than that of single scale systems. The foremost and crucial step in the development of any method for data-driven multiscale analysis is to determine whether the system warrants a multiscale treatment or otherwise. Existing works in the associated literature either assume that this non-trivial knowledge is readily available or do not necessarily assess the need for a multiscale analysis. The present work is aimed at addressing this fundamental issue. The main objectives of this work are to develop a method for (i) detecting the presence and (ii) counting the number of time scales for linear time-invariant (LTI) systems solely from input-output data. The problem is formulated in the sparse optimization framework with a non-orthogonal dictionary consisting of filtered inputs resulting from finite-order Laguerre basis filter expansions of transfer functions over a highly redundant pole grid. A clustering of the most informative poles selected by the sparse optimizer reveals the presence of multiscale nature and aids in the cardinality of time scales. The proposed method can be applied to multi-input, multi-output systems under open-loop conditions. Simulation studies demonstrate the success of the proposed methodology.

Keywords:Networked control systems, Estimation Abstract: Event-triggered remote state estimation scheduling problems have been heavily studied, where the local sensor transmits to a remote estimator when the triggering threshold is satisfied. Different from the existing literature, we take the sensor dormancy into consideration along with the traditional framework, consisting of three transmission energy levels: the high-energy level, the low-energy level and zero. Thus, a new scheduling scheme is required under this new problem setup. A double-phase based event-triggered scheduling algorithm is presented to coordinate this three energy levels under the given energy constraint. The optimal offline scheduling scheme is proposed followed by rigorous proof of optimality. Comparison between two schedules is conducted to show the out-performance of the online schedule.

Keywords:Numerical algorithms, Estimation Abstract: Recursive least squares (RLS) is widely used in signal processing, identification, and control, but is plagued by the inability to adjust quickly to changes in the unknown parameters. RLS with standard forgetting factor overcomes this problem but causes divergence due to the lack of persistency. Variable and directional forgetting factors have been proposed for overcoming this deficiency. The present paper proposes a textit{targeted forgetting factor} that looks directly at recent data in order to determine which directions possess new information. Targeted forgetting applies a forgetting factor directly to these directions, thereby providing a simple and effective technique for avoiding covariance divergence. Numerical examples compare targeted forgetting to standard and directional forgetting.

Keywords:Observers for Linear systems, Compartmental and Positive systems, Estimation Abstract: This paper discusses an interval-valued state estimator for linear dynamic systems. In particular, we derive an expression of the tightest possible interval estimator in the sense that it is the intersection of all interval-valued estimators. This estimator appears, in a general setting, to be an infinite dimensional dynamic system. Therefore practical implementation requires some over-approximations which would yield a good trade-off between computational complexity and tightness.

Keywords:Estimation, Agents-based systems, Autonomous robots Abstract: In this paper we address the problem of autonomous Impedance Mapping (IM) of an environment using a team of mobile robots. IM of a domain provides the boundary information required to model the sound propagation in the domain. We equip the robots with a speaker and two microphones and utilize the two-microphone reflection method to estimate the normal surface impedance of the boundaries. Specifically, while a speaker robot plays white noise, a listener robot measures the pressure values at two adjacent points next to the sample and uses this data to estimate its impedance. We model the collaborative IM task using Linear Temporal Logic and design motion plans that allow the robots to switch between speaker and listener roles while maintaining desired distances from each other and the samples, and measure the impedance of every boundary segment. We present experimental results and validate our impedance measurements by comparing to a standard method.

Keywords:Stability of nonlinear systems, Variable-structure/sliding-mode control, Uncertain systems Abstract: This paper extends the use of a recently proposed Terminal Sliding surface to nonlinear plants of arbitrary order. The proposed surface ensures the finite-time robust stabilization of systems of arbitrary order with matched uncertainties. Mathematical characteristics of the proposed surface are such that a fixed bound naturally exists for the settling time of the state variable, once the surface has been reached. A simulation study has been performed using a magnetic levitation system.

Keywords:Stability of nonlinear systems, Uncertain systems Abstract: A general framework for Region of Attraction (ROA) analysis is presented. The considered system consists of the feedback interconnection of a plant with polynomial dynamics and a bounded operator. The input/output behavior of the latter is characterized using an Integral Quadratic Constraint (IQC), for which it is assumed an hard factorization holds. This formulation allows to analyze problems involving hard-nonlinearities and uncertainties, adding to the state of practice typically limited to polynomial vector fields. An iterative algorithm based on Sum of Squares optimization is proposed to compute inner estimates of the ROA. The effectiveness of this approach is demonstrated on a numerical example featuring a nonlinear closed-loop system with saturated inputs.

Keywords:Sampled-data control, Quantized systems Abstract: An appropriate approximation model can significantly reduce the computational costs in model-based approaches. This paper aims to develop discrete-time models to approximate distributed continuous-time nonlinear dynamical systems, in which subsystems are physically coupled and can receive information from their neighbors. To approximate such a system, we present asynchronous Lebesgue approximation approach, where each subsystem is approximated by an individual Lebesgue approximation model (LAM). Each LAM updates its state, depending on its own state as well as the neighboring states. Different LAMs execute asynchronously. The proposed distributed LAM is cost-efficient because it can automatically adjust its iteration frequency based on state's variation. To show stability of the distributed LAM, we construct a distributed event-triggered feedback system and prove that it generates the same state trajectories as the LAM with linear interpolation. Through this specific distributed event-triggered system, we show that the distributed LAM is uniformly ultimately bounded. Finally, we carry out some simulations on a nonlinear system to show the efficiency of the proposed method.

Keywords:Stability of nonlinear systems, Algebraic/geometric methods Abstract: Through recent research combining the Geometric Desingularization method and classical control tools, it has been possible to locally stabilize non-hyperbolic points of singularly perturbed control systems. In this letter we propose a simple method to enlarge the region of attraction of a non-hyperbolic point in the aforementioned setting by expanding the geometric analysis around the singularity. In this way, we can synthesize improved controllers that stabilize non-hyperbolic points within a large domain of attraction. Our theoretical results are showcased in a couple of numerical examples.

Keywords:Stability of nonlinear systems, Uncertain systems Abstract: We construct Zames-Falb multipliers for second order systems with time delay. There are at least two equality constraints on the multiplier phase in the limiting case as the damping ratio tends to zero and the gain approaches the Nyquist gain. Nevertheless, we demonstrate a multiplier exists for every system we consider. Our results depend on numerical examples and searches; thus while the Kalman Conjecture is apparently verified for this class of system, a formal proof is beyond the scope of the paper.

Keywords:Stability of nonlinear systems, Delay systems, Lyapunov methods Abstract: The integral-input-to-state stability is one of the central stability notions for nonlinear systems. Many applications of this stability property were based on the Lyapunov approach. The main concern of this work is to provide the existence of Lyapunov-Krasovskii functionals for the integral-input-to-state stability for systems with time delays.

Keywords:Discrete event systems, Supervisory control Abstract: To make a supervisor comprehensible to a designer has been a long-standing goal in the supervisory control community. One strategy is to reduce the size of a supervisor to generate a control equivalent version, whose size is optimistically much smaller than the original one so that a user or control designer can easily check whether a designed controller fulfils its objectives and requirements. After the first journal paper on this topic appeared in 1986 by Vaz and Wonham, which relied on the concept of control covers, Su and Wonham proposed in 2004 to use control congruences to ensure computational viability. This work was later adopted in supervisor localization theory, which aims for a control equivalent distributed implementation of a given centralized supervisor. Despite these publications some fundamental questions, which might have been addressed in the first place, have not yet been answered, namely what information is critical to ensure control equivalence, what information is responsible for size reduction, and whether partial observation makes the problem essentially different. In this paper we address these questions by showing that there exists a unified supervisor reduction theory, which is applicable to all feasible supervisors regardless of whether they are under full observation or partial observation. Our theory proposes a preorder (called leanness) over all control equivalent feasible supervisors based on their enabling, disabling and marking information such that, if a supervisor S1 is leaner than another supervisor S2, then the size of the minimal control cover defined over the state set of S1 is no bigger than that of S2.

Keywords:Discrete event systems, Supervisory control Abstract: In this paper, we introduce conditional decisions for enforcing forcible events in the decentralized supervisory control framework for timed discrete event systems. We present necessary and sufficient conditions for the existence of a decentralized supervisor with conditional decisions under the assumption that if the occurrence of the event tick, which represents the passage of one time unit, is illegal, then a legal forcible event that should be forced to occur uniquely exists. These necessary and sufficient conditions are weaker than those for the existence of a decentralized supervisor without conditional decisions. In addition, we present how to verify the presented necessary and sufficient conditions.

Keywords:Discrete event systems, Supervisory control, Automata Abstract: In a formal approach to controller synthesis, temporal logic is used as a rigorous description of a control specification. In this paper, we describe control specifications by extended linear temporal logic formulas with propositional quality operators, which are evaluated with real numbers between 0 and 1. Such quantitatively extended logic enables us to consider how better the specification is satisfied. Our control objective is to design a controller such that the satisfaction value of the specification formula on the controlled system is larger than or equal to a given threshold. We propose a game-based controller synthesis algorithm. First, the specification formula and the threshold are translated into a generalized nondeterministic Buchi automaton, which is composed with the plant model. Next, we extend events of the product automaton in order to make its transitions deterministic. The extended product automaton is then transformed into a generalized Buchi game, from whose solution we obtain a desirable controller.

Keywords:Discrete event systems, Supervisory control Abstract: The problem of maximally permissive deadlock avoidance for complex resource allocation systems (RAS) is a well-defined problem in the relevant controls literature. In some of the prevailing approaches to this problem, the sought supervisor -- also known as the maximally permissive deadlock avoidance policy (DAP) -- is perceived as a classifier, and its design boils down to the development of an efficient representation of the classification logic that it effects on the underlying RAS states. A popular such representation is the ``linear classifier'', where state admissibility is resolved based on their ability to satisfy a given set of linear inequalities. However, linear classifiers cannot provide effective representation of the maximally permissive DAP for all RAS instantiations. Hence, this paper provides a methodology for synthesizing linear DAPs for any given RAS instance that might not be maximally permissive in the original sense of this term, but observe a more relaxed notion of ``maximality''. The presented developments formally define this new DAP class, and provide effective computational algorithms for the synthesis of a maximal linear DAP for any given RAS instance.

Keywords:Discrete event systems, Supervisory control, Automata Abstract: In this paper, we consider a problem of synthesizing a nondeterministic supervisor for the plant and the specification modeled as nondeterministic automata. A bisimilarity control problem requires us to synthesize a supervisor such that the supervised plant is bisimilar to the specification. When there does not exist a solution to the bisimilarity control problem, we generally construct a supervisor for a feasible subspecification that is stronger than the original specification. We present a necessary and sufficient condition for the existence of such a subspecification. It is desirable that the constructed supervisor be as permissive as possible. Thus, we develop a method for synthesizing a maximally permissive supervisor that achieves a supremal feasible subspecification.

Keywords:Discrete event systems, Supervisory control, Game theory Abstract: The problem under investigation is mean payoff supervisory control on a partially observed quantitative discrete event system modeled by a finite state weighted automaton. We intend to design a partial-observation supervisor such that the limit-average weights of all infinite sequences in the supervised system remain nonnegative. This problem may be viewed as a two-player mean payoff game between the supervisor and the environment, with asymmetric information and a quantitative objective. To cope with the partial observation, we introduce the energy information state which incorporates both the state information and the weight information for supervisor's decision making. Based on that, we transfer the supervisory control problem into a two-player reachability game under full observation and propose a finite bipartite structure called First Cycle Energy Inclusive Controller (FCEIC). Further analysis demonstrates that winning strategies in the FCEIC lead to solutions to the original control problem.

Keywords:Learning, Modeling Abstract: The current discrete-time (e.g., hourly) modeling and prediction methods fall short in capturing and anticipating the sub-interval variations of electricity load. This leads to inability of power system operators to appropriately utilize the available resources to follow and compensate the load variations. This paper takes a novel and different approach on modeling electricity load, and proposes a continuous-time model for characterizing the uncertainty and variability of load. More specifically, the electricity load is modeled as a continuous-time stochastic process that is projected on a reduced-order function space spanned by Bernstein polynomials, which ensures the continuity of the process over the estimation and forecasting horizons. We assume a Gaussian process (GP) prior on the load process and design a covariance function that reflects the periodicity and smoothness of electricity load. We develop a computationally efficient method for estimating the hyper-parameters of the model using the solution of a maximum likelihood estimation problem and form the posterior GP process. The proposed method is utilized to model and predict the load of California Independent System Operator (CAISO). The proposed model uniquely predicts the continuous-time mean value and uncertainty envelopes of future CAISO load, which inherently embeds information on the continuous-time variations and the associated ramping requirements of the load.

Keywords:Power systems, Stochastic optimal control, Statistical learning Abstract: In the classical risk limiting dispatch (RLD) formulation, the system operator dispatches generators relying on information about the distribution of demand. In practice, such information is not readily available and therefore is estimated using historical demand and auxiliary information (or features) such as weather forecasts. In this paper, instead of using a separated estimation and optimization procedure, we propose learning methods that directly compute the RLD decision rule based on historical data. Using tools from statistical learning theory, we then develop generalization bounds and sample complexity results of the proposed methods. These algorithms and performance guarantees, developed for the single-bus network, are then extended to a general network setting for the uniform reserve case.

Keywords:Power systems, Identification, Learning Abstract: We address the problem of distributed estimation of eigenvectors for power system models using online phasor measurements. The power system is considered to be divided into a set of non-overlapping areas, each of which is equipped with a local estimator. Online measurements of bus voltage and current phasors are first used to generate estimates of the generator states in each area using decentralized Kalman filters. Thereafter, these estimates are used for identifying a reduced-order model of the system in a completely distributed way by sharing state information between the estimators over a strongly connected communication graph. The identified model is then utilized to estimate its right eigenvectors over the same distributed graph. Results are validated using a 50-bus power system model with four areas.

Keywords:Estimation, Smart grid, Statistical learning Abstract: Proliferation of Phasor Measurement Units (PMUs) that allow for a synchronous and distributed collection of data can be leveraged to obtain reliable information about the power system model. In practice, one has to account for the system being partially observed as not every bus hosts a PMU. We consider the problem of partial recovery of the underlying dynamic state matrix of transmission power grids from time-stamped PMU measurements on a subset of nodes in a network. We propose a data-driven method which does not assume any knowledge of system parameters and only relies on basic assumptions about the system dynamics. The method is based on a least-squares regression with a nuclear norm regularization that accounts for the effect of hidden observations, supplemented with structural physics-informed constraints that enforce the identifiability. Performance of the method is demonstrated on an IEEE test case example.

Keywords:Fault detection, Machine learning, Power systems Abstract: This paper presents a shape preserving incremental learning algorithm that employs a novel shape-based metric called the Fisher-Rao Amplitude-Phase Distance (FRAPD) metric. The combined amplitude and phase distance metric is achieved on a function space from the Fisher-Rao elastic registration. We utilize an exhaustive search method for selecting the optimal parameter that captures the amplitude and phase distance contribution in FRAPD when performing a clustering process. The proposed incremental learning structure based on the shape preserving FRAPD distance metric utilizes continuously updated fault shape templates with the Karcher mean. The seamless updating of abnormal events textcolor{blue}{enhances} the clustering performance for power systems fault detection. The algorithm is validated using the actual data from real-time hardware-in-the-loop testbed.

Keywords:Smart grid, Machine learning Abstract: In this paper, we propose a day-ahead scheduling method under uncertain renewable energy generation based on a machine learning approach. An aggregator, which has renewable energy generation devices, needs to schedule the energy production and consumption (prosumption) in a situation where the renewable power generation amount is not exactly predicted at day-ahead scheduling. If imbalance, defined as the difference between a day-ahead schedule and a prosumption profile on the next day in the day-ahead energy market, occurs, the aggregator must pay imbalance adjustment costs. As a scheduling method to avoid paying imbalance adjustment costs, we propose a scheduling model by machine learning based on the results of past transactions. We first formulate a problem of constructing a scheduling model as a problem of finding parameters involved in the scheduling model. Next, by introducing a kernel method, we show that the problem of finding the parameter maximizing the mean of profits of past transactions is a concave program. Furthermore, by introducing piecewise affine cost functions, we also show that the problem of finding the parameter can be formulated as a quadratic program. Finally, we show the efficiency of the proposed method through a numerical example.

Keywords:Computational methods, Optimization, Optimization algorithms Abstract: This paper introduces a notion of decomposition and completion of sum-of-squares (SOS) matrices. We show that a subset of sparse SOS matrices with chordal sparsity patterns can be equivalently decomposed into a sum of multiple SOS matrices that are nonzero only on a principal submatrix. Also, the completion of an SOS matrix is equivalent to a set of SOS conditions on its principal submatrices and a consistency condition on the Gram representation of the principal submatrices. These results are partial extensions of chordal decomposition and completion of scalar matrices to matrices with polynomial entries. We apply the SOS decomposition result to exploit sparsity in matrix-valued SOS programs. Numerical results demonstrate the high potential of this approach for solving large-scale sparse matrix-valued SOS programs.

Keywords:Computational methods, Hybrid systems, Fault tolerant systems Abstract: In this paper, we consider searching for fault tolerant control strategies for linear systems to satisfy some high level requirements specified by linear temporal logic. By the term fault tolerant, we mean the obtained control strategy can respond to a fault that leads to a sudden change of the system dynamics. We first show how open-loop fault tolerant strategies (associated with each initial state) can be synthesized by leveraging Mixed Integer Linear Programming (MILP) based encodings used for linear temporal logic. These open-loop strategies, however, are not robust to the disturbances because of two reasons. First, since the disturbed system cannot be predicted precisely, the fault will be detected with a delay. Secondly, even if the faulty status is known, the true system trajectory may still deviate from the planned trajectory as the impact of the disturbance accumulates. To solve the two problems, we present a MILP formulation of the problem that incorporates finite detection delays, the open-loop strategy defined by the MILP's solution is then robustified with additional linear regulation.

Keywords:Computational methods, Numerical algorithms, Modeling Abstract: We consider the problem of computing certain parameterized minimum volume outer ellipsoidal (MVOE) approximation of the Minkowski sum of a finite number of ellipsoids. We clarify connections among several parameterizations available in the literature, obtain novel analysis results regarding the conditions of optimality, and based on the same, propose two new algorithms for computing the parameterized MVOE. Numerical results reveal faster runtime for the proposed algorithms than the standard semidefinite programming approach for computing the same.

Keywords:Computational methods, Large-scale systems, Optimal control Abstract: Optimal control of bilinear ensemble systems has been of great importance and interest in the areas of mathematical and computational optimal control. However, effective methods for solving these emerging optimal control problems remain underdeveloped. In this work, we extend the iterative method developed in our previous work for solving the fixed-endpoint optimal control problems to solve for the optimal control with free-endpoint conditions. The method is based on solving the corresponding optimal control problem for a linear ensemble system at each iteration and does not require numerical optimization. We discuss the convergence of the iterative method and explore the stochastic ensemble systems driven by Gaussian noise. We also illustrate its robustness and applicability with numerical examples.

Keywords:Computational methods, Uncertain systems, Identification for control Abstract: We propose a data-driven framework to compute an approximation of a minimal robust control invariant set (mRCI) for an uncertain dynamical system where the model of the system is also unknown and should be learned from data. First, the set of admissible models is characterized via a set of linear constraints extracted from the experimental data. Each model in the set of admissible models contains information about the nominal model, as well as the characterization of the model uncertainty, including additive and multiplicative uncertainties. Then an iterative algorithm based on robust optimization is proposed to simultaneously compute a minimal robust control invariant set while selecting an optimal model from the admissible set. The numerical results show that the proposed method greatly reduces the size of the invariant set compared to a benchmark method that sequentially selects a model with least squares and then computes the invariant set.

Keywords:Lyapunov methods, Numerical algorithms, Computational methods Abstract: Complete Lyapunov functions are of much interest in control theory because of their capability to describe the long-time behaviour of nonlinear dynamical systems.

The state-space of a system can be divided in two different regions determined by a complete Lyapunov function: the region of the gradient-like flow, where the Lyapunov function is strictly decreasing along solution trajectories, and the chain-recurrent set whose chain-transitive components are level sets of the Lyapunov function.

There has been continuous effort to properly identify both regions and in this paper we discuss the extension of our methods to compute complete Lyapunov functions in the plane to the three-dimensional case, which is directly applicable to higher dimensions, too.

When extending the methods to higher dimensions, the number of points for collocation and evaluation grows exponentially. To keep the number of evaluation points under control, we propose a new way to choose them, which does not depend on the dimension.

Keywords:Optimization algorithms, Optimization Abstract: Systems with a redundant set of actuators can be found in many domains which are characterized by high demands on reliability and performance. The ambiguity in the choice of actuator commands caused by the redundancy can be overcome by control allocation (CA). One variant of CA leads to the formulation of a constrained quadratic program which has to be solved during operation of the control loop. The corresponding method proposed in this work is based on the well-known penalty function method and enables a fast solution of those optimization problems. Two strategies for dealing with infeasible CA problems are suggested. After introducing the concepts extensive randomized tests with comparisons to established solvers demonstrate the effectiveness of the algorithm.

Keywords:Optimization algorithms, Distributed control Abstract: In this paper, we exploit the possibility of combining nonsmooth control jointly with projected gradient approaches to solve convex optimization problems. Our development gives rise to a nonsmooth projected gradient method which has the finite-time convergence capability, thus overcoming the shortcoming of slow convergence speed of conventional projected gradient approaches, as well as preserves the simplicity. Our primary objective is to understand the design principle of the projection matrix in the nonsmooth setting and to investigate some key features of the method, such as finite-time convergence and sensitivity to initialization errors. Specifically, we offer a set of criteria for the design of the projection matrix. The convergence results, derived via nonsmooth analysis, reveal that the algorithm has a finite-time convergence property, provided that it meets the proposed design criteria. When there exists an initialization error, the optimization error is doomed inevitably. Nevertheless, we show that the optimization error incurred by the initialization error is upper bounded, and we can prescribe the upper bound by the maximal Lipschitz constant of the optimal value function over some compact set.

Keywords:Optimization algorithms, Optimization, Machine learning Abstract: In this paper, we propose a framework to design a class of fast gradient-based methods in continuous-time that, in comparison with the existing literature including Nesterov's fast-gradient method, features a state-dependent, time-invariant damping term that acts as a feedback control input. The proposed design scheme allows for a user-defined, exponential rate of convergence for a class of nonconvex, unconstrained optimization problems in which the objective function satisfies the so-called Polyak-Lojasiewicz inequality. Formulating the optimization algorithm as a hybrid control system, a state-feedback input is synthesized such that a desired rate of convergence is guaranteed. Furthermore, we establish that the solution trajectories of the hybrid control system are Zeno-free.

Keywords:Optimization algorithms, Robotics, Stability of nonlinear systems Abstract: Navigation functions are a common alternative to navigate cluttered environments. The main idea is to combine repulsive potentials from the obstacles and an attractive potential with minimum at the desired destination. By following the negative gradient of the navigation function convergence to the destination while avoiding the obstacles is guaranteed. Rimon-Koditschek artificial potentials are a particular class of potentials that can be tuned to be navigation functions in the case of focally admissible obstacles. While this provides a large class of problems in which they can be used, they suffer from the drawback that by design unstable manifolds of the saddle points have associated Hessian eigenvalues that are smaller than those associated to the stable manifold. This makes the escape from the saddle point to take a large time. To tackle this issue, we propose a second-order method that pre-multiplies the gradient by a modified Hessian to account for the curvature of the function. The method is shown to escape saddles exponentially with base 3/2 independently of the condition number of the Hessian.

Keywords:Optimization algorithms, Optimal control Abstract: We consider least-squares approximation of a function of one variable by a continuous, piecewise-linear approximand that has a small number of breakpoints. This problem was notably considered by Bellman who proposed an approximate algorithm based on dynamic programming. Many suboptimal approaches have been suggested, but so far, the only exact methods resort to mixed integer programming with superpolynomial complexity growth.

In this paper, we present an exact and efficient algorithm based on dynamic programming with a hybrid value function. Empirical evidence suggest that the algorithm has a polynomial time complexity.

Keywords:Optimization algorithms, Optimization, Randomized algorithms Abstract: In the last several years, stochastic quasi-Newton (SQN) methods have assumed increasing relevance in solving a breadth of machine learning and stochastic optimization problems. Inspired by recently presented SQN schemes [1], [2], [3], we consider merely convex and possibly nonsmooth stochastic programs and utilize increasing sample-sizes to allow for variance reduction. To this end, we make the following contributions. (i) A regularized and smoothed variable sample- size BFGS update (rsL-BFGS) is developed that can accommodate nonsmooth convex objectives by utilizing iterative smoothing; (ii) A regularized variable sample-size SQN (rVS- SQN) is developed that admits a rate and oracle complexity bound of mathcal{O}(1/k^{1−varepsilon}) and mathcal{O}(epsilon^{-(3+varepsilon)/(1-varepsilon)}), respectively (where varepsilon,epsilon > 0 are arbitrary scalars), improving on past rate statements. In addition, this scheme produces sequences that converge a.s. to a solution; (iii) By leveraging (rsL-BFGS), we develop rate statements for the function of the ergodic average through a regularized and smoothed VS-SQN scheme that can accommodate nonsmooth (but smoothable) functions with the convergence rate mathcal O(1/k^{1/3-2varepsilon}).

Keywords:Stochastic optimal control, Power systems, Energy systems Abstract: Motivated by the potential of utilizing used electric vehicle (EV) batteries as the battery energy storage system (BESS) in EV charging stations, we study the joint scheduling of EV charging and BESS operation in the presence of random renewable generation, EV arrivals, and electricity prices. We formulate cost-minimizing scheduling problem faced by an EV charging station operator as a dynamic program. We characterize an important priority rule for an optimal scheduling policy, and apply the established optimal policy characterization to improve the performance of existing heuristic policies. Numerical results demonstrate that optimal policy characterization established in this paper can significantly improve the performance of an least laxity first (LLF) policy. We also show by counter-intuitive examples that an optimal policy may charge the BESS and discharge an EV simultaneously, even when the EV's per-unit non-completion penalty is higher than the per-unit salvage value of the BESS and the highest possible electricity price.

Keywords:Stochastic optimal control, Stochastic systems, Optimal control Abstract: In this paper we investigate whether the linearly solvable stochastic optimal control framework generalizes to the case of stochastic differential equations in infinite dimensional spaces. In particular, we show that the connection between the relative entropy-free energy relation and dynamic programming principles caries over to infinite dimensional spaces. Our analysis is based on a generalization of the Feynman-Kac lemma for certain classes of infinite dimensional diffusions and Hilbert space-valued Q-Wiener processes. We observe that the utilized information theoretic representation allows the formulation of variational problems for parameterized policy optimization of infinite dimensional systems. This work creates new research avenues towards the development of parallelizable stochastic control and inference algorithms for infinite dimensional dynamical systems in physics, fluid mechanics, partially observable stochastic control and open quantum systems.

Keywords:Stochastic optimal control, Decentralized control, Mean field games Abstract: This paper studies the existence and uniqueness of a solution to linear quadratic (LQ) mean field social optimization problems with uniform agents. We exploit a Hamiltonian matrix structure of the associated ordinary differential equation (ODE) system and apply a subspace decomposition method to find the solution. This approach is effective for both the existence analysis and numerical computations. We further extend the decomposition method to LQ mean field games.

Keywords:Stochastic optimal control, Decentralized control, Networked control systems Abstract: We study stochastic static teams with countably infinite number of decision makers, with the goal of obtaining (globally) optimal policies under a decentralized information structure. We present sufficient conditions to connect the concepts of team optimality and person by person optimality for static teams with countably infinite number of decision makers. We show that under uniform integrability and uniform convergence conditions, an optimal policy for static teams with countably infinite number of decision makers can be established as a limit of a sequence of optimal policies for static teams with N decision makers as N to infty. Under the presence of a symmetry condition, we relax the conditions and this leads to optimality results for a large class of mean-field optimal team problems where the existing results have been limited to person-by-person-optimality and not global optimality (under strict decentralization). We consider a number of illustrative examples where the theory is applied to setups with either infinitely many decision makers or an infinite-horizon classical stochastic control problem reduced to a static team.

Keywords:Mean field games, Stochastic systems, Stochastic optimal control Abstract: Networks are ubiquitous in modern society and the need to analyse, design and control them is evident. However many technical and social networks apparently grow unboundedly over time. This has the undesirable consequence that, inevitably, any method founded upon techniques whose effectiveness decreases with the size of the network will eventually be overwhelmed. This paper presents a framework called Graphon Mean Field Game (GMFG) theory for the analysis and control of non-cooperative dynamical game systems distributed over networks of unbounded size. This work is based upon the recently developed and profoundly influential graphon theory of large networks and their infinite limits. A theory for the centralized control of asymptotically infinite networks has already been formulated within the framework of dynamical systems on graphons [Gao and Caines, CDC 2017]. The current work greatly extends that analysis to populations of competing dynamical agents for which the game theoretic equilibria are expressed in terms of the newly defined Graphon Mean Field (GMFG) equations, these being a significant generalization of the classical MFG PDEs. Furthermore, in this paper, existence and uniqueness theorems for GMFG equations are given together with a sketch of the corresponding epsilon-Nash theory for GMFG systems.

Keywords:Stochastic optimal control, Stochastic systems, Markov processes Abstract: In this article, we focus on erasure of a bit of information in finite time. Landauer’s principle, states that the average heat dissipation due to erasure of information is kT ln2, which is achievable only in an asymptotic manner. Recent theoretical developments in non-equilibrium thermodynamics and stochastic control, predict a more general bound for finite time erasure dependent on the Wasserstein distances between the initial and final configurations. These predictions suggest improvements to experimental protocol with regards to minimizing average heat dissipation for bit erasure in finite time from a bistable well, under overdamped Langevin dynamics. We present a comparative study of a theoretically optimal protocol with an existing protocol, and highlight the closeness and deviation from optimality

Keywords:Autonomous systems, Learning, Intelligent systems Abstract: This work addresses the problem of learning optimal control policies for a multi-agent system in an adversarial environment. Specifically, we focus on multi-agent systems where the mission objectives are expressed as signal temporal logic (STL) specifications. The agents are classified as either defensive or adversarial. The defensive agents are maximizers, namely, they maximize an objective function that enforces the STL specification; the adversarial agents, on the other hand, are minimizers. The interaction among the agents is modeled as a finite-state team stochastic game with an unknown transition probability function. The synthesis objective is to determine optimal control policies for the defensive agents that implement the STL specification against the best responses of the adversarial agents.

Keywords:Autonomous systems, Networked control systems, Stability of linear systems Abstract: In this paper we investigate sufficient conditions for consensus of double integrators interconnected under constant directed graphs, under the condition that there exists a rooted spanning tree. We assume that only relative position as well as absolute own velocity measurements are available that is, each agent disposes of its own velocity only as well as its position relatively to that of its neighbours. In addition, it is assumed that the relative position measurements are unreliable, in the sense that they are affected by a constant bias. Under these conditions, we provide a consensus algorithm which ensures that the systems stabilize near a common equilibrium point. The analysis is based on Lyapunov direct method and a recent novel approach of analysis of networked systems that takes into account both the synchronization and the collective behavior.

Keywords:Autonomous systems, Modeling, Autonomous vehicles Abstract: This paper studies the problem of penalizing rule violation in the context of logic-based motion planning. Translating a given Linear Temporal Logic (LTL) rule into a penalty structure requires a design decision, since the discrete automata obtained from the rule do not provide a straightforward method to penalize rule violation. We propose a design method that explicitly specifies violation to allow for more flexibility in parametrization of desired behaviors and differentiation of penalty semantics. Case study results are shown in the context of an autonomous driving scenario.

Keywords:Autonomous systems, Automata Abstract: We provide a novel framework for synthesis of a controller for a robot with a surveillance objective, that is, the robot is required to maintain knowledge of the location of a moving, possibly adversarial target. We formulate this problem as a one-sided partial-information game in which the winning condition for the agent is specified as a temporal logic formula. The specification formalizes the surveillance requirement given by the user by quantifying and reasoning over the agent's belief in a target's location. We also incorporate additional non-surveillance tasks. In order to synthesize a surveillance strategy that meets the specification, we transform the partial-information game into a perfect-information one, using abstraction to mitigate the exponential blow-up typically incurred by such transformations. This transformation enables the use of off-the-shelf tools for reactive synthesis. We evaluate the proposed method on two case-studies, demonstrating its applicability to diverse surveillance requirements.

Keywords:Autonomous systems, Agents-based systems, Game theory Abstract: The two-phase capture-the-flag differential game considers a Defender and its opponent, an Attacker. In Phase I the Attacker aims at capturing the flag while the Defender tries to prevent this outcome by intercepting the Attacker. Phase II is conditioned by the outcome of Phase I. If the Attacker is able to actually capture the flag at the end of Phase I, then Phase II takes place where the Attacker attempts to reach the safe zone while the Defender strives to intercept the Attacker before the latter can reach the safe haven. The saddle-point state-feedback strategies for each player and for each phase of the game are determined in this paper. Furthermore, for each phase, the Value function is obtained and it is shown to be continuous and continuously differentiable, and to satisfy the Hamilton-Jacobi-Isaacs equation.

Keywords:Autonomous systems, Aerospace, Information theory and control Abstract: Emerging applications in autonomy require the need for control techniques that take into account uncertain environments, communication and sensing constraints while satisfying high-level mission specifications. Motivated by this need, we consider a class of Markov decision processes (MDPs), along with a emph{transfer entropy} cost function. In this context, we study high-level mission specifications as co-safe linear temporal logic (LTL) formulae. We provide a method to synthesize a policy that minimizes the weighted sum of the transfer entropy and the probability of failure to satisfy the specification. We derive a set of coupled non-linear equations that an optimal policy must satisfy. We then use a modified Arimoto-Blahut algorithm to synthesize solve the non-linear algorithms. Finally, we demonstrated the proposed method on a navigation and path planning scenario of a Mars rover.

Keywords:Communication networks, Sensor networks, Simulation Abstract: We investigate the problem of reliable communication between two legitimate parties over deletion channels under an active eavesdropping (aka, jamming) adversarial model. To this goal, we develop a theoretical framework based on probabilistic finite-state automata to define novel encoding and decoding schemes that ensure small error probability in both message decoding as well as tamper detecting. We then experimentally verify the reliability and tamper-detection property of our scheme.

Keywords:Communication networks, Discrete event systems, Modeling Abstract: Several wireless communication systems operating in parallel are typical for industrial applications. These systems have to be coexistent in order to fulfil all their application communication requirements. Ensuring this coexistence is called coexistence management. In this contribution we investigate a decentralised control approach for an automated coexistence management. Here we use a model predictive control approach in max - plus algebra for timed Petri-net methods. We show a theoretical stability proof of the controller to the reference value. For that, we convert the original coordinates into error coordinates. Finally, we use a practical hardware-in-the-loop setup with WiFi-technology as test system for validation the controller.

Keywords:Network analysis and control, Automata, Observers for Linear systems Abstract: We consider the problem of analyzing observability in discrete-time linear systems when the sensors, deployed in a distributed manner, may not communicate to an observer at once, and a protocol determines the communication pattern among different sensors. We use the formalism of automata to model the sequence of measurements determined by a protocol and show that the question of observability is decidable for the resulting system. We give upper bounds on the number of measurements required for deciding observability. In addition, we consider the effects of dropouts, which may occur in communicating the measurements across the channel. Again using the formalism of automatons to model certain classes of dropouts combined with the protocol, it is shown that observability is decidable in finite time for measurements sent across using a protocol, and subject to dropouts.

Keywords:Communication networks, Control of networks, Game theory Abstract: In the standard Mechanism Design framework (Hurwicz-Reiter), there is a central authority that gathers agents' messages and subsequently determines the allocation and tax for each agent. We consider a scenario where, due to communication overhead and other constraints, such broadcasting of messages to a central authority cannot take place. Instead, only local message exchange is allowed between agents. As a result, each agent should be able to determine her own allocation and tax based on the messages in the local neighborhood, as defined by a given message graph describing the communication constraints. This scenario gives rise to a novel research direction that we call ``Distributed Mechanism Design". In this paper, we propose such a distributed mechanism for the problem of rate allocation in a multicast transmission network. The proposed mechanism fully implements the optimal allocation in Nash equilibria and its message space dimension is linear with respect to the number of agents in the network.

Keywords:Computational methods, Communication networks, Statistical learning Abstract: Data has become increasingly important in net- work systems because a lot of data is needed in new tech- nologies such as machine learning. To obtain statistics (e.g. maximum, average, distribution) in a fully distributed way with low complexity is challenging. Existing research on consensus algorithms can successfully obtain the max/min, average and median in a distributed network, but few work has been done on how to compute other statistics, especially probability density function (PDF). In this paper, consensus-based algorithms are proposed to obtain PDF in a fully distributed way and with low complexity. The key idea of our algorithms is to divide the range of nodes’ values into several sections and calculate the proportions of values in each section in a fully distributed way. If nodes have their unique identifications (IDs), repeatedly run max/min consensus algorithm to reach the partially max/min value and then erase them in order to reach all values exactly once. We prove that the algorithm converges in finite time. When nodes’ IDs are not available, the main challenge is to solve the conflicts when two or more nodes have the same value. We propose an asymptotically converged algorithm to solve the problem in this scenario.

Gwangju Institute of Science and Technology (GIST)

Keywords:Distributed control, Communication networks, Network analysis and control Abstract: This paper presents a number of ideas combining consensus algorithms and different inclusions to effectively solve exact potential games with continuous strategy space in a multi-agent network. Solving these games or finding their Nash equilibrium (NE) is conducted in a distributed manner via the forms of two interconnected subsystems, first one estimating necessary information by average consensus algorithm, and another using differential inclusion to seek NE with respect to distributed constraints on players’ actions. Firstly, a special form of exact potential game is considered. Secondly, larger potential games are taken into consideration. It is shown that designed dynamical systems are semi-practically globally asymptotically stable (SPA), enabling players’ actions to converge to NE non-locally. Two simulations on an energy network and on a cognitive radio network (CRN) are carried out to investigate the correctness of our algorithms.

Keywords:Distributed control, Network analysis and control, Cooperative control Abstract: We consider push-sum algorithms for average consensus over a random time-varying sequence of directed graphs. Motivated by the notion of infinite flow property used in the consensus literature, we introduce the notion of directed infinite flow property, which allows us to establish the ergodicity of matrices corresponding to the push-sum protocol. Using this result and the assumption that the auxiliary states of agents are uniformly bounded away from zero infinitely often, we prove the almost sure convergence of the evolutions of this class of algorithms to the average of initial states. We demonstrate that many interesting time-varying sequences of random directed graphs satisfy our condition. In particular, for a random sequence of graphs, we obtain convergence rates for the push-sum algorithm, establishing first such rates for random sequences of directed graphs.

Keywords:Machine learning, Optimization, Statistical learning Abstract: We consider the problem of stochastic optimization with nonlinear constraints, where the decision variable is not vector-valued but instead a function belonging to a reproducing Kernel Hilbert Space (RKHS). Currently, there exist solutions to only special cases of this problem. To solve this constrained problem with kernels, we first generalize the Representer Theorem to a class of saddle-point problems defined over RKHS. Furthermore, we develop a primal-dual method which executes alternating projected primal/dual stochastic descent/ascent on the dual-augmented Lagrangian of this problem. The primal projection sets are low-dimensional subspaces of the ambient function space which are greedily constructed using matching pursuit. By tuning the projection-induced error to the algorithm step-size, we are able to establish mean convergence both in primal objective sub-optimality and constraint violation, respectively to the mathcal{O}(sqrt{T}) and mathcal{O}(T^{3/4}) neighborhoods, where T is the total number of iterations. We evaluate the proposed method through numerical tests for the application of risk-aware supervised learning.

Keywords:Optimization, Networked control systems, Control of networks Abstract: As multi-agent networks grow in size and scale, they become increasingly difficult to synchronize, though agents must work together even when generating and sharing different information at different times. Targeting such cases, this paper presents an asynchronous optimization framework in which the time between successive communications and computations is unknown and unspecified for each agent. Agents’ updates are carried out in blocks, with each agent updating only a small subset of all decision variables. To provide robustness to asynchrony, each agent uses an independently chosen Tikhonov regularization. Convergence is measured with respect to a weighted block-maximum norm in which convergence of agents’ blocks can be measured in different p-norms and weighted differently to heterogeneously normalize problems. Asymptotic convergence is shown and convergence rates are derived explicitly in terms of a problem’s parameters, with only mild restrictions imposed upon them. Simulation results are provided to verify the theoretical developments made.

Keywords:Optimization algorithms, Large-scale systems, Stochastic systems Abstract: We establish the O(1/k) convergence rate for distributed stochastic gradient methods that operate over strongly convex costs and random networks. The considered class of methods is standard -- each node performs a weighted average of its own and its neighbors’ solution estimates (consensus), and takes a negative step with respect to a noisy version of its local function’s gradient (innovation). The underlying communication network is modeled through a sequence of temporally independent identically distributed (i.i.d.) Laplacian matrices such that the underlying graphs are connected on average; the local gradient noises are also i.i.d. in time, have finite second moment, and possibly unbounded support. We show that, after a careful setting of the consensus and innovations potentials (weights), the distributed stochastic gradient method achieves a (order-optimal) O(1/k) convergence rate in the mean square distance from the solution. To the best of our knowledge, this is the first order-optimal convergence rate result on distributed strongly convex stochastic optimization when the network is random and the gradient noises have unbounded support. Simulation examples confirm the theoretical findings.

Keywords:Optimization algorithms, Distributed control, Networked control systems Abstract: Many modern large-scale and distributed optimization problems can be cast into a form in which the objective function is a sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal gradient method which generalizes standard gradient descent to a nonsmooth setup. In this paper, we leverage the tools from control theory to study global convergence of proximal gradient flow algorithms. We utilize the fact that the proximal gradient algorithm can be interpreted as a variable-metric gradient method on the forward-backward envelope. This continuously differentiable function can be obtained from the augmented Lagrangian associated with the original nonsmooth problem and it enjoys a number of favorable properties. We prove that global exponential convergence can be achieved even in the absence of strong convexity. Moreover, for in-network optimization problems, we provide a distributed implementation of the gradient flow dynamics based on the proximal augmented Lagrangian and prove global exponential stability for strongly convex problems.

Keywords:Optimization algorithms, Large-scale systems, Numerical algorithms Abstract: We consider a large-scale convex program with functional constraints, where interior point methods are intractable due to the problem size. The effective solution techniques for these problems permit only simple operations at each iteration, and thus are based on primal-dual first order methods such as the Arrow-Hurwicz-Uzawa subgradient method, which utilize only gradient computations and projections at each iteration. Such primal-dual algorithms admit the interpretation of solving the associated saddle point problem arising from the Lagrange dual. We revisit these methods through the lens of regret minimization from online learning and present a flexible framework. While it is well known that two regret-minimizing algorithms can be used to solve a convex-concave saddle point problem at the standard rate of O(1/sqrt(T)), our framework for primal-dual algorithms allows us to exploit structural properties such as smoothness and/or strong convexity and achieve better convergence rates in favorable cases. In particular, for non-smooth problems with strongly convex objectives, our primal-dual framework equipped with an appropriate modification of Nesterov's dual averaging algorithm achieves O(1/T) convergence rate.

Keywords:Flight control, Feedback linearization, Aerospace Abstract: The adoption of the dual quaternion formalism to represent the pose (position and orientation) of a rigid body entails the need of designing a single controller to stabilize both its position and its attitude. In this work, we adopt such a pose representation to develop an exponentially stable maneuver regulation control law, ensuring robust path following in the presence of disturbances. The designed solution relies on the feedback linearized model of the dual quaternion based dynamics of the rigid body. Numerical results confirm the effectiveness of the proposed maneuver regulation approach when compared with trajectory tracking in a noisy scenario.

Keywords:Flight control, Fault tolerant systems, Autonomous robots Abstract: This paper presents a method for analyzing hoverability of multirotor unmanned aerial vehicles (UAVs). These vehicles need to be able to remain at a constant position in the air and should keep safe flight even after rotor failure. However, there has been no systematic method so far to analyze such an ability of multirotor UAVs. This is due to the difficulty in finding equilibria of a multirotor UAV system whose rotors can exert force only in one direction. The present method only requires mechanical properties of the vehicles: the center of mass; rotor positions; and directions of rotor rotation. First, dynamics of a generalized multirotor UAV model is introduced. Second, the hoverability analysis method is proposed. Third, an example of multirotor UAV structure is presented, and the present hoverability analysis method is conducted. Finally, the method is applied to investigation of multirotor UAVs’ hoverability in the case of rotor failure, and some kinds of vehicles which can tolerate the failure are introduced.

Keywords:Flight control, Autonomous vehicles, Hierarchical control Abstract: This paper presents a new hierarchical guidance and flight control system for the path following problem of scale-model airplanes. The proposed control solution exploits a simple but pertinent nonlinear model of aerodynamic forces acting on the aircraft. Practical implementation aspects are discussed, and successful flight test results are presented that illustrate the soundness and performance of the proposed control design.

Keywords:Flight control, Robotics, Lyapunov methods Abstract: This paper presents a controller for the transition maneuver of a tail-sitter drone. The tail-sitter model considers aerodynamic terms whereas the proposed controller considers the time-scale separation between drone attitude and position dynamics. The controller design is based on Lyapunov approach and linear saturation functions. Simulations experiments demonstrate the effectiveness of the derived theoretical results.

Keywords:Flight control, Feedback linearization, Robotics Abstract: In this paper, we propose a novel control law for accurate tracking of aggressive (i.e., high-speed and high-acceleration) quadcopter trajectories. The proposed method tracks position and yaw angle with their derivatives of up to fourth order, specifically, the position, velocity, acceleration, jerk, and snap along with the yaw angle, yaw rate and yaw acceleration. Two key aspects of the proposed method are the following. First, the controller exploits the differential flatness of the quadcopter dynamics to generate feedforward inputs for attitude rate and attitude acceleration in order to track the jerk and snap references. The tracking is enabled by direct control of body torque using closed-loop control of all four propeller speeds based on optical encoders attached to the motors. Second, the controller utilizes the incremental nonlinear dynamic inversion (INDI) method for accurate tracking of linear and angular accelerations despite external disturbances. Hence, no prior modeling of aerodynamic effects is required. We evaluate the proposed control law in experiments under motion capture. Using a 1-kg quadcopter, we are able to track a complex 3D trajectory, reaching speeds up to 8.2 m/s and accelerations up to 2g, while keeping the root-mean-square tracking error down to 4.0 cm, in a flight volume that is roughly 6.5 m long, 6.5 m wide, and 1.5 m tall.

Keywords:Flight control, Robust control, Flexible structures Abstract: This paper investigates the preview-based altitude control of a very flexible flying wing model. The preview control system employs a two-loop control scheme, which is designed based on the reduced-order linear model. The outer loop employs PI/LADRC (linear active disturbance rejection control) algorithms to track the altitude reference command and generate pitch angle command to the inner loop, based on which the inner loop uses H^{infty} preview control to compute the control inputs to the corresponding control effectors. A Lidar (light detection and ranging) simulator is developed to measure the wind disturbances at a distance in front of the aircraft, which are provided to the inner-loop H^{infty} preview controller as prior knowledge to improve control performance. Simulation tests are conducted based on the full-order nonlinear model, which show that the preview-based altitude control system achieves better tracking effectiveness and disturbance rejection performance than the baseline non-preview control system.

Keywords:Predictive control for nonlinear systems, Optimal control, Lyapunov methods Abstract: Receding Horizon Control (RHC) is a very effective control methodology which has been employed in an extensive range of industrial applications. However, most of the stability results involve terminal costs or constraints which are sometimes not computationally desirable. In this work, it is shown that the smoothness of the value function is sufficient to ensure stability for control affine systems under RHC laws with no terminal cost or constraint. In order to find the infimum for all stabilizing horizons, an ODE problem based on the linearized system is developed that provides the set of stabilizing and destabilizing horizons. It is shown that under certain conditions, the explicit estimate for the infimum of stabilizing horizons can be found without the need to solve the nonlinear optimal control problem. Simulations are provided to illustrate the application of these methods to some nonlinear systems.

Keywords:Predictive control for nonlinear systems, Optimal control, Numerical algorithms Abstract: This paper investigates the convergence performance of second-order needle variation methods for nonlinear control-affine systems. Control solutions have a closed-form expression that is derived from the first- and second-order mode insertion gradients of the objective and are proven to exhibit superlinear convergence near equilibrium. Compared to first-order needle variations, the proposed synthesis scheme exhibits superior convergence at smaller computational cost than alternative nonlinear feedback controllers. Simulation results on the differential drive model verify the analysis and show that second-order needle variations outperform first-order variational methods and iLQR near the optimizer. Last, even when implemented in a closed-loop, receding horizon setting, the proposed algorithm demonstrates superior convergence against the iterative linear quadratic Gaussian (iLQG) controller.

Keywords:Predictive control for nonlinear systems, Robust control, Optimal control Abstract: This paper presents a tube-based robust economic MPC controller for discrete-time nonlinear systems that are perturbed by disturbance inputs. The proposed algorithm minimizes a modified economic objective function which considers the worst cost within a tube around the solution of the associated nominal system. Recursive feasibility and an a-priori upper bound to the closed-loop asymptotic average performance are ensured. Thanks to the use of dissipativity of the nominal system with a suitable supply rate, the closed-loop system under the proposed controller is shown to be asymptotically stable, in the sense that it is driven to an optimal robust invariant set. Finally, some illustrative examples, optimally operated at qualitatively different regimes, are addressed and the performances by using our new controller and those in the literature are compared.

Keywords:Predictive control for nonlinear systems, Machine learning, Constrained control Abstract: A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. Any standard supervised learning technique (e.g. neural networks) can be employed to approximate the MPC from samples. In order to obtain closed-loop guarantees for the learned MPC, a robust MPC design is combined with statistical learning bounds. The MPC design ensures robustness to inaccurate inputs within given bounds, and Hoeffding’s Inequality is used to validate that the learned MPC satisfies these bounds with high confidence. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the learned MPC. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem, for which we learn a neural network controller with guarantees.

Keywords:Autonomous robots, Optimal control, Predictive control for nonlinear systems Abstract: Improving endurance is crucial for extending the spatial and temporal operation range of autonomous underwater vehicles (AUVs). Considering the hardware constraints and the performance requirements, an intelligent energy management system is required to extend the operation range of AUVs. This paper presents a novel model predictive control (MPC) framework for energy-optimal point-to-point motion control of an AUV. In this scheme, the energy management problem of an AUV is reformulated as a surge motion optimization problem in two stages. First, a system-level energy minimization problem is solved by managing the trade-off between the energies required for overcoming the positive buoyancy and surge drag force in static optimization. Next, an MPC with a special cost function formulation is proposed to deal with transients and system dynamics. A switching logic for handling the transition between the static and dynamic stages is incorporated to reduce the computational efforts. Simulation results show that the proposed method is able to achieve near-optimal energy consumption with considerable lower computational complexity.

Keywords:Autonomous vehicles, Predictive control for nonlinear systems, Optimal control Abstract: We present an optimization-based approach for autonomous parking. Building on recent advances in the area of optimization-based collision avoidance (OBCA), we show that the autonomous parking problem can be formulated as a smooth non-convex optimization problem. Unfortunately, such problems are numerically challenging to solve in general and require appropriate warm-starting. To address this limitation, we propose a novel algorithm called Hierarchical OBCA (H-OBCA). The main idea is to first use a generic path planner, such as Hybrid A*, to compute a coarse trajectory using a simplified vehicle model and by discretizing the state-input space. This path is subsequently used to warm-start the OBCA algorithm, which optimizes and smoothens the coarse path using a full vehicle model and continuous optimization. Our studies indicate that the proposed H-OBCA parking algorithm combines Hybrid A*'s global path planning capability with OBCA's ability to generate smooth, collision-free, and dynamically feasible paths. Extensive simulations suggest that the proposed H-OBCA algorithm is robust and admits real-time parking for autonomous vehicles. Sample code is provided at https://github.com/XiaojingGeorgeZhang/H-OBCA.

Keywords:Biomolecular systems, Genetic regulatory systems, Modeling Abstract: CRISPR-mediated gene regulation is known for its ability to control multiple targets simultaneously due to its modular nature: the same dCas9 effector can target different genes simply by changing the associated gRNA. However, multiplexing requires the sharing of limited amounts of dCas9 protein among multiple gRNAs, leading to resource competition. In turn, competition between gRNAs for the same resource may hamper network function. In this work, we develop a general model that takes into account the sharing of limited amounts of dCas9 protein for arbitrary CRISPR-mediated gene repression networks. We demonstrate that, as a result of resource competition, hidden interactions appear, which modifies the intended network regulations. As a case study, we analyze the effects of these hidden interactions on repression cascades. In particular, we illustrate that perfect adaptation to resource fluctuations can be achieved in cascades with an even number of repressors. In contrast, cascades with an odd number of repressors are substantially impacted by resource competition.

Keywords:Biomolecular systems, Model/Controller reduction, Output regulation Abstract: A long-standing challenge in synthetic biology is to engineer biomolecular systems that can perform robustly in highly uncertain cellular environments. Recently, there has been increasing interest to design biomolecular feedback controllers to address this challenge. Molecular sequestration is one of the proposed feedback mechanisms. For this type of design, when all reactions within the controller are sufficiently fast, the process output can reach a set-point regardless of parametric uncertainties. However, as we demonstrate in this paper, the way in which molecular sequestration affects the fast controller dynamics leads to a singular singularly perturbed (SSP) system. In an SSP system, the boundary layer Jacobian is singular and thus standard singular perturbation approaches cannot be applied, posing difficulties to analytically determine the performance of sequestration-based controllers. In this paper, we consider a class of linear systems that capture the key structure of sequestration-based controllers. We show that, under certain technical conditions, these SSP systems can still be approximated by reduced-order systems that are dependent on the small parameter. This result allows us to analytically evaluate the tracking performance of the linearized model of a sequestration-based controller.

Keywords:Biomolecular systems, Systems biology, Robust control Abstract: For control in biomolecular systems, the most basic objective of maintaining a small error in a target variable, say the expression level of some protein, is often difficult due to the presence of both large uncertainty of every type and intrinsic limitations on the controller's implementation. This paper explores the limits of biochemically plausible controller design for the problem of robust perfect adaptation (RPA), biologists' term for robust steady state tracking. It is well-known that for a large class of nonlinear systems, a system has RPA iff it has integral feedback control (IFC), which has been used extensively in real control systems to achieve RPA. However, we show that due to intrinsic physical limitations on the dynamics of chemical reaction networks (CRNs), cells cannot implement IFC directly in the concentration of a chemical species. This contrasts with electronic implementations, particularly digital, where it is trivial to implement IFC directly in a single state. Therefore, biomolecular systems have to achieve RPA by encoding the integral control variable into the network architecture of a CRN. We describe a general framework to implement RPA in CRNs and show that well-known network motifs that achieve RPA, such as (negative) integral feedback (IFB) and incoherent feedforward (IFF), are examples of such implementations. We also develop methods to designing integral feedback variables for unknown plants. This standard control notion is surprisingly nontrivial and relatively unstudied in biomolecular control. The methods developed here connect different existing fields and approaches on the problem of biomolecular control, and hold promise for systematic chemical reaction controller synthesis as well as analysis.

Keywords:Cellular dynamics, Biomolecular systems, Biological systems Abstract: MicroRNA mediated incoherent feedforward loops (IFFLs) are recurrent network motifs in mammalian cells and have been a topic of study for their noise rejection and buffering properties. Previous work showed that IFFLs can adapt to varying promoter activity and are less prone to noise than similar circuits without the feedforward loop. Furthermore, it has been shown that microRNAs are better at rejecting extrinsic noise than intrinsic noise. This work studies the biological mechanisms that lead to extrinsic noise rejection for microRNA mediated feedforward network motifs. Specifically, we compare the effects of microRNA-induced mRNA degradation and translational inhibition on extrinsic noise rejection, and identify the parameter regimes where noise is most efficiently rejected. In the case of static extrinsic noise, we find that translational inhibition can expand the regime of extrinsic noise rejection. We then analyze rejection of dynamic extrinsic noise in the case of a single-gene feedfoward loop (sgFFL), a special case of the IFFL motif where the microRNA and target mRNA are co-expressed. For this special case, we demonstrate that depending on the time-scale of fluctuations in the extrinsic variable compared to the mRNA and microRNA decay rates, the feedforward loop can both buffer or amplify fluctuations in gene product copy numbers.

Keywords:Biological systems, Cellular dynamics, Biomolecular systems Abstract: Chemotaxis, the directed motion of cells in response to chemical gradients, is important for a variety of biological processes ranging from embryogenesis to killing of pathogens. Increasing the speed and efficiency of directed migration is critical in such situations. We provide a control mechanism by which one can minimize the noise-driven firings at the back of the cell, enabling faster motion towards the front. We achieve this through a mechanism called absolute concentration robustness (ACR), which robustly maintains the steady-state concentration of intracellular biochemical species and, at the same time, provides control over the concentration variance. More particularly, by incorporating ACR, we develop a correspondence between the concentration mean and variance — both of which are independent of total concentrations. We show that by incorporating ACR into the back of a moving cell, we can create a mechanism to robustly control the noise variance at the back — thus limiting the deterring firings while the cell moves in the direction of the gradient.

Keywords:Cellular dynamics, Hybrid systems, Stochastic systems Abstract: It is outstanding and intriguing how robustly bacteria can maintain its preferred size despite recurrent rounds of growth and divisions. We model cell size using the stochastic hybrid system framework (SHS), where a cell grows either linearly or exponentially in size over time and random division events are fired at discrete time intervals. We ask for growth and division rates that reproduce the uncorrelated behavior of the added size at division and the newborn cell size in experiments. We provide simple close-form expression of the distribution of key cell cycle events (like the distribution of the size right after division). Furthermore, we propose scenarios (in the form of division rates) in which alternative size control strategies arise, and compare them with those observed in species different from bacteria. Additionally we discuss how division rates might be useful in teasing out biomolecular mechanisms that may explain the cell size control strategies observed in nature.

Keywords:Network analysis and control, Agents-based systems, Networked control systems Abstract: In this paper, we investigate a recently proposed opinion dynamics model which considers a network of individuals simultaneously discussing a set of logically interdependent topics. The logical interdependence between the topics is captured by a ``logic matrix''. Previous works have investigated the model under the assumption that all individuals have the same logic matrix, or that individuals have different logic matrices but each individual has some stubbornness, which are restrictive assumptions. In contrast, we investigate heterogeneous logic matrices for the individuals, and assume that no stubborn individuals are present. We show that such heterogeneity can lead to a stable system with persistent disagreement among the final opinions. This indicates heterogeneity in individuals' logical interdependence structures, and not just the stubbornness of individuals (as in the Friedkin--Johnsen model), may explain the phenomenon of strong diversity of opinions often observed in a strongly connected network: the opinions at equilibrium are not at a complete consensus and opinions in any cluster are similar but not equal.

Keywords:Agents-based systems, Cooperative control, Autonomous robots Abstract: Distributed decision making in multi-agent networks has recently attracted significant research attention thanks to its wide applicability, e.g. in the management and optimization of computer networks, power systems, robotic teams, sensor networks and consumer markets. Distributed decision-making problems can be modeled by inter-dependent optimization problems, i.e., multi-agent game-equilibrium seeking problems, where noncooperative agents seek an equilibrium by communicating over a network. To achieve a network equilibrium, the agents may decide to update their decision variables via proximal dynamics, driven by the decision variables of the neighboring agents. In this paper, we first provide an operator-theoretic characterization of convergence with a time-invariant communication network. Then, for the time-varying case, we consider adjacency matrices that may switch subject to a dwell time. We illustrate our investigations with a distributed robotic exploration scenario.

Keywords:Network analysis and control, Game theory, Optimization Abstract: In the game theory literature, there appears to be little research on equilibrium selection for normal-form games with an infinite strategy space and discontinuous utility functions. Moreover, many existing selection methods are not applicable to games involving both cooperative and noncooperative scenarios (e.g., ``games on signed graphs''). With the purpose of equilibrium selection, the power allocation game developed in cite{allocation}, which is a static, resource allocation game on signed graphs, will be reformulated into an extensive form. Results about the subgame perfect Nash equilibria in the extensive-form game will be given. This appears to be the first time that subgame perfection based on time-varying graphs is used for equilibrium selection in network games. This idea of subgame perfection proposed in the paper may be extrapolated to other network games such as congestion games.

Keywords:Game theory, Mean field games Abstract: We model the effect of networks on the uptake of risky innovations by workers and the policy-making of their managers as a Stackelberg game. We specifically examine (networked) semi-anonymous (SA) whistleblowing policies, where workers can report specific observed instances of unsanctioned behavior to management. This setting is labeled semi-anonymous in contrast with the anonymous case, where only the existence of such behavior is reported without mention of potential culprits. We compare the subgame-perfect equilibria of the SA Stackelberg game for general networks and for regular graphs with the corresponding equilibria of the anonymous whistleblowing case, in which whistleblowing has been shown to only flourish in a light-punishment regime.

We observe that SA whistleblowing can lead to better equilibrium outcomes for the manager, as the network structure induces a heterogeneity in responses from the workers which can be exploited by the manager to maintain moderate amounts of unsanctioned, but potentially beneficial, behavior. Workers will exhibit different behavior depending on how many peers they observe and are observed by, cheating if the audit probability is below a specific threshold and reporting observed cheating otherwise. Without this network-induced behavioral heterogeneity (e.g., for regular graphs), SA whistleblowing equilibria resemble those arising from anonymous policies. Finally, we show that in a light-punishment regime, workers with the fewest neighbors will be the most likely to cheat.

Keywords:Game theory, Biologically-inspired methods, Stochastic systems Abstract: We propose a novel graph-based reformulation for the concept of evolutionarily stable strategies. Evolutionarily Stable Strategy (ESS) analysis cannot always explain the long-term behavior of a natural selection-mutation process. Stochastic stability is a more general analysis tool as compared to ESS analysis that does precisely characterize long-term stochastic behavior. However, one of the reasons why ESS analysis is still widely popular is its computational simplicity. Our objective is to provide a balance between the convenience of ESS analysis and the generality of stochastic stability. The fundamental object in our development is the Transitive Stability (TS) graph of an evolutionary process. From the TS-graph, we show that we can efficiently compute the smallest set of strategies that always contains the stochastically stable strategies for a particular class of evolutionary processes. In particular, we prove that each terminal class of the TS-graph is potentially a stochastically stable group of strategies. In case there is a unique terminal class, then it corresponds exactly to the set of stochastically stable strategies. In case there are multiple terminal classes, then these contain the set of possible stochastically stable strategies, and we show that a unique determination is impossible without higher order analysis.

Keywords:Mean field games, Stochastic optimal control, Stochastic systems Abstract: In this work we pose and solve the problem to guide a collection of weakly interacting dynamical systems e.g., agents, to a specified target distribution. The problem is formulated using the mean-field game theory where each agent seeks to minimize its own cost. The underlying dynamics is assumed to be linear and the cost is assumed to be quadratic. In our framework a terminal cost is added as an incentive term to accomplish the task; we establish that the map between terminal costs and terminal probability distributions is onto. By adding a proper terminal cost/incentive, the agents will reach any desired terminal distribution provided they are adopting the Nash equilibrium strategy. A similar problem is considered in the cooperative game setting where the agents work together to minimize a total cost. Our approach relies on and extends the theory of optimal mass transport and its generalizations.

Keywords:Autonomous robots, Optimization, Predictive control for nonlinear systems Abstract: Reach-avoid games are excellent proxies for studying many problems in robotics and related fields, with applications including multi-robot systems, human-robot interactions, and safety-critical systems. However, solving reach-avoid games is difficult due to the conflicting and asymmetric goals of agents, and trade-offs between optimality, computational complexity, and solution generality are commonly required. This paper seeks to find attacker strategies in reach-avoid games that reduce computational complexity while retaining solution quality by using a receding horizon strategy. To solve for the open-loop strategy fast enough to enable a receding horizon approach, the problem is formulated as a mixed-integer second-order cone program. This formulation leverages the use of sums-of-squares optimization to provide guarantees that the strategy is robust to all possible defender policies. The method is demonstrated through numerical and hardware experiments.

Keywords:Optimization, Numerical algorithms, Compartmental and Positive systems Abstract: We propose a method to compute convergent lower bounds for the state-feedback controller design problem [ inf_F{ L(F) : A + BF text{ is Metzler & stable } } ] where L is a convex loss function of F. The theory behind the approach is simple: relying only on an extension of Perron-Frobenius to Metzler matrices, and popular discrete optimization techniques. The method itself has two tuning parameters (which enable faster recovery of solutions, with possible introduction of optimality gaps) and is practical for systems with a non-trivial state dimension. A convergence result with respect to the optimal solution is derived, and a direct heuristic algorithm based on linear programming is given. We explain how projecting A onto the set of stable Metzler matrices is essentially the hardest of these problems, and focus our numerical examples on precisely this case.

Keywords:Stochastic optimal control, Robotics, Optimization algorithms Abstract: We propose a method for real-time motion planning in stochastic, dynamic environments via a receding horizon framework that exploits computationally efficient algorithms for forward stochastic reachability analysis and non-convex optimization. Our method constructs a dynamically feasible trajectory for a robot, modeled as an LTI dynamical system, while ensuring 1) a desired probabilistic collision-avoidance guarantee is achieved, 2) state and control constraints are satisfied, and 3) a convex performance objective is minimized. We first compute ``keep-out'' regions at each time instant to assure a probabilistic collision avoidance guarantee. These keep-out regions are convex and compact, and can be tightly overapproximated by ellipsoids which may be computed in a grid-free, recursion-free, and sample-free manner. The regions are constraints in a non-convex optimization problem, solved via successive convexification. This algorithm can uses interior point methods for real-time implementation. We present numerical simulations to demonstrate the efficacy of the approach.

Keywords:Stochastic systems, Stochastic optimal control, Uncertain systems Abstract: This work addresses the optimal covariance control problem for stochastic discrete-time linear systems subject to chance constraints. To the best of our knowledge, covariance steering problems with probabilistic chance constraints have not been discussed previously in the literature, although their treatment seems to be a natural extension. In this work, we first show that, unlike the case with no chance constraints, the covariance steering problem with chance constraints cannot be decoupled to mean and covariance steering sub-problems. We then propose an approach to solve the covariance steering problem with chance constraints by converting it to a convex programming problem. The proposed algorithm is verified using a numerical example.

Keywords:Network analysis and control, Control of networks, Agents-based systems Abstract: Distributed decision-making in the presence of multiple manipulative actors is studied, in the context of a linear distributed-consensus algorithm which has been enhanced to feedback controls enacted by these actors. The main contribution of the work is to evaluate the interplay among the manipulative actors in deciding the asymptotic decisions reached by the network of decision-making agents. In particular, the dependence of the asymptotic opinions on the network's topology and the manipulative actors' control schemes is characterized. Also, an example is used to illustrate that interactions among the actors may impact the dynamics of the decision-making algorithm in sophisticated ways.

Keywords:Optimization, Optimization algorithms, Robust control Abstract: In this paper, we propose a framework based on sum-of-squares programming to design iterative first-order optimization algorithms for smooth and strongly convex problems. Our starting point is to develop a polynomial matrix inequality as a sufficient condition for exponential convergence of the algorithm. The entries of this matrix are polynomial functions of the unknown parameters (exponential decay rate, stepsize, momentum coefficient, etc.). We then formulate a polynomial optimization, in which the objective is to optimize the exponential decay rate over the parameters of the algorithm. Finally, we use sum-of-squares programming as a tractable relaxation of the proposed polynomial optimization problem. We illustrate the utility of the proposed framework by designing a first-order algorithm that shares the same structure as Nesterov's accelerated gradient method.

Keywords:Autonomous robots, Reduced order modeling, Estimation Abstract: This paper presents a novel flow estimation approach that assimilates distributed pressure measurements of autonomous underwater robots through coalescing recursive Bayesian estimation and proper orthogonal decomposition (POD)-based flow model reduction. The proposed flow estimation approach does not rely on any analytical flow models and is thus applicable to many and various complicated flow fields for arbitrarily shaped underwater robots while most of the existing flow estimation methods apply only to those with simple and well-defined shapes. Neural network is further used to establish the relationship between the POD flow model and the flow parameters of interest, e.g., the angle of attack and flow-relative velocity. To demonstrate the effectiveness of the proposed distributed flow estimation approach, two simulation studies, one with a circular-shaped robot and one with a Joukowski-foil-shaped robot, are presented.

Keywords:Nonholonomic systems, Autonomous vehicles, Robotics Abstract: Nearest-Neighbor Search arises as a key component of sampling-based motion planning algorithms and it is known as their asymptotic computational bottleneck. Algorithms for exact Nearest-Neighbor Search rely on explicit distance comparisons to different extents. However, in motion planning, evaluating distances is generally a computationally demanding task, since the metric is induced by the minumum cost of steering a dynamical system between states. In the presence of driftless nonholonomic constraints, we propose efficient pruning techniques for the k-d tree algorithm that drastically reduce the number of distance evaluations performed during a query. These techniques exploit computationally convenient lower and upper bounds to the geodesic distance of the corresponding sub-Riemannian geometry. Based on asymptotic properties of the reachable sets, we show that the proposed pruning techniques are optimal, modulo a constant factor, and we provide experimental results with the Reeds-Shepp vehicle model.

Keywords:Autonomous robots, Autonomous vehicles, Automotive control Abstract: A key requirement of autonomous vehicles is the capability to safely navigate in their environment. However, outside of controlled environments, safe navigation is a very difficult problem. In particular, the real-world often contains both complex 3D structure, and dynamic obstacles such as people or other vehicles. Dynamic obstacles are particularly challenging, as a principled solution requires planning trajectories with regard to both vehicle dynamics, and the motion of the obstacles. Additionally, the real-time requirements imposed by obstacle motion, coupled with real-world computational limitations, make classical optimality and completeness guarantees difficult to satisfy. We present a unified optimization-based motion planning and control solution, that can navigate in the presence of both static and dynamic obstacles. By combining optimal and receding-horizon control, with temporal multi-resolution lattices, we can precompute optimal motion primitives, and allow real-time planning of physically-feasible trajectories in complex environments with dynamic obstacles. We demonstrate the framework by solving difficult indoor 3D quadcopter navigation scenarios, where it is necessary to plan in time. Including waiting on, and taking detours around, the motions of other people and quadcopters.

Keywords:Autonomous robots, Robotics, Stability of nonlinear systems Abstract: Path following serves as one of the most basic functions for industrial or mobile robots used in different scenarios. In this paper, a general 3D guiding vector field (GVF) is analyzed rigorously that extends the existing results on 2D GVFs. The desired 3D path is described by the intersection of two zero-level surfaces in their implicit forms, which can be used to describe various desired paths. Although the same path can be represented by the intersection of different surfaces, convergence to the path is not always guaranteed. However, under some mild assumptions, the existence of solutions and the local and global convergence results are proved rigorously for both bounded and unbounded desired paths. Examples and counter-examples from simulations further validate the theoretical results.

Keywords:Cooperative control, Autonomous robots, Smart cities/houses Abstract: In this paper, we study the coordinated robot-assisted human crowd evacuation problem, and our aim is to optimally deploy robots and choose proper human-robot interactions to evacuate human crowd in an efficient and safe manner. For such a purpose, we propose a stochastic differential equation model to capture the motion of each individual pedestrian in a crowd. Furthermore, we incorporate the impact of the robots on individual pedestrians in the stochastic differential equation model. From the microscopic pedestrian model, we obtain its corresponding Kolmogorov equation to describe the crowd dynamics evolution at the macroscopic level. The robot deployment and command selection issues are then formulated as an optimal control problem, and a two-step hierarchical structure is proposed to solve the optimal control problem. Simulations are given to illustrate our proposed approach and validate the effectiveness of using multiple robots to assist human crowd evacuation process.

Keywords:Cooperative control, Autonomous robots, Networked control systems Abstract: A platoon is a suitable model to study self-operating (e.g., driving or flying) vehicles, where a team of vehicles are lined up in a chain and travel in close proximity of each other. These vehicles form a dynamical network where the objective is to match their speed and traverse safely without inter-vehicle collisions. In this paper, the unknown effect of environment is modeled by an additive exogenous stochastic disturbance. We impose the realistic constraint that vehicles communicate with some certain time delay. We use a second order model for the platoon and define a risk measure that quantifies possibility of an inter-vehicle collision. A closed form expression is derived for the risk measure that uncovers an inherent interplay among communication topology, statistics of the exogenous disturbance, and time delay. We explain that the combination of noise and delay puts a limit on our ability to leverage connectivity in order to decrease risk. In some cases we show that more connectivity, increases the risk of collision.

Keywords:Network analysis and control, Identification, Stochastic systems Abstract: The structure of a complex networked system can be modeled as a graph with nodes representing the agents and the links describing a notion of dynamic coupling between them. Data driven methods to identify such influence pathways is central to many application domains. However, such dynamically related data-streams originating at different sources are prone to corruption caused by asynchronous time-stamps of different streams, packet drops and noise. In this article, we provide a tight characterization of the connectivity structure of the agents that can be constructed based solely on measured data streams that are corrupted. A necessary and sufficient condition that delineates the effects of corruption on a set of nodes is obtained. Here, the generative system that yields the data admits nonlinear dynamic influences between agents and can involve feedback loops. Directed information based concepts are utilized in conjunction with tools from graphical models theory to arrive at the results.

Keywords:Network analysis and control, Randomized algorithms, Distributed control Abstract: Gossip protocols play an important role in disseminating information and solving global tasks over networks in a distributed fashion. In this paper, we propose gossip algorithms that preserve the sum of network states (and therefore the average), while fully protecting node privacy even against eavesdroppers possessing the entire information flow and network knowledge. At each time step, a node is selected to interact with one of its neighbors via deterministic or random gossiping. The selected node generates a random number to replace its current state, and sends to the neighbor the difference between the current state and the random number. On receiving the data from the selected node, the neighbor sets its new state as the sum of its current state and the difference. The algorithms can be used as a simple encryption step in distributed optimization and computation algorithms. In this Part I, we study the output statistics of the proposed algorithms with deterministic edge sequence selection, in addition to