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IEEE Transactions on Automatic Control
Journal Prestige (SJR): 3.433
Citation Impact (citeScore): 6
Number of Followers: 67  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0018-9286
Published by IEEE Homepage  [228 journals]
  • IEEE Transactions on Automatic Control Publication Information

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      Abstract: Presents a listing of the editorial board, board of governors, current staff, committee members, and/or society editors for this issue of the publication.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • IEEE Control Systems Society Information

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      Abstract: Presents a listing of the editorial board, board of governors, current staff, committee members, and/or society editors for this issue of the publication.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Lyapunov Function PDEs to the Stability of Some Complex Balancing
           Derivative and Compound Networks

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      Authors: Yafei Lu;Chuanhou Gao;Denis Dochain;
      Pages: 5026 - 5038
      Abstract: This article contributes to extending the validity of Lyapunov function partial differential equations (PDEs) whose solution is conjectured to be able to behave as a Lyapunov function in stability analysis to more mass-action chemical reaction networks. First, we have proved that the Lyapunov function PDEs method is valid in capturing the asymptotic stability of the networks compounded of a complex balanced network and any species-dependent two-species autocatalytic network if some moderate conditions are included. Then, by defining a new class of networks, called complex balanced produced networks, we also show the asymptotic stability of this class of networks, and also to their compound with any species-independent one-dimensional network and with any species-dependent two-species autocatalytic network under some conditions by using the same method. A notable point is that these classes of networks are nonweakly reversible, of any dimension, and of any deficiency. Finally, we apply our results to some practical biochemical reaction networks, including birth-death processes, motifs related networks, etc., to illustrate validity.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Control Design for Iterative Methods in Solving Linear Algebraic Equations

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      Authors: Deyuan Meng;Yuxin Wu;
      Pages: 5039 - 5054
      Abstract: In the interaction between control and mathematics, mathematical tools are fundamental for all control methods, but it is unclear how control impacts mathematics. This article attempts to give an answer with focus on solving linear algebraic equations (LAEs) from the perspective of systems and control. By proposing an iterative method that integrates a learning control mechanism, a class of tracking problems for iterative learning control (ILC) is explored for the problem solving of LAEs. A trackability property of ILC is newly developed, by which analysis and synthesis results are established to disclose the equivalence between the solvability of LAEs and the controllability of discrete control systems. Hence, LAEs can be solved by equivalently achieving the perfect tracking tasks of resulting ILC systems via the classic state feedback-based design and analysis methods. It is shown that the solutions for any solvable LAE can all be calculated with different selections of the initial input. Moreover, the presented ILC method is applicable to determining all the least squares solutions of any unsolvable LAE. In particular, a deadbeat design is incorporated to ILC such that the solving of LAEs can be completed within finite iteration steps. The trackability property is also generalized to conventional two-dimensional ILC systems, which creates feedback-based methods, instead of commonly known contraction mapping-based methods, for the design and convergence analysis of ILC.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Probably Approximately Correct Learning in Adversarial Environments With
           Temporal Logic Specifications

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      Authors: Min Wen;Ufuk Topcu;
      Pages: 5055 - 5070
      Abstract: Reinforcement learning (RL) algorithms have been used to learn how to implement tasks in uncertain and partially unknown environments. In practice, environments are usually uncontrolled and may affect task performance in an adversarial way. In this article, we model the interaction between an RL agent and its potentially adversarial environment as a turn-based zero-sum stochastic game. The task requirements are represented both qualitatively as a subset of linear temporal logic (LTL) specifications, and quantitatively as a reward function. For each case in which the LTL specification is realizable and can be equivalently transformed into a deterministic Büchi automaton, we show that there always exists a memoryless almost-sure winning strategy that is $varepsilon$-optimal for the discounted-sum objective for any arbitrary positive $varepsilon$. We propose a probably approximately correct (PAC) learning algorithm that learns such a strategy efficiently in an online manner with a priori unknown reward functions and unknown transition distributions. To the best of our knowledge, this is the first result on PAC learning in stochastic games with independent quantitative and qualitative objectives.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Temporal Logic Trees for Model Checking and Control Synthesis of Uncertain
           Discrete-Time Systems

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      Authors: Yulong Gao;Alessandro Abate;Frank J. Jiang;Mirco Giacobbe;Lihua Xie;Karl Henrik Johansson;
      Pages: 5071 - 5086
      Abstract: We propose algorithms for performing model checking and control synthesis for discrete-time uncertain systems under linear temporal logic (LTL) specifications. We construct temporal logic trees (TLTs) from LTL formulae via reachability analysis. In contrast to automaton-based methods, the construction of the TLT is abstraction-free for infinite systems; that is, we do not construct discrete abstractions of the infinite systems. Moreover, for a given transition system and an LTL formula, we prove that there exist both a universal TLT and an existential TLT via minimal and maximal reachability analysis, respectively. We show that the universal TLT is an underapproximation for the LTL formula and the existential TLT is an overapproximation. We provide sufficient conditions and necessary conditions to verify whether a transition system satisfies an LTL formula by using the TLT approximations. As a major contribution of this work, for a controlled transition system and an LTL formula, we prove that a controlled TLT can be constructed from the LTL formula via a control-dependent reachability analysis. Based on the controlled TLT, we design an online control synthesis algorithm, under which a set of feasible control inputs can be generated at each time step. We also prove that this algorithm is recursively feasible. We illustrate the proposed methods for both finite and infinite systems and highlight the generality and online scalability with two simulated examples.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • $H^infty$ +Control+for+Linear+Quantum+Systems&rft.title=IEEE+Transactions+on+Automatic+Control&rft.issn=0018-9286&rft.date=2022&rft.volume=67&rft.spage=5087&rft.epage=5101&rft.aulast=Yonezawa;&rft.aufirst=Yanan&rft.au=Yanan+Liu;Daoyi+Dong;Ian+R.+Petersen;Qing+Gao;Steven+X.+Ding;Shota+Yokoyama;Hidehiro+Yonezawa;">Fault-Tolerant Coherent $H^infty$ Control for Linear Quantum Systems

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      Authors: Yanan Liu;Daoyi Dong;Ian R. Petersen;Qing Gao;Steven X. Ding;Shota Yokoyama;Hidehiro Yonezawa;
      Pages: 5087 - 5101
      Abstract: Robustness and reliability are two key requirements for developing practical quantum control systems. The purpose of this article is to design a coherent feedback controller for a class of linear quantum systems suffering from Markovian jumping faults so that the closed-loop quantum system has both fault tolerance and $H^infty$ disturbance attenuation performance. This article first extends the physical realization conditions from the time-invariant case to the time-varying case for linear stochastic quantum systems. By relating the fault-tolerant $H^infty$ control problem to the dissipation properties and the solutions of Riccati differential equations, an $H^infty$ controller for the quantum system is then designed by solving a set of linear matrix inequalities. In particular, an algorithm is employed to introduce additional quantum inputs and to construct the corresponding input matrices to ensure the physical realizability of the quantum controller. Also, we propose a real application of the developed fault-tolerant control strategy to quantum optical systems. A linear quantum system example from quantum optics, where the amplitude of the pumping field randomly jumps among different values due to the fault processes, can be modeled as a linear Markovian jumping system. It is demonstrated that a quantum $H^infty$ controller can be designed and implemented using some basic optical components to achieve the desired control goal for this class of systems.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Risk Aware Minimum Principle for Optimal Control of Stochastic
           Differential Equations

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      Authors: Jukka Isohätälä;William B. Haskell;
      Pages: 5102 - 5117
      Abstract: We present a probabilistic formulation of risk aware optimal control problems for stochastic differential equations. Risk awareness is in our framework captured by objective functions in which the risk neutral expectation is replaced by a risk function, a nonlinear functional of random variables that accounts for the controller's risk preferences. We state and prove a risk aware minimum principle that gives necessary and sufficient conditions for optimality of generalized control processes taking values on probability measures defined on a given action space. We show that going from the risk neutral to the risk aware case, the minimum principle is modified by the introduction of one additional real-valued stochastic process that acts as a risk adjustment factor. This adjustment process is explicitly given as the expectation, conditional on the filtration at the given time, of an appropriately defined functional derivative of the risk function evaluated at the random total cost. The control model we employ differs from standard relaxed controls, and we elaborate on the differences, and benefits and drawbacks, of the control types; we further give conditions under which the generalized control can be realized using a strict control process. We present an application of the results for a portfolio allocation problem and show that the risk awareness of the objective function gives rise to a risk premium term that is characterized by the risk adjustment process described above. This suggests uses of our results in e.g. pricing of risk modeled by generic risk functions in financial applications.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • A Continuation Method for Large-Scale Modeling and Control: From ODEs to
           PDE, a Round Trip

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      Authors: Denis Nikitin;Carlos Canudas-de-Wit;Paolo Frasca;
      Pages: 5118 - 5133
      Abstract: In this article, we present a continuation method, which transforms spatially distributed ordinary differential equation (ODE) systems into a continuous partial differential equation (PDE). We show that this continuation can be performed for both linear and nonlinear systems, including multidimensional, space-varying, and time-varying systems. When applied to a large-scale network, the continuation provides a PDE describing the evolution of a continuous-state approximation that respects the spatial structure of the original ODE. Our method is illustrated by multiple examples, including transport equations, Kuramoto equations, and heat diffusion equations. As a main example, we perform the continuation of a Newtonian system of interacting particles and obtain the Euler equations for compressible fluids, thereby providing an original solution to Hilbert’s sixth problem. Finally, we leverage our derivation of Euler equations to solve a control problem multiagent systems, by designing a nonlinear control algorithm for robot formation based on its continuous approximation.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Signed Social Networks With Biased Assimilation

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      Authors: Lingfei Wang;Yiguang Hong;Guodong Shi;Claudio Altafini;
      Pages: 5134 - 5149
      Abstract: A biased assimilation model of opinion dynamics is a nonlinear model, in which opinions exchanged in a social network are multiplied by a state-dependent term having the bias as exponent and expressing the bias of the agents toward their own opinions. The aim of this article is to extend the bias assimilation model to signed social networks. We show that while for structurally balanced networks, polarization to an extreme value of the opinion domain (the unit hypercube) always occurs regardless of the value of the bias, for structurally unbalanced networks, a stable state of indecision (corresponding to the centroid of the opinion domain) also appears, at least for small values of the bias. When the bias grows and passes a critical threshold, which depends on the amount of “disorder” encoded in the signed graph, then a bifurcation occurs and opinions become again polarized.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • A Fast Randomized Incremental Gradient Method for Decentralized Nonconvex
           Optimization

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      Authors: Ran Xin;Usman A. Khan;Soummya Kar;
      Pages: 5150 - 5165
      Abstract: In this article, we study decentralized nonconvex finite-sum minimization problems described over a network of nodes, where each node possesses a local batch of data samples. In this context, we analyze a single-timescale randomized incremental gradient method, called GT-SAGA. GT-SAGA is computationally efficient as it evaluates one component gradient per node per iteration and achieves provably fast and robust performance by leveraging node-level variance reduction and network-level gradient tracking. For general smooth nonconvex problems, we show the almost sure and mean-squared convergence of GT-SAGA to a first-order stationary point and further describe regimes of practical significance, where it outperforms the existing approaches and achieves a network topology-independent iteration complexity, respectively. When the global function satisfies the Polyak–Łojaciewisz condition, we show that GT-SAGA exhibits linear convergence to an optimal solution in expectation and describe regimes of practical interest where the performance is network topology independent and improves upon the existing methods. Numerical experiments are included to highlight the main convergence aspects of GT-SAGA in nonconvex settings.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Inherent Stochastic Robustness of Model Predictive Control to Large and
           Infrequent Disturbances

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      Authors: Robert D. McAllister;James B. Rawlings;
      Pages: 5166 - 5178
      Abstract: We introduce a new class of large, infrequent disturbances to complement the small, persistent disturbances typically considered in robustness analysis. This new class of disturbances includes discrete disturbances that become pertinent when considering discrete actuators and production scheduling in control problems. To properly account for the infrequent nature of these disturbances, we define a stochastic form of robustness. Under suitable assumptions, we prove that certain closed-loop systems subject to large, infrequent disturbances admit an SISS-Lyapunov function and are robust in this stochastic context. We apply these results to economic model predictive control (MPC) with a strictly dissipative nominal system and stage cost, which includes tracking MPC as a special case, and prove that economic MPC is robust to large, infrequent disturbances. Without dissipativity assumptions, we define and establish robust asymptotic performance for economic MPC. We present a simple tracking problem to illustrate the results of this work, and a production scheduling (economic MPC) problem, to demonstrate the relevance of this analysis to practical applications.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Potential Impacts of Delay on Stability of Impulsive Control Systems

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      Authors: Jianquan Lu;Bangxin Jiang;Wei Xing Zheng;
      Pages: 5179 - 5190
      Abstract: In this article, the exponential stability of impulsive control systems with time delay is studied. By using the average impulsive interval method, some sufficient Lyapunov-based conditions are established for the stability of impulsive time-delay systems, and the impacts of delay on the stability analysis method are further revealed. It is interesting to show that some unstable impulsive time-delay systems may be stabilized by increasing the time delay in continuous dynamics. More interestingly, it is proved that along with the increase of the delay within a certain range, the convergence rate of such impulsive time-delay systems also increases correspondingly. Further, a strict comparison principle for impulsive control systems with delay is established. Then by utilizing this comparison principle, it can be shown that for some stable impulsive systems with delay, under certain conditions, the stability is robust against any large but bounded delay. Compared with the previous results on delay-free impulsive systems, some potential impacts of delay on the stability are investigated. Particularly, the obtained results are extended to the case of impulsive control systems with hybrid impulses, which contain both stabilizing impulses and destabilizing impulses. Three illustrative examples are presented to reveal the potential impacts of delay on the stability of impulsive control systems.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • The Role of Frustration in Collective Decision-Making Dynamical Processes
           on Multiagent Signed Networks

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      Authors: Angela Fontan;Claudio Altafini;
      Pages: 5191 - 5206
      Abstract: In this article, we consider a collective decision-making process in a network of agents described by a nonlinear interconnected dynamical model with sigmoidal nonlinearities and signed interaction graph. The decisions are encoded in the equilibria of the system. The aim is to investigate this multiagent system when the signed graph representing the community is not structurally balanced and in particular as we vary its frustration, i.e., its distance to structural balance. The model exhibits bifurcations, and a “social effort” parameter, added to the model to represent the strength of the interactions between the agents, plays the role of bifurcation parameter in our analysis. We show that, as the social effort increases, the decision-making dynamics exhibit a pitchfork bifurcation behavior where, from a deadlock situation of “no decision” (i.e., the origin is the only globally stable equilibrium point), two possible (alternative) decision states for the community are achieved (corresponding to two nonzero locally stable equilibria). The value of social effort for which the bifurcation is crossed (and a decision is reached) increases with the frustration of the signed network.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Hybrid Adaptive Output Feedback Tracking for Stable Systems With Unknown
           Input Constraints

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      Authors: Riccardo Marino;Patrizio Tomei;
      Pages: 5207 - 5217
      Abstract: The problem of global output tracking is addressed for stable minimum phase systems, with constant uncertain parameters and constant disturbances belonging to a known compact set, in the presence of input constraints such as amplitude saturation. The relative degree, the system order, and the sign of the high frequency gain are assumed to be known. A hybrid adaptive output feedback control is designed to achieve global asymptotic output tracking, provided that there exists an input within the input constraints capable of tracking exactly the output reference signal. By virtue of the hybrid control approach, the closed-loop system is linear within each time interval between parameter updating. Moreover, no information on input saturation is required by the controller. In addition to the standard assumptions in adaptive control design when inputs are unconstrained, further requirements on the reference signals, on system stability and on parameter bounds, are needed when inputs are constrained.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Distributed Mean-Field Density Estimation for Large-Scale Systems

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      Authors: Tongjia Zheng;Qing Han;Hai Lin;
      Pages: 5218 - 5229
      Abstract: This article studies how to estimate the mean-field density of large-scale systems in a distributed manner. Such problems are motivated by the recent swarm control technique that uses mean-field approximations to represent the collective effect of the swarm, wherein the mean-field density (especially its gradient) is usually used in feedback control design. In the first part, we formulate the density estimation problem as a filtering problem of the associated mean-field partial differential equation (PDE), for which we employ Kernel density estimation to construct noisy observations and use filtering theory of PDE systems to design an optimal (centralized) density filter. It turns out that the covariance operator of observation noise depends on the unknown density. Hence, we use approximations for the covariance operator to obtain a suboptimal density filter, and prove that both the density estimates and their gradient are convergent and remain close to the optimal one using the notion of input-to-state stability (ISS). In the second part, we continue to study how to decentralize the density filter such that each agent can estimate the mean-field density based on only its own position and local information exchange with neighbors. We prove that the local density filter is also convergent and remains close to the centralized one in the sense of ISS. Simulation results suggest that the centralized suboptimal density filter is able to generate convergent density estimates, and the local density filter is able to converge and remain close to the centralized filter.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Decentralized Learning for Optimality in Stochastic Dynamic Teams and
           Games With Local Control and Global State Information

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      Authors: Bora Yongacoglu;Gürdal Arslan;Serdar Yüksel;
      Pages: 5230 - 5245
      Abstract: Stochastic dynamic teams and games are rich models for decentralized systems and challenging testing grounds for multiagent learning. Previous work that guaranteed team optimality assumed stateless dynamics, or an explicit coordination mechanism, or joint-control sharing. In this article, we present an algorithm with guarantees of convergence to team optimal policies in teams and common interest games. The algorithm is a two-timescale method that uses a variant of Q-learning on the finer timescale to perform policy evaluation while exploring the policy space on the coarser timescale. Agents following this algorithm are “independent learners”: they use only local controls, local cost realizations, and global state information, without access to controls of other agents. The results presented here are the first, to the best of our knowledge, to give formal guarantees of convergence to team optimality using independent learners in stochastic dynamic teams and common interest games.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • An Optimization Framework for Resilient Batch Estimation in Cyber-Physical
           Systems

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      Authors: Alexandre Kircher;Laurent Bako;Eric Blanco;Mohamed Benallouch;
      Pages: 5246 - 5261
      Abstract: This article proposes a class of resilient state estimators for linear time-varying discrete-time systems. The dynamic equation of the system is assumed to be affected by a bounded process noise. As to the available measurements, they are potentially corrupted by a noise of both dense and impulsive natures. The latter, in addition to being arbitrary in its form, need not be strictly bounded. In this setting, we construct the estimator as the set-valued map, which associates with the measurements the minimizing set of some appropriate performance functions. We consider a family of such performance functions, each of which yielding a specific instance of the proposed general estimation framework. It is then shown that the proposed class of estimators enjoys the property of resilience, i.e., it induces an estimation error, which, under certain conditions, is independent of the extreme values of the (impulsive) measurement noise. Hence, the estimation error may be bounded, while the measurement noise is virtually unbounded. Moreover, we provide several error bounds (in different configurations), whose expressions depend explicitly on the degree of observability of the system being observed and on the considered performance function. Finally, a few simulation results are provided to illustrate the resilience property.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Reactive and Risk-Aware Control for Signal Temporal Logic

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      Authors: Lars Lindemann;George J. Pappas;Dimos V. Dimarogonas;
      Pages: 5262 - 5277
      Abstract: The deployment of autonomous systems in uncertain and dynamic environments has raised fundamental questions. Addressing these is pivotal to build fully autonomous systems and requires a systematic integration of planning and control. We first propose reactive risk signal interval temporal logic (ReRiSITL) as an extension of signal temporal logic (STL) to formulate complex spatiotemporal specifications. Unlike STL, ReRiSITL allows to consider uncontrollable propositions that may model humans as well as random environmental events such as sensor failures. Additionally, ReRiSITL allows to incorporate risk measures, such as (but not limited to) the conditional value-at-risk, to measure the risk of violating certain spatial specifications. Second, we propose an algorithm to check if an ReRiSITL specification is satisfiable. For this purpose, we abstract the ReRiSITL specification into a timed signal transducer and devise a game-based approach. Third, we propose a reactive planning and control framework for dynamical control systems under ReRiSITL specifications.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • A New Approach to Stability Analysis for Stochastic Hopfield Neural
           Networks With Time Delays

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      Authors: Xiang Lv;
      Pages: 5278 - 5288
      Abstract: This article is devoted to the existence and the global stability of stationary solutions for stochastic Hopfield neural networks with time delays and additive white noises. Using the method of random dynamical systems, we present a new approach to guarantee that the infinite-dimensional stochastic flow generated by stochastic delay differential equations admits a globally attracting random equilibrium in the state-space of continuous functions. An example is given to illustrate the effectiveness of our results, and the forward trajectory synchronization will occur.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Extended Insertion Functions for Opacity Enforcement in Discrete-Event
           Systems

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      Authors: Xiaoyan Li;Christoforos N. Hadjicostis;Zhiwu Li;
      Pages: 5289 - 5303
      Abstract: Opacity is a confidentiality property that holds if certain secret behavior of a system, typically represented by a predicate, cannot be revealed under any system evolution. Among other proposed methodologies, when opacity is violated, it can be enforced using insertion mechanisms, i.e., by inserting symbols before an actual system output (in real time as the system evolves) in order to replace observation sequences that lead to opacity violations with observation sequences that can be generated by system behavior that does not violate opacity. This article focuses on opacity enforcement in discrete-event systems modeled with finite-state automata and proposes an extended insertion mechanism that can enforce opacity in a practical manner to a wide class of systems by inserting symbols before and after an actual system output. This article also introduces event insertion constraints that require only certain specific symbols to be inserted before and after an actual system output. For each case, we obtain a necessary and sufficient condition (based on the construction of an appropriate verifier) for opacity enforceability using the proposed extended insertion mechanism and devise a pertinent extended insertion strategy.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Approximate and Exact Controllability of Switched Infinite-Dimensional
           Linear Systems

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      Authors: Yacun Guan;Hao Yang;Bin Jiang;
      Pages: 5304 - 5317
      Abstract: This article addresses the approximate and exact controllability issues of switched infinite-dimensional linear systems. First, a controllability map that is related to switching sequence and a controllability Gramian operator are proposed, based on which two necessary and sufficient conditions are established for approximate and exact controllability, respectively. Second, it shows that the obtained conditions can degenerate into the existing controllability criteria of infinite-dimensional linear systems, switched finite-dimensional linear systems, and a single finite-dimensional linear system. Finally, the new results are applied to analyze the approximate controllability of switched linear parabolic systems and the exact controllability of switched linear wave systems. Two examples are given to illustrate the effectiveness of the proposed approaches.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Global Stabilization for Stochastic Continuous Cascade Nonlinear Systems
           Subject to SISS Inverse Dynamics and Time-Delay: A Dynamic Gain Approach

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      Authors: Yu Shao;Ju H. Park;Shengyuan Xu;
      Pages: 5318 - 5331
      Abstract: This article is devoted to the global continuous control for stochastic low-order cascade nonlinear systems with time-varying delay and stochastic inverse dynamics. Compared with existing results, the nature of only continuous, but nonsmooth, is unfolded since the power of the stochastic cascade system is of low order; and all the traditional growth conditions on unknown drift and diffusion nonlinearities and local Lipschitz condition are quitted, which largely extends the scope of application. Combining with stochastic input-to-state stability, two new lemmas are developed with rigorous proofs to deal with uncertain nonlinear terms and unmeasurable stochastic inverse dynamics. A continuous control scheme consisting of a delay-independent partial state feedback controller and a serial of dynamic update laws is proposed to guarantee the globally asymptotical stability of the closed-loop system.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Event-Triggered Tracking Control of Networked Multiagent Systems

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      Authors: Wei Ren;Dimos V. Dimarogonas;
      Pages: 5332 - 5347
      Abstract: This article studies the tracking control problem of networked multiagent systems under both multiple networks and event-triggered mechanisms. Multiple networks are to connect multiple agents and reference systems with decentralized controllers to guarantee their information transmission, whereas the event-triggered mechanisms are to reduce the information transmission via the networks. In this article, each agent has a network to communicate with its controller and reference system, and all networks are independent and asynchronous and have local event-triggered mechanisms, which are based on local measurements and determine whether the local measurements need to be transmitted via the corresponding network. To address this scenario, we first implement the emulation-based approach to develop a novel hybrid model for the tracking control of networked multiagent systems. Next, sufficient conditions are derived and decentralized event-triggered mechanisms are designed to guarantee the desired tracking performance. Furthermore, the proposed approach is applied to derive novel results for the event-triggered observer design problem of networked multiagent systems. Finally, two numerical examples are presented to illustrate the validity of the developed results.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Sensor Fault-Tolerant State Estimation by Networks of Distributed
           Observers

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      Authors: Guitao Yang;Hamed Rezaee;Andrea Serrani;Thomas Parisini;
      Pages: 5348 - 5360
      Abstract: We propose a state estimation methodology using a network of distributed observers. We consider a scenario in which the local measurement at each node may not guarantee the system's observability. In contrast, the ensemble of all the measurements does ensure that the observability property holds. As a result, we design a network of observers such that the estimated state vector computed by each observer converges to the system's state vector by using the local measurement and the communicated estimates of a subset of observers in its neighborhood. The proposed estimation scheme exploits sensor redundancy to provide robustness against faults in the sensors. Under suitable conditions on the redundant sensors, we show that it is possible to mitigate the effects of a class of sensor faults on the state estimation. Simulation trials demonstrate the effectiveness of the proposed distributed estimation scheme.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Relative Stability in the Sup-Norm and Input-to-State Stability in the
           Spatial Sup-Norm for Parabolic PDEs

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      Authors: Jun Zheng;Guchuan Zhu;Sergey Dashkovskiy;
      Pages: 5361 - 5375
      Abstract: In this article, we introduce the notion of relative $mathcal {K}$-equi-stability (RKES) to characterize the uniformly continuous dependence of (weak) solutions on external disturbances for nonlinear parabolic partial differential equations (PDEs). Based on the RKES, we prove the input-to-state stability (ISS) in the spatial sup-norm for a class of nonlinear parabolic PDEs with either Dirichlet or Robin boundary disturbances. An example concerned with a superlinear parabolic PDE with Robin boundary condition is provided to illustrate the obtained ISS results. Besides, as an application of the notion of RKES, we conduct stability analysis for a class of parabolic PDEs in cascade coupled over the domain or on the boundary of the domain, in the spatial and time sup-norm, and in the spatial sup-norm, respectively. The technique of De Giorgi iteration is extensively used in the proof of the results presented in this article.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Exponential Control Lyapunov-Barrier Function Using a Filtering-Based
           Concurrent Learning Adaptive Approach

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      Authors: Vahid Azimi;Seth Hutchinson;
      Pages: 5376 - 5383
      Abstract: The state-of-the-art quadratic-program-based control Lyapunov-barrier function (QP-CLBF) is a powerful control approach to balance safety and stability in an optimal fashion. However, under this approach, modeling inaccuracies may degrade the performance of closed-loop systems and cause violation or restriction of safety-critical constraints. This article presents an adaptive QP-CLBF approach for a class of nonlinear systems in the presence of parameter uncertainties with an unknown control coefficient. We begin by presenting a filtering-based concurrent learning (FCL) adaptive technique to guarantee simultaneous exponential convergence of system parameters and control coefficient. The proposed FCL extends and encompasses the baseline concurrent learning technique, which was developed to achieve exponential convergence of either system parameters exclusively or control coefficient while relying on the estimation of state derivatives using numerical smoothing. The proposed FCL adaptive method is then unified with a modified version of QP-CLBF to achieve exponential convergence of system parameters, control coefficient, and control Lyapunov and control barrier functions while establishing safety with the largest safe region. Under this unification, all results are exponential in the presence of modeling error without the need for numerical methods to estimate state derivatives. This is formally proven by employing a Lyapunov argument. Simulations are finally carried out to validate the theoretical results.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Security Investment in Cyber-Physical Systems: Stochastic Games With
           Asymmetric Information and Resource-Constrained Players

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      Authors: Wei Xing;Xudong Zhao;Tamer Başar;Weiguo Xia;
      Pages: 5384 - 5391
      Abstract: This article considers remote state estimation in cyber-physical systems (CPSs) with multiple sensors. Each plant is modeled by a discrete-time stochastic linear system with measurements of each sensor transmitted to the corresponding remote estimator over a shared communication network when their securities are interdependent due to network-induced risks. A dynamic nonzero-sum game with asymmetric information is formulated in which each sensor subject to a resource budget constraint needs to decide whether to invest in security for sending data packets, taking the behaviors of other sensors into account. To overcome the difficulty in characterizing or computing the Nash equilibria (NE), the game with asymmetric information is transformed into another game with symmetric information such that the equilibrium of the original game can be obtained by solving the equilibrium of the new game. Under certain conditions, we devise a backward induction algorithm to obtain a subclass of NE of the original game, known as common information-based Markov perfect equilibria (CIBMPE). Finally, a numerical example is provided to illustrate the results obtained.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Adaptive Second-Order Sliding Mode Control: A Lyapunov Approach

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      Authors: Shihong Ding;Keqi Mei;Xinghuo Yu;
      Pages: 5392 - 5399
      Abstract: This article proposes an adaptive second-order sliding mode (ASOSM) controller design by means of the Lyapunov method. The notable feature of the proposed algorithm is that it only needs boundedness of the uncertainties, whereas boundedness of the derivatives of uncertainties is not demanded. Under the proposed ASOSM control scheme, the gain can be dynamically tuned, which avoids gain overestimation. The finite-time stability of the closed-loop ASOSM dynamics is proved via the Lyapunov theory. Finally, the simulation results are shown to validate the theoretical analysis.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Anytime Control Under Practical Communication Models

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      Authors: Wanchun Liu;Daniel E. Quevedo;Yonghui Li;Branka Vucetic;
      Pages: 5400 - 5407
      Abstract: In this article, we investigate a novel anytime control algorithm for wireless networked control with random dropouts. The controller computes sequences of tentative future control commands using time-varying (Markovian) computational resources. The sensor–controller and controller–actuator channel states are spatial- and time-correlated, respectively, and are modeled as a multistate Markov process. To compensate the effect of packet dropouts, a dual-buffer mechanism is proposed. We develop a novel cycle-cost-based approach to obtain the stability conditions on the nonlinear plant, controller, network, and computational resources.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Distributed Recursive Filtering Over Sensor Networks With Nonlogarithmic
           Sensor Resolution

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      Authors: Hongwei Chen;Zidong Wang;Bo Shen;Jinling Liang;
      Pages: 5408 - 5415
      Abstract: Sensor resolution, which is one of the most important parameters/specifications for almost all kinds of sensors, plays an important role in any signal processing problems. This article deals with the distributed filtering problem for a class of discrete time-varying stochastic systems subject to nonlogarithmic sensor resolution and stochastic nonlinearities. The soft measurement technique is exploited in the filter design to overcome the difficulties resulting from the sensor-resolution-induced (SRI) uncertainty. The aim of the presented filtering problem is to construct the distributed filter over a sensor network such that in the presence of SRI uncertainty and stochastic nonlinearity, an upper bound on the filtering error covariance is guaranteed and subsequently minimized by appropriately designing the filer parameters at each time instant. Moreover, a matrix simplification method is utilized to tackle the difficulties stemming from the sparsity of sensor networks. Finally, a numerical example is employed to illustrate the effectiveness of the proposed filtering scheme.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Fast Hands-Off Control Using ADMM Real-Time Iterations

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      Authors: Moritz Schulze Darup;Gerrit Book;Daniel E. Quevedo;Masaaki Nagahara;
      Pages: 5416 - 5423
      Abstract: We investigate the implementation of a sparsitypromoting hands-off control scheme using the alternating direction method of multiplies (ADMM). In order to minimize the numerical control effort along with the actuation one, only a single ADMM iteration per time step is considered. We analyze the resulting closed-loop dynamics for linear systems with additive disturbances and show that the proposed scheme provides sparse controls as desired and, in addition, ensures input-to-state practical stability. We further point out a close relation between the proposed real-time scheme and (nonminimum time) dead-beat control. Finally, characteristics and effectiveness of the novel hands-off controller(s) are illustrated with numerical examples.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Online State Estimation for Time-Varying Systems

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      Authors: Guido Cavraro;Emiliano Dall’Anese;Joshua Comden;Andrey Bernstein;
      Pages: 5424 - 5431
      Abstract: The article investigates the problem of estimating the state of a time-varying system with a linear measurement model; in particular, the article considers the case where the number of measurements available can be smaller than the number of states. In lieu of a batch linear least-squares approach—well-suited for static networks, where a sufficient number of measurements could be collected to obtain a full-rank design matrix—the article proposes an online algorithm to estimate the possibly time-varying state by processing measurements as and when available. The design of the algorithm hinges on a generalized least-squares cost augmented with a proximal-point-type regularization. With the solution of the regularized least-squares problem available in closed-form, the online algorithm is written as a linear dynamical system where the state is updated based on the previous estimate and based on the new available measurements. Conditions under which the algorithmic steps are in fact a contractive mapping are shown, and bounds on the estimation error are derived for different noise models. Numerical simulations are provided to corroborate the analytical findings.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Constrained Controller and Observer Design by Inverse Optimality

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      Authors: Mario Zanon;Alberto Bemporad;
      Pages: 5432 - 5439
      Abstract: Model predictive control (MPC) is often tuned by trial and error. When a baseline linear controller exists that is already well tuned in the absence of constraints and MPC is introduced to enforce them, one would like to avoid altering the original linear feedback law whenever they are not active. We formulate this problem as a controller matching similar to the works of Di Cairano and Bemporad (2009), Di Cairano and Bemporad (2010), and Tran et al. (2015), which we extend to a more general framework. We prove that a positive-definite stage-cost matrix yielding this matching property can be computed for all stabilizing linear controllers. In addition, we prove that the constrained estimation problem can also be solved similarly, by matching a linear observer with a moving horizon estimator. Finally, we discuss various aspects of the practical implementation of the proposed technique in some examples.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Parameter Estimation in Adaptive Control of Time-Varying Systems Under a
           Range of Excitation Conditions

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      Authors: Joseph E. Gaudio;Anuradha M. Annaswamy;Eugene Lavretsky;Michael A. Bolender;
      Pages: 5440 - 5447
      Abstract: This article presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error trajectories to tend exponentially fast toward a compact set whenever excitation conditions are satisfied. This algorithm is employed in a large class of problems where unknown parameters are present and are time-varying. It is shown that this algorithm guarantees global boundedness of the state and parameter errors of the system, and avoids an often used filtering approach for constructing key regressor signals. In addition, intervals of time over which these errors tend exponentially fast toward a compact set are provided, both in the presence of finite and persistent excitation. A projection operator is used to ensure the boundedness of the learning rate matrix, as compared to a time-varying forgetting factor. Numerical simulations are provided to complement the theoretical analysis.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Stabilization of Discrete-Time Multiplicative-Noise System Under
           Decentralized Controllers

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      Authors: Juanjuan Xu;Wei Wang;Huanshui Zhang;
      Pages: 5448 - 5455
      Abstract: In this article, we study the mean-square stabilization of discrete-time multiplicative-noise stochastic systems under decentralized controllers. Two controllers are involved in the system where each controller has access to different information and one information set is contained by another one. The adopted information structure is adapted open-loop. The main contribution of the article is twofold. On one hand, we give the unique explicit solution of the finite-horizon optimization problem in terms of difference Riccati equations. On the other hand, we characterize the equivalent condition for the mean-square stabilization under the decentralized controllers via the corresponding algebraic Riccati equations. Moreover, we derive the optimal and stabilizing solution for the infinite-horizon optimization problem.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Suboptimal Filtering Over Sensor Networks With Random Communication

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      Authors: Aneel Tanwani;
      Pages: 5456 - 5463
      Abstract: The problem of filter design is considered for continuous-time linear stochastic systems using distributed sensors. Each sensor unit, represented by a node in an undirected and connected graph, collects some information about the state and communicates its own estimate with the neighbors. It is stipulated that this communication between sensor nodes connected by an edge is time-sampled randomly and for each edge, the sampling process is an independent Poisson counter. Our proposed filtering algorithm for each sensor node is a stochastic hybrid system: It comprises a continuous-time differential equation, and at random time instants when communication takes place, each sensor node updates its state estimate based on the information received by its neighbors. In this setting, we compute the expectation of the error covariance matrix for each unit which is governed by a matrix differential equation. To study the asymptotic behavior of these covariance matrices, we show that if the gain matrices are appropriately chosen and the mean sampling rate is large enough, then the error covariances practically converge to a constant matrix.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • An Interpolatory Algorithm for Distributed Set Membership Estimation in
           Asynchronous Networks

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      Authors: Francesco Farina;Andrea Garulli;Antonio Giannitrapani;
      Pages: 5464 - 5470
      Abstract: This article addresses distributed estimation problems over asynchronous networks in a set membership framework. The agents in the network asynchronously collect and process measurements, communicate over a possibly time-varying and unbalanced directed graph and may have nonnegligible computation times. Measurements are affected by bounded errors so that they define feasible sets containing the unknown parameters to be estimated. The proposed algorithm requires each agent to compute a weighted average of its estimate and those of its neighbors and to project it onto a local feasible set. By assuming convexity of the measurement sets, the local estimates are shown to converge to a common point belonging to the global feasible set.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Learning Dynamical Systems From Quantized Observations: A Bayesian
           Perspective

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      Authors: Dario Piga;Manas Mejari;Marco Forgione;
      Pages: 5471 - 5478
      Abstract: Identification of dynamical systems from low-resolution quantized observations presents several challenges because of the limited amount of information available in the data and since proper algorithms have to be designed to handle the error due to quantization. In this article, we consider identification of infinite impulse response models from quantized outputs. Algorithms both for maximum-likelihood estimation and Bayesian inference are developed. Finally, a particle-filter approach is presented for recursive reconstruction of the latent nonquantized outputs from past quantized observations.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Partial Exponential Stability Analysis of Slow–Fast Systems via
           Periodic Averaging

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      Authors: Yuzhen Qin;Yu Kawano;Brian D. O. Anderson;Ming Cao;
      Pages: 5479 - 5486
      Abstract: This article presents some new criteria for the partial exponential stability of a slow–fast nonlinear system with a fast scalar variable using periodic averaging methods. Unlike classical averaging techniques, we construct an averaged system by averaging over this fast scalar variable instead of the time variable. We show that the partial exponential stability of the averaged system implies that of the original one. We then apply the obtained criteria to the study of remote synchronization of Kuramoto–Sakaguchi oscillators coupled by a star network with two peripheral nodes. We show that detuning the natural frequency of the central mediating oscillator increases the robustness of the remote synchronization against phase shifts. This article appears to be the first-known attempt to analytically study the phase-unlocked remote synchronization.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Stochastic Failure Prognosis of Discrete Event Systems

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      Authors: Jun Chen;Ratnesh Kumar;
      Pages: 5487 - 5492
      Abstract: This article studies the prognosis of failure, i.e., its prediction prior to its occurrence, in stochastic discrete event systems. Prior work has focused on the definition and offline verification of $m$-steps stochastic-prognosability, or $S_m$-prognosability, which allows the prediction of a fault at least $m$-steps in advance. This article complements the existing work by proposing an algorithm for the computation of online failure prognoser. The proposed algorithm reduces the condition for issuing an affirmative prognostic decision to verification condition of a safety property of a Markov chain. We discuss how such a verification condition can be computed using a finitely terminating algorithm.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Positivity and Stability Analysis of Homogeneous Coupled
           Differential-Difference Equations With Time-Varying Delays

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      Authors: Yukang Cui;Jun Shen;Wei Zhang;Zhiguang Feng;Xin Gong;
      Pages: 5493 - 5500
      Abstract: This article studies the positivity and stability of homogeneous coupled differential-difference equations with time-varying delays. First, a sufficient positivity condition is proposed for the nonlinear coupled differential-difference equations with delays. Then, based on this positivity condition, we present necessary and sufficient conditions ensuring the exponential stability and bounding the decay rate for time-delay homogeneous coupled differential-difference equations with homogeneity of degree one. Furthermore, the necessary and sufficient condition is extended to the global polynomial stability analysis of homogeneous coupled differential-difference equations when the degree of homogeneity is greater than one, and the decay rate is also investigated. Two numerical examples are employed to show the effectiveness of the obtained results.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • A Feasibility Governor for Enlarging the Region of Attraction of Linear
           Model Predictive Controllers

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      Authors: Terrence Skibik;Dominic Liao-McPherson;Torbjørn Cunis;Ilya Kolmanovsky;Marco M. Nicotra;
      Pages: 5501 - 5508
      Abstract: This article proposes a method for enlarging the region of attraction of linear model predictive controllers (MPC) when tracking piecewise-constant references in the presence of pointwise-in-time constraints. It consists of an add-on unit, the feasibility governor (FG), that manipulates the reference command so as to ensure that the optimal control problem that underlies the MPC-feedback law remains feasible. Offline polyhedral projection algorithms based on multiobjective linear programming are employed to compute the set of feasible states and reference commands. Online, the action of the FG is computed by solving a convex quadratic program. The closed-loop system is shown to satisfy constraints, be asymptotically stable, exhibit zero-offset tracking, and display finite-time convergence of the reference.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • A Zeno-Free Event-Triggered Control Strategy for Asymptotic Stabilization
           of Switched Affine Systems

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      Authors: Zhuoyu Li;Jun Zhao;
      Pages: 5509 - 5516
      Abstract: This article investigates the event-triggered control problem for switched affine systems (SASs). The presence of affine terms brings many difficulties on the exclusion of triggering Zeno behavior when ensuring asymptotic stability. We propose an event-triggered control strategy dynamically updated with triggering to solve this problem, in which the triggering condition is associated with the affine terms and given with a time-varying term that is updated at triggering instants. Based on the triggering strategy, the controllers for subsystems and a switching rule are designed to achieve asymptotic stability of the resulting closed-loop system. Moreover, due to the special feature of event-triggered SASs, a new method for proving the exclusion of Zeno behavior is given. Finally, the developed results are illustrated by an electric circuit example.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Path-Based Stability Analysis for Monotone Control Systems on Proper Cones

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      Authors: Yu Kawano;Bart Besselink;
      Pages: 5517 - 5524
      Abstract: In this article, we study positive invariance and attractivity properties for nonlinear control systems, which are monotone with respect to proper cones. Monotonicity simplifies such analysis for specific sets defined by the proper cones. Instead of Lyapunov functions, a pair of so-called paths in the state space and input space play important roles. As applications, our results are utilized for analysis of asymptotic stability and also input-to-state stability on proper cones. The results are illustrated by means of examples.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Connectivity Preserving Formation Stabilization in an Obstacle-Cluttered
           Environment in the Presence of Time-Varying Communication Delays

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      Authors: Savvas G. Loizou;Dario Giuseppe Lui;Alberto Petrillo;Stefania Santini;
      Pages: 5525 - 5532
      Abstract: This technical article addresses the formation stabilization problem for multiagent systems (MASs) composed of dynamical agents moving within an obstacle-cluttered environment and sharing information via nonideal wireless communication networks. A novel distributed cooperative navigation function based control strategy is proposed, which drives the MAS to a desired formation without any collision while counteracting the presence of unavoidable communication impairments originated by the wireless network. By recasting the formation stabilization problem into a consensus one and by combining the Lyapunov stability theory with Halanay’s lemma, uniformly ultimately bounded stability of the whole delayed closed-loop system is proved. In the special case of an obstacle-free environment, our approach guarantees exponential stability of the closed-loop networked system. The stability analysis also provides an estimation of the delay upper bound and allows to evaluate the stability margins with respect to the latencies that can be observed in practical application scenarios. Theoretical derivations are verified through nontrivial simulations.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Input Constraint Sets for Robust Regulation of Linear Systems

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      Authors: Sampath Kumar Mulagaleti;Alberto Bemporad;Mario Zanon;
      Pages: 5533 - 5540
      Abstract: In robust control under state constraints, the set of admissible inputs is usually considered as given, under the assumption that the actuators have been already designed. However, if the input set is too small, any controller will fail in stabilizing the closed-loop system while satisfying all prescribed constraints for some initial states of interest, or vice versa the chosen actuators may be oversized. To handle this issue, in this article, we address the problem of computing the smallest input constraint set such that the closed-loop system is stabilizable from a prescribed set of initial states while respecting all constraints. We focus our attention on linear systems with additive disturbances, and develop the algorithm based on recursive feasibility of robust model predictive control. We demonstrate the results using numerical examples, in which we consider different metrics for the input constraint set selection.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Prognosability Analysis and Enforcement of Bounded Labeled Petri Nets

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      Authors: Ning Ran;Jinyuan Hao;Carla Seatzu;
      Pages: 5541 - 5547
      Abstract: In this article, we deal with two problems related to bounded labeled Petri nets (PNs), namely prognosability analysis and enforcement. The solution we propose is based on a single tool, called prognosability verifier. Such a tool uses the notion of basis marking that avoids the exhaustive enumeration of all the reachable markings. This leads to advantages in terms of computational complexity that may be enormous in certain real applications. Finally, the enforcement problem can be solved associating a cost with each sensor eventually added to the system. A systematic way to compute a solution that minimizes the total cost of the new sensors while guaranteeing prognosability of the resulting system, is computed using linear integer programming.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Exact Minimum Number of Bits to Stabilize a Linear System

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      Authors: Victoria Kostina;Yuval Peres;Gireeja Ranade;Mark Sellke;
      Pages: 5548 - 5554
      Abstract: We consider an unstable scalar linear stochastic system, $X_{n+1}=a X_n + Z_n - U_n$, where $a geq 1$ is the system gain, $Z_n$s are independent random variables with bounded $alpha$th moments, and $U_n$s are the control actions that are chosen by a controller who receives a single element of a finite set $lbrace 1, ldots, Mrbrace$ as its only information about system state $X_i$. We show new proofs that $M> a$ is necessary and sufficient for $beta$-moment stability, for any $beta < alpha$. Our achievable scheme is a uniform quantizer of the zoom-in/zoom-out type that codes over multiple time instants for data rate efficiency; the controller uses its memory of the past to correctly interpret the received bits. We analyze the performance of our scheme using probabilistic arguments. We show a simple proof of a matching converse using information-theoretic techniques. Our results generalize to vector systems, to systems with dependent Gaussian noise, and to the scenario in which a small fraction of transmitted messages is lost.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Distributed Newton Optimization With Maximized Convergence Rate

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      Authors: Damián Marelli;Yong Xu;Minyue Fu;Zenghong Huang;
      Pages: 5555 - 5562
      Abstract: The distributed optimization problem is set up in a collection of nodes interconnected via a communication network. The goal is to find the minimizer of a global objective function formed by the sum of local functions known at individual nodes. A number of methods, having different advantages, are available for addressing this problem. The goal of this article is to achieve the maximum possible convergence rate. As the first step toward this end, we propose a new method, which we show converges faster than other available options. As the second step toward our goal, we complement the proposed method with a fully distributed method for estimating the optimal step size that maximizes the convergence rate. We provide theoretical guarantees for the convergence of the resulting method in a neighborhood of the solution. We present numerical experiments showing that, when using the same step size, our method converges significantly faster than its rivals. Experiments also show that the distributed step-size estimation method achieves an asymptotic convergence rate very close to the theoretical maximum.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Combining Online Diagnosis and Prognosis for Safe Controllability

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      Authors: Ana T. Y. Watanabe;André B. Leal;José E. R. Cury;Max H. de Queiroz;
      Pages: 5563 - 5569
      Abstract: In this article, we combine fault diagnosis and prognosis to generalize the notion of safe controllability of discrete-event systems. To do so, we reformulate the notions of safe diagnosability, prognosability, safe controllability by diagnosis, and safe controllability by prognosis in the context of strings. Moreover, we combine these notions to introduce the concept of safe controllability by diagnosis or prognosis, or simply DP-safe controllability. We show that a language can be DP-safe controllable even if it is not safe controllable either only by diagnosis or only by prognosis. Thus, the DP-safe controllability can be considered a generalization of the safe controllability concept found in the literature. If a DES is DP-safe controllable, to achieve fault tolerance using an active approach, reconfiguration actions could be forced based not only on online fault diagnosis, but also on online fault prognosis. Thus, our approach outperforms the previous ones, since it provides additional control options to keep the system away from forbidden zones and to switch from the nominal supervisor to a postfault-detection supervisor designed to achieve postfault performance objectives. Necessary and sufficient conditions for DP-safe controllability are presented and an example is used to illustrate the introduced concepts.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • $L^2$ -Gain&rft.title=IEEE+Transactions+on+Automatic+Control&rft.issn=0018-9286&rft.date=2022&rft.volume=67&rft.spage=5570&rft.epage=5577&rft.aulast=Fridman;&rft.aufirst=Rami&rft.au=Rami+Katz;Emilia+Fridman;">Finite-Dimensional Boundary Control of the Linear Kuramoto-Sivashinsky
           Equation Under Point Measurement With Guaranteed $L^2$ -Gain

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      Authors: Rami Katz;Emilia Fridman;
      Pages: 5570 - 5577
      Abstract: Finite-dimensional observer-based controller design for PDEs is a challenging problem. Recently, such controllers were introduced for the one dimensional (1D) heat equation, under the assumption that one of the observation or control operators is bounded. This article suggests a constructive method for such controllers for 1D parabolic partial differential equations (PDEs) with both observation and control operators being unbounded. We consider the Kuramoto–Sivashinsky equation under either boundary or in-domain point measurement and boundary actuation in the presence of disturbances in the PDE and measurement. We employ a modal decomposition approach via dynamic extension, using eigenfunctions of a Sturm–Liouville operator. The controller dimension is defined by the number of unstable modes, whereas the observer dimension $N$ may be larger. We suggest a direct Lyapunov approach to the full-order closed-loop system, which results in a linear matrix inequality (LMI), for input-to-state stabilization (ISS) and guaranteed $L^2$-gain, whose elements and dimension depend on $N$. The value of $N$ and the decay rate are obtained from the LMI. We prove that the LMI is always feasible provided $N$ and the $L^2$ or ISS gains are large enough, thereby obtaining guarantees for our approach. Moreover, for the case of stabilization, we show that feasibility of the LMI for some $N$ implies its feasibility for $N+-$. Numerical examples demonstrate the efficiency of the method.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • On Input-to-Output Stability and Robust Synchronization of Generalized
           Persidskii Systems

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      Authors: Wenjie Mei;Denis Efimov;Rosane Ushirobira;
      Pages: 5578 - 5585
      Abstract: In this article, we study a class of generalized Persidskii systems with external disturbances and establish conditions, in the form of linear matrix inequalities, for input-to-output stability and robust synchronization for these systems. We apply the obtained results to the robust control design for synchronizing linear systems and to the synchronization of Hindmarsh–Rose models of neurons.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Finite-Time and Fixed-Time Attractiveness for Nonlinear Impulsive Systems

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      Authors: Hongxiao Hu;Bei Gao;Liguang Xu;
      Pages: 5586 - 5593
      Abstract: In this article, the finite-time and fixed-time attractiveness problems are investigated for nonlinear impulsive systems. The aim of the proposed problems is to establish some general Lyapunov theorems and settling-time estimates for finite-time and fixed-time attractiveness of nonlinear impulsive systems by analysis technics. Moreover, some comparisons with the existing results are also given. The classical finite-time and fixed-time convergence theorems for nonlinear impulse-free systems are well extended to nonlinear impulsive systems by our results. Furthermore, the existing results of finite-time and fixed-time attractiveness for nonlinear impulsive systems are well improved. Finally, some simulations are utilized to illustrate the usefulness of the theoretical analysis.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Finite-Time Stabilization of Linear Systems With Unknown Control Direction
           via Extremum Seeking

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      Authors: Adriano Mele;Gianmaria De Tommasi;Alfredo Pironti;
      Pages: 5594 - 5601
      Abstract: In this article, the finite-time stabilization problem is solved for a linear time-varying system with unknown control direction by exploiting a modified version of the classical extremum-seeking algorithm. We propose to use a suitable oscillatory input to modify the system dynamics, at least in an average sense, so as to satisfy a differential linear matrix inequality condition, which in turn guarantees that the system’s state remains inside a prescribed time-varying hyperellipsoid in the state space. The finite-time stability (FTS) of the averaged dynamics implies the FTS of the original system, as the distance between the original and the averaged dynamics can be made arbitrarily small by choosing a sufficiently high value of the dithering frequency used by the extremum-seeking algorithm. The main advantage of the proposed approach resides in its capability of dealing with systems with unknown control direction, and/or with a control direction that changes over time. Being FTS a quantitative approach, this article also gives an estimate of the necessary minimum dithering/mixing frequency provided, and the effectiveness of the proposed finite-time stabilization approach is analyzed by means of numerical examples.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Frequency Regulation With Thermostatically Controlled Loads: Aggregation
           of Dynamics and Synchronization

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      Authors: Andreas Kasis;Ioannis Lestas;
      Pages: 5602 - 5609
      Abstract: Thermostatically controlled loads (TCLs) can provide ancillary services to the power network by aiding existing frequency-control mechanisms. TCLs are, however, characterized by an intrinsic limit cycle behavior, which raises the risk that these could synchronize when coupled with the frequency dynamics of the power grid, i.e., simultaneously switch, inducing persistent and possibly catastrophic power oscillations. To address this problem, schemes with a randomized response time in their control policy have been proposed in the literature. However, such schemes introduce delays in the response of TCLs to frequency feedback that may limit their ability to provide fast support at urgencies. In this article, we present a deterministic control mechanism for TCLs such that those switch when prescribed frequency thresholds are exceeded in order to provide ancillary services to the power network. For the considered scheme, we provide analytic conditions, which ensure that synchronization is avoided. In particular, we show that as the number of loads tends to infinity, there exist arbitrarily long time intervals where the frequency deviations are arbitrarily small. Our analytical results are verified with simulations on the Northeast Power Coordinating Council 140-bus system, which demonstrate that the proposed scheme offers improved frequency response compared with existing implementations.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • On the Stability of Linear Dynamic Controllers With Integer Coefficients

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      Authors: Nils Schlüter;Moritz Schulze Darup;
      Pages: 5610 - 5613
      Abstract: In this article, we show that linear dynamic controllers with integer coefficients are usually unstable. In fact, asymptotic stability can only be achieved if all controller eigenvalues are equal to zero. Moreover, for a fixed controller order, there exist only finitely many characteristic polynomials with integer coefficients that lead to marginally stable eigenvalues on the unit circle and we characterize these setups. The obtained results are, in particular, relevant to encrypted control, where (nontrivial) stable controllers with integer coefficients were on the “wish list.”
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Further Geometric and Lyapunov Characterizations of Incrementally Stable
           Systems on Finsler Manifolds

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      Authors: Dongjun Wu;Guang-Ren Duan;
      Pages: 5614 - 5621
      Abstract: In this article, we report several new geometric and Lyapunov characterizations of incrementally stable systems on Finsler and Riemannian manifolds. A new and intrinsic proof of an important theorem in contraction analysis is given via the complete lift of the system. Based on this, two Lyapunov characterizations of incrementally stable systems are derived, namely, converse contraction theorems, and revelation of the connection between incremental stability and stability of an equilibrium point, in which the second result recovers and extends the classical Krasovskii’s method.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • A Compressed Gradient Tracking Method for Decentralized Optimization With
           Linear Convergence

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      Authors: Yiwei Liao;Zhuorui Li;Kun Huang;Shi Pu;
      Pages: 5622 - 5629
      Abstract: Communication compression techniques are of growing interests for solving the decentralized optimization problem under limited communication, where the global objective is to minimize the average of local cost functions over a multiagent network using only local computation and peer-to-peer communication. In this article, we propose a novel compressed gradient tracking algorithm (C-GT) that combines gradient tracking technique with communication compression. In particular, C-GT is compatible with a general class of compression operators that unifies both unbiased and biased compressors. We show that C-GT inherits the advantages of gradient tracking-based algorithms and achieves linear convergence rate for strongly convex and smooth objective functions. Numerical examples complement the theoretical findings and demonstrate the efficiency and flexibility of the proposed algorithm.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Distributed Variable Sample-Size Stochastic Optimization With Fixed
           Step-Sizes

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      Authors: Jinlong Lei;Peng Yi;Jie Chen;Yiguang Hong;
      Pages: 5630 - 5637
      Abstract: In this article, we consider distributed stochastic optimization over randomly switching networks, where agents collaboratively minimize the average of all agents’ local expectation-valued convex cost functions. Due to the stochasticity in gradient observations, distributedness of local functions, and randomness of communication topologies, distributed algorithms with an exact convergence guarantee under fixed step-sizes have not been achieved yet. This work incorporates variance reduction scheme into the distributed stochastic gradient tracking algorithm, where local gradients are estimated by averaging across a variable number of sampled gradients. With an identically and independently distributed random network, we show that all agents’ iterates converge almost surely to the same optimal solution under fixed step-sizes. When the global cost function is strongly convex and the sample size increases at a geometric rate, we prove that the iterates geometrically converge to the unique optimal solution, and establish the iteration, oracle, and communication complexity. The algorithm performance, including rate and complexity analysis, are further investigated with constant step-sizes and a polynomially increasing sample size. Finally, the empirical algorithm performance are illustrated with numerical examples.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • From Small-Gain Theory to Compositional Construction of Barrier
           Certificates for Large-Scale Stochastic Systems

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      Authors: Mahathi Anand;Abolfazl Lavaei;Majid Zamani;
      Pages: 5638 - 5645
      Abstract: This article is concerned with a compositional approach for the construction of control barrier certificates for large-scale interconnected stochastic systems while synthesizing hybrid controllers against high-level logic properties. Our proposed methodology involves decomposition of interconnected systems into smaller subsystems and leverages the notion of control sub-barrier certificates of subsystems, enabling one to construct control barrier certificates of interconnected systems by employing some $max$-type small-gain conditions. The main goal is to synthesize hybrid controllers enforcing complex logic properties, including the ones represented by the accepting language of deterministic finite automata, while providing probabilistic guarantees on the satisfaction of given specifications in bounded-time horizons. To do so, we propose a systematic approach to first decompose high-level specifications into simple reachability tasks by utilizing automata corresponding to the complement of specifications. We then construct control sub-barrier certificates and synthesize local controllers for those simpler tasks and combine them to obtain a hybrid controller that ensures satisfaction of the complex specification with some lower bound on the probability of satisfaction. We finally apply our proposed techniques to a fully-interconnected Kuramoto network composed of 100 nonlinear oscillators.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Generalized Super-Twisting for Control Under Time- and State-Dependent
           Perturbations: Breaking the Algebraic Loop

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      Authors: Hernan Haimovich;Leonid Fridman;Jaime A. Moreno;
      Pages: 5646 - 5652
      Abstract: Application of sliding-mode control strategies based on (generalized) super-twisting (ST) algorithms in the presence of time- and state-dependent perturbations is highly challenging. One of the difficulties lies in the occurrence of a kind of algebraic loop; the bounds required for control design require bounds on the control variable, which itself depends on the control to be designed. Existing results were able to partially solve this problem by means of one form of generalized ST, provided that some perturbation-related functions admit constant bounds. In this article, we provide an important generalization by employing disturbance-tailored ST ideas. The current results allow for far greater applicability, since the bounds required need not be constant as long as their growth can be related to the sliding variable.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Exponential Time-Stepping Method for Linear Complementarity Systems

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      Authors: Zhengyu Wang;
      Pages: 5653 - 5660
      Abstract: Linear complementarity system (LCS) consists of an ordinary differential equation (ODE) and a linear complementarity problem (LCP). In this article, we propose an exponential time-stepping method for solving LCS, which uses exponential integrator to discretize the ODE and solves the LCPs at the discrete time points. Numerical results are reported for illustrating its good performance.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Convergence of Dynamic Programming on the Semidefinite Cone for
           Discrete-Time Infinite-Horizon LQR

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      Authors: Donghwan Lee;
      Pages: 5661 - 5668
      Abstract: The goal of this article is to investigate new and simple convergence analysis of dynamic programming for the linear–quadratic regulator problem of discrete-time linear time-invariant systems. In particular, bounds on errors are given in terms of both matrix inequalities and matrix norm. Under a mild assumption on the initial parameter, we prove that the $Q$-value iteration exponentially converges to the optimal solution. Moreover, a global asymptotic convergence is also presented. These results are then extended to the policy iteration. We prove that in contrast to the $Q$-value iteration, the policy iteration always converges exponentially fast. An example is given to illustrate the results.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Optimal Transmission Power and Controller Design for Networked Control
           Systems Under State-Dependent Markovian Channels

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      Authors: Bin Hu;Tua A. Tamba;
      Pages: 5669 - 5676
      Abstract: This article considers a codesign problem for industrial networked control systems to ensure both stability and efficiency properties of such systems. This problem is particularly challenging due to the fact that wireless communications in industrial environments are not only subject to shadow fading, but also stochastically correlated with their surrounding environments. This article first introduces a novel state-dependent Markov channel (SD-MC) model that explicitly captures the state-dependent features of industrial wireless communication systems by defining the proposed model’s transition probabilities as a function of both environments’ states and transmission power. Under the SD-MC model, sufficient conditions on Maximum Allowable Transmission Interval are presented to ensure both asymptotic stability in expectation and almost sure asymptotic stability properties of a nonlinear control system with state-dependent fading channels. Based on these stability conditions, the codesign problem is then formulated as a constrained polynomial optimization problem (CPOP), which can be efficiently solved using semidefinite programming methods for the case of a two-state SD-MC model. The solutions to such a CPOP represent optimal control and power strategies that optimize the average expected joint costs in an infinite time horizon while respecting the stability constraints. For a general SD-MC model, this article further shows that suboptimal solutions can be obtained from linear programming formulations of the considered CPOP. Simulation results are given to illustrate the efficacy of the proposed codesign scheme.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • Correction to “A Framework for Control System Design Subject to Average
           Data-Rate Constraints”

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      Authors: Milan S. Derpich;Jan Østergaard;
      Pages: 5677 - 5679
      Abstract: Theorem 4.1 in the 2011 paper “A Framework for Control System Design Subject to Average Data-Rate Constraints” allows one to lower bound average operational data rates in feedback loops (including the situation in which encoder and decoder have side information). Unfortunately, its proof is invalid. In this note, we first state the theorem and explain why its proof is flawed, and then provide a correct proof under weaker assumptions.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
  • TechRxiv: Share Your Preprint Research with the World!

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      Pages: 5680 - 5680
      Abstract: Prospective authors are requested to submit new, unpublished manuscripts for inclusion in the upcoming event described in this call for papers.
      PubDate: Oct. 2022
      Issue No: Vol. 67, No. 10 (2022)
       
 
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