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IEEE Transactions on Automatic Control
Journal Prestige (SJR): 3.433  Citation Impact (citeScore): 6 Number of Followers: 70  Hybrid journal (It can contain Open Access articles)ISSN (Print) 0018-9286 Published by IEEE  [228 journals]
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- IEEE Control Systems Society Information
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Pages: C2 - C2
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- IEEE Control Systems Society Information
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Pages: C3 - C3
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Sufficient Conditions for Convergent Recursive Extrapolation of qLPV
Scheduling Parameters Along a Prediction Horizon-
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Authors: Marcelo Menezes Morato;Julio Elias Normey-Rico;Olivier Sename;
Pages: 3182 - 3193
Abstract: Model predictive control (MPC) algorithms have long been applied to nonlinear processes. In a quasi-linear parameter varying (qLPV) setting, nonlinearities are included into bounded scheduling parameters, which are given as a function of endogenous variables; these scheduling parameters are a priori unknown along a future prediction horizon, which complicates MPC design. To address this problem, the literature points out two options: robust MPC approaches, considering the scheduling to be uncertain; or suboptimal ones that set values for these parameters along the horizon. With respect to the latter group, this article proposes an extrapolation algorithm that estimates the future values of the qLPV scheduling parameters for a fixed prediction horizon of $N$ steps; the method is based on a recursive procedure using simple Taylor expansions. Sufficient conditions for convergent extrapolation are presented with regard to the form and class of the scheduling function and the robustness of the MPC. Different benchmark examples from the literature are presented to illustrate the algorithm, which is also compared to state-of-the-art techniques.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- A Piecewise Linear Regression and Classification Algorithm With
Application to Learning and Model Predictive Control of Hybrid Systems-
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Authors: Alberto Bemporad;
Pages: 3194 - 3209
Abstract: This article proposes an algorithm for solving multivariate regression and classification problems using piecewise linear predictors over a polyhedral partition of the feature space. The resulting algorithm that we call piecewise affine regression and classification (PARC) alternates between first, solving ridge regression problems for numeric targets, softmax regression problems for categorical targets, and either softmax regression or cluster centroid computation for piecewise linear separation, and second, assigning the training points to different clusters on the basis of a criterion that balances prediction accuracy and piecewise-linear separability. We prove that PARC is a block-coordinate descent algorithm that minimizes a suitably constructed objective function and that it converges in a finite number of steps. The algorithm is used to learn hybrid numerical/categorical dynamical models from data that contain real and discrete labeled values. The resulting model has a piecewise linear structure that is particularly useful to formulate model predictive control problems and solve them by mixed-integer programming.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Data-Driven Analysis and Controller Design for Discrete-Time Systems Under
Aperiodic Sampling-
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Authors: Stefan Wildhagen;Julian Berberich;Michael Hertneck;Frank Allgöwer;
Pages: 3210 - 3225
Abstract: This article is concerned with data-driven analysis of discrete-time systems under aperiodic sampling, and in particular with a data-driven estimation of the maximum sampling interval (MSI). The MSI is relevant for the analysis of and controller design for cyber-physical, embedded and networked systems, since it gives a limit on the time span between sampling instants such that stability is guaranteed. We propose tools to compute the MSI for a given controller and to design a controller with a preferably large MSI, both directly from a finite-length, noise-corrupted state-input trajectory of the system. We follow two distinct approaches for stability analysis, one taking a robust control perspective and the other a switched systems perspective on the aperiodically sampled system. In a numerical example and a subsequent discussion, we demonstrate the efficacy of our developed tools and compare the two approaches.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Global Stabilizability Theorems on Discrete-Time Nonlinear Uncertain
Systems-
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Authors: Zhaobo Liu;Chanying Li;
Pages: 3226 - 3240
Abstract: This article focuses on the stabilizability problem for a basic class of discrete-time nonlinear systems with multiple unknown parameters. We claim that such a system is stabilizable if its nonlinear growth rate is dominated by a polynomial rule. This rule cannot be relaxed in general since it becomes a necessary and sufficient condition when the system has a polynomial form (Li and Lam, 2013). We further prove that the concerned stabilizable system is possible to grow exponentially fast. Meanwhile, optimality and closed-loop identification are also discussed herein.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Stochastic Programming Using Expected Value Bounds
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Authors: Raphael Chinchilla;João P. Hespanha;
Pages: 3241 - 3256
Abstract: In this article, we address the problem of minimizing an expected value with stochastic constraints, known in the literature as stochastic programming. Our approach is based on computing and optimizing bounds for the expected value that are obtained by solving a deterministic optimization problem that uses the probability density function (pdf) to penalize unlikely values for the random variables. The suboptimal solution obtained through this approach has performances guarantees with respect to the optimal one, while satisfying stochastic and deterministic constraints. We illustrate this approach in the context of the following three different classes of optimization problems: finite horizon optimal stochastic control, with state or output feedback; parameter estimation with latent variables; and nonlinear Bayesian experiment design. By the means of several numerical examples, we show that our suboptimal solution achieves results similar to those obtained with Monte Carlo methods with a fraction of the computational burden, highlighting the usefulness of this approach in real-time optimization problems.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Optimal Dynamic Mechanism Design With Stochastic Supply and Flexible
Consumers-
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Authors: Shiva Navabi;Ashutosh Nayyar;
Pages: 3257 - 3272
Abstract: In this article, we consider the problem of designing an expected-revenue-maximizing mechanism for allocating multiple nonperishable goods of $k$ varieties to flexible consumers over $T$ time steps. In our model, a random number of goods of each variety may become available to the seller at each time, and a random number of consumers may enter the market at each time. Each consumer is present in the market for one time step and wants to consume one good of one of its desired varieties. Each consumer is associated with a flexibility level that indicates the varieties of goods it is equally interested in. A consumer’s flexibility level and the utility it gets from consuming a good of its desired varieties are its private information. We characterize the allocation rule for a Bayesian-incentive-compatible, individually rational, and expected-revenue-maximizing mechanism in terms of the solution to a dynamic program. The corresponding payment function is also specified in terms of the optimal allocation function. We leverage the structure of the consumers’ flexibility model to simplify the dynamic program. Our simplified dynamic program allows us to provide an explicit allocation procedure and a simple payment rule in terms of the solution of the dynamic program.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Finite-Sample Analysis of Two-Time-Scale Natural Actor–Critic
Algorithm-
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Authors: Sajad Khodadadian;Thinh T. Doan;Justin Romberg;Siva Theja Maguluri;
Pages: 3273 - 3284
Abstract: Actor–critic style two-time-scale algorithms are one of the most popular methods in reinforcement learning, and have seen great empirical success. However, their performance is not completely understood theoretically. In this article, we characterize the global convergence of an online natural actor–critic algorithm in the tabular setting using a single trajectory of samples. Our analysis applies to very general settings, as we only assume ergodicity of the underlying Markov decision process. In order to ensure enough exploration, we employ an $epsilon$-greedy sampling of the trajectory. For a fixed and small enough exploration parameter $epsilon$, we show that the two-time-scale natural actor–critic algorithm has a rate of convergence of $tilde{mathcal {O}}(1/T^{1/4})$, where $T$ is the number of samples, and this leads to a sample complexity of $tilde{mathcal {O}}(1/delta ^{8})$ samples to find a policy that is within an error of $delta$ from the global optimum. Moreover, by carefully decreasing the exploration parameter $epsilon$ as the iterations proceed, we present an improved sample complexity of $tilde{mathcal {O}}(1/delta ^{6})$ for convergence to the global optimum.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Deep Filtering With Adaptive Learning Rates
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Authors: Hongjiang Qian;George Yin;Qing Zhang;
Pages: 3285 - 3299
Abstract: This article develops a new deep learning framework for general nonlinear filtering. Our main contribution is to present a computationally feasible procedure. The proposed algorithms have the capability of dealing with challenging (infinitely dimensional) filtering problems involving diffusions with randomly-varying switching. First, we convert it to a problem in a finite-dimensional setting by approximating the optimal weights of a neural network. Then, we construct a stochastic gradient-type procedure to approximate the neural network weight parameters, and develop another recursion for adaptively approximating the optimal learning rate. The convergence of the combined approximation algorithms is obtained using stochastic averaging and martingale methods under suitable conditions. Robustness analysis of the approximation to the network parameters with the adaptive learning rate is also dealt with. We demonstrate the efficiency of the algorithm using highly nonlinear dynamic system examples.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Watermark-Based Proactive Defense Strategy Design for Cyber-Physical
Systems With Unknown-but-Bounded Noises-
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Authors: Hao Liu;Yuzhe Li;Qing-Long Han;Tarek Raïssi;
Pages: 3300 - 3315
Abstract: In this article, a novel proactive attack defense strategy is proposed to deal with the secure remote estimation issue in cyber-physical systems with unknown-but-bounded noises in the presence of man-in-the-middle attacks. It is assumed that the residue calculated by the smart sensor is sent to the remote estimator and the abnormal intrusion detector via a wireless network, and the watermark is assumed to belong to a zonotope. In order to guarantee the detection rate, the data processes and the watermark are time-varying and secret to an adversary. Moreover, the effect on system performance caused by the watermark can be removed when the system is attack free. Furthermore, four different attack scenarios are discussed to analyze the detection ability of the proposed defense approach, and the designed strategy can be applied to detect replay attacks. Finally, an unmanned aircraft system subject to malicious attacks is leveraged to illustrate the effectiveness of the proposed proactive defense strategy.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Inaccuracy Matters: Accounting for Solution Accuracy in Event-Triggered
Nonlinear Model Predictive Control-
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Authors: Omar J. Faqir;Eric C. Kerrigan;
Pages: 3316 - 3330
Abstract: We consider the effect of using approximate system predictions in event-triggered control schemes. These approximations often result from using numerical transcription methods for solving continuous-time optimal control problems. Mesh refinement can guarantee upper bounds on the error in the differential equations that model the system dynamics. We employ the accuracy guarantees of a mesh refinement scheme to show that the proposed event-triggering scheme, which compares the measured system with approximate state predictions, can be used with a guaranteed strictly positive interupdate time. Furthermore, if knowledge of the employed transcription scheme or the approximation errors are available, then better online estimates of interupdate times can be obtained. We also detail a method of tightening constraints on the approximate system trajectory to guarantee constraint satisfaction of the continuous-time system. This is the first work to incorporate prediction accuracy in triggering metrics to guarantee reliable lower bounds for interupdate times and perform solution-dependent constraint tightening.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Practical Learning-Tracking Framework Under Unknown Nonrepetitive Channel
Randomness-
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Authors: Dong Shen;
Pages: 3331 - 3347
Abstract: In this study, we consider the learning-tracking problem for stochastic systems through unreliable communication channels. The channels suffer from both multiplicative and additive randomness subject to unknown probability distributions. The statistics of this randomness, such as mean and covariance, are nonrepetitive in the iteration domain. This nonrepetitive randomness introduces nonstationary contamination and drifts to the actual signals, yielding essential challenges in signal processing and learning control. Therefore, we propose a practical framework constituted by an unbiased estimator of the mean inverse, a signal correction mechanism, and learning control schemes. The convergence and tracking performance are strictly established for both constant and decreasing step-lengths. If the statistics satisfy asymptotic repetitiveness in the iteration domain, a consistent estimator applies to the framework while retaining the framework’s asymptotic properties. Illustrative examples are provided to verify the theoretical results.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Filippov's Solution and Finite-Time Stability of Stochastic Systems
for Discontinuous Control-
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Authors: Sheng Chen;Tao Li;Qiang Zang;Yunping Liu;
Pages: 3348 - 3361
Abstract: In this article, a suite of theoretic tools is provided for discontinuous control design and finite-time stability analysis of a class of stochastic differential systems. The notion of Filippov's solutions for stochastic differential systems is proposed, and the corresponding solution existence problem is explored. The classical Itô differentiation formula is generalized for quasi-$C_{0}^{2}(mathbb {R}^{n},mathbb {R})$-class functions along Filippov's solutions of stochastic differential systems, and two involved set-valued stochastic integrals are introduced with a study on their properties. Some finite-time stability results of stochastic differential systems are revealed with Filippov's solutions, and one of them is applied to neural synchronization, together with case simulations.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Transmission Power Policies for Energy-Efficient Wireless Control of
Nonlinear Systems-
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Authors: Vineeth Satheeskumar Varma;Romain Postoyan;Daniel E. Quevedo;Irinel-Constantin Morărescu;
Pages: 3362 - 3376
Abstract: We present an emulation-based controller and transmission policy design procedure for nonlinear wireless networked control systems. The objective is to ensure the stability of the closed-loop system, in a stochastic sense, together with given control performance, while minimizing the average power used for communications. The controller is designed by emulation, i.e., ignoring the network, and the transmission power is given by threshold policies. These policies involve waiting a given amount of time since the last successful transmission instant, as well as requiring that the measured wireless channel gain is above a given threshold, before attempting a new transmission. Two power control laws are investigated: 1) a constant power and 2) a power level inversely proportional to the channel gain. We explain how to select the waiting time, the channel threshold, and the power level to minimize the induced average communication power while ensuring the desired control objectives.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Inference in Opinion Dynamics Under Social Pressure
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Authors: Ali Jadbabaie;Anuran Makur;Elchanan Mossel;Rabih Salhab;
Pages: 3377 - 3392
Abstract: We introduce a new opinion dynamics model where a group of agents holds two kinds of opinions: inherent and declared. Each agent’s inherent opinion is fixed and unobservable by the other agents. At each time step, agents broadcast their declared opinions on a social network, which are governed by the agents’ inherent opinions and social pressure. In particular, we assume that agents may declare opinions that are not aligned with their inherent opinions to conform with their neighbors. This raises the natural question: Can we estimate the agents’ inherent opinions from observations of declared opinions' For example, agents’ inherent opinions may represent their true political alliances (Democrat or Republican), while their declared opinions may model the political inclinations of tweets on social media. In this context, we may seek to predict the election results by observing voters’ tweets, which do not necessarily reflect their political support due to social pressure. We analyze this question in the special case where the underlying social network is a complete graph. We prove that, as long as the population does not include large majorities, estimation of aggregate and individual inherent opinions is possible. On the other hand, large majorities force minorities to lie over time, which makes asymptotic estimation impossible.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Anytime Proximity Moving Horizon Estimation: Stability and Regret
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Authors: Meriem Gharbi;Bahman Gharesifard;Christian Ebenbauer;
Pages: 3393 - 3408
Abstract: In this article, we address the efficient implementation of moving horizon state estimation of constrained discrete-time linear systems. We propose a novel iteration scheme that employs a proximity-based formulation of the underlying optimization algorithm and reduces computational effort by performing only a limited number of optimization iterations each time a new measurement is received. We outline conditions under which global exponential stability of the underlying estimation errors is ensured. Performance guarantees of the iteration scheme in terms of regret upper bounds are also established. A combined result shows that both exponential stability and a sublinear regret, which can be rendered smaller by increasing the number of optimization iterations, can be guaranteed. The stability and regret results of the proposed estimator are showcased through numerical simulations.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Reactive Symbolic Planning and Control in Dynamic Adversarial Environments
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Authors: Laya Shamgah;Tadewos G. Tadewos;Abdullah Al Redwan Newaz;Ali Karimoddini;Albert C. Esterline;
Pages: 3409 - 3424
Abstract: Satisfying both safety and reachability requirements in dynamic adversarial environments is very challenging, particularly when little or no information about the dynamics and intentions of the adversarial objects is available. Therefore, this article addresses the problem of path planning and control of autonomous vehicles in a dynamic adversarial reach–avoid scenario with two noncooperative vehicles and their competitive objectives: 1) “reaching a target and avoiding the other vehicle” for one of them, called attacker, and 2) “protecting the target and capturing the opponent vehicle” for the other one, called defender. In the proposed solution, first, a discrete version of the problem is formulated and solved using linear temporal logic, temporal games, and $mu$-calculus to construct winning discrete strategies that guarantee safety and reachability. A comprehensive discussion on the existence, correctness, and complexity analysis of the solution is also provided. Finally, a novel correct-by-design hybrid controller is designed to generate smooth control signals that preserve the satisfaction of safety and reachability.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Synchronization of Frequency-Modulated Multiagent Systems
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Authors: Zhiyong Chen;
Pages: 3425 - 3439
Abstract: Oscillation synchronization is a widely observed phenomenon in natural systems through frequency-modulated signals, especially in biological neural networks. Frequency modulation is also one of the most widely used technologies in engineering. However, due to technical difficulties, oscillations have always been simplified as unmodulated sinusoidal-like waves in studying the synchronization mechanism in the bulky literature. The application of mathematical principles, especially systems and control theories, is lacking for frequency modulated multiagent systems (MASs). This article aims to introduce a new formulation of the synchronization of frequency-modulated MASs. It develops new tools to solve the synchronization problem by addressing the following three issues: frequency observation in nonlinear frequency-modulated oscillators subject to network influence, frequency consensus via network interaction subject to observation error, and a well-placed small-gain condition among them. The architecture of this article consists of a novel problem formulation, rigorous theoretical development, and numerical verification.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Ellipsotopes: Uniting Ellipsoids and Zonotopes for Reachability Analysis
and Fault Detection-
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Authors: Shreyas Kousik;Adam Dai;Grace Xingxin Gao;
Pages: 3440 - 3452
Abstract: Ellipsoids are a common representation for reachability analysis, because they can be transformed efficiently under affine maps, and they allow conservative approximation of Minkowski sums, which let one incorporate uncertainty and linearization error in a dynamical system by expanding the size of the reachable set. Zonotopes, a type of symmetric, convex polytope, are similarly frequently used, because they allow efficient numerical implementations of affine maps and exact Minkowski sums. Both of these representations also enable efficient, convex collision detection for fault detection or formal verification tasks, wherein one checks if the reachable set of a system collides (i.e., intersects) with an unsafe set. However, both representations often result in conservative representations for reachable sets of arbitrary systems, and neither is closed under intersection. Recently, representations, such as constrained zonotopes and constrained polynomial zonotopes, have been shown to overcome some of these conservativeness challenges, and are closed under intersection. However, constrained zonotopes cannot represent shapes with smooth boundaries, such as ellipsoids, and constrained polynomial zonotopes can require solving a nonconvex program for collision checking or fault detection. This article introduces ellipsotopes, a set representation that is closed under affine maps, Minkowski sums, and intersections. Ellipsotopes combine the advantages of ellipsoids and zonotopes while ensuring convex collision checking. The utility of this representation is demonstrated on several examples.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Synthesis of the Supremal Covert Attacker Against Unknown Supervisors by
Using Observations-
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Authors: Ruochen Tai;Liyong Lin;Yuting Zhu;Rong Su;
Pages: 3453 - 3468
Abstract: In this article, we consider the problem of synthesizing the supremal covert damage-reachable attacker, in the setup where the model of the supervisor is unknown to the adversary but the adversary has recorded a (prefix-closed) finite set of observations of the runs of the closed-loop system. The synthesized attacker needs to ensure both the damage-reachability and the covertness against all the supervisors, which are consistent with the given set of observations. There is a gap between the de facto supremality, assuming the model of the supervisor is known, and the supremality that can be attained with a limited knowledge of the model of the supervisor, from the adversary's point of view. We consider the setup where the attacker can exercise sensor replacement/deletion attacks and actuator enablement/disablement attacks. The solution methodology proposed in this article is to reduce the synthesis of the supremal covert damage-reachable attacker, given the model of the plant and the finite set of observations, to the synthesis of the supremal safe supervisor for certain transformed plant, which shows the decidability of the observation-assisted covert attacker synthesis problem. The effectiveness of our approach is illustrated on a water tank example adapted from the literature.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Nonparameteric Event-Triggered Learning With Applications to Adaptive
Model Predictive Control-
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Authors: Kaikai Zheng;Dawei Shi;Yang Shi;Junzheng Wang;
Pages: 3469 - 3484
Abstract: In this article, an event-triggered online learning problem for Lipschitz continuous systems with nonlinear model mismatch is considered, with the aim of building a data-efficient nonparameteric estimation approach for learning-based control. The system considered is composed of known linear dynamics and unknown nonlinearity, and the main focus of this work includes the design and analysis of event-triggered learning mechanisms, and the application of the learning method to adaptive model predictive control (MPC). First, a sample grid-based event-triggering mechanism and a prediction uncertainty-based event-triggering mechanisms are designed on the basis of the lazily adapted constant kinky inference framework. Then, the properties of the designed event-triggered learning methods are analyzed, and it is proved that the proposed approach provides error-bounded predictions with limited computational complexity. Third, a tube-based adaptive MPC design approach is developed utilizing the proposed event-triggered learning approach, and the closed-loop stability of the adaptive MPC is analyzed and proved based on the properties of the event-triggered learning algorithms. Implementation issues are discussed, and the effectiveness of the results is illustrated by numerical examples and comparative simulations.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Solid Boundary Output Feedback Control of the Stefan Problem: The Enthalpy
Approach-
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Authors: Bryan Petrus;Zhelin Chen;Hamza El-Kebir;Joseph Bentsman;Brian G. Thomas;
Pages: 3485 - 3500
Abstract: By taking enthalpy—an internal energy of a diffusion-type system—as the system state and expressing it in terms of the temperature profile and the phase-change interface position, the output feedback boundary control laws for a fundamentally nonlinear single-phase one-dimensional (1-D) PDE process model with moving boundaries, referred to as the Stefan problem, are developed. The control objective is tracking of the spatiotemporal temperature and temporal interface (solidification front) trajectory generated by the reference model. The external boundaries through which temperature sensing and heat flux actuation are performed are assumed to be solid. First, a full-state single-sided tracking feedback controller is presented. Then, an observer is proposed and proven to provide a stable full-state reconstruction. Finally, by combining a full-state controller with an observer, the output feedback trajectory tracking control laws are presented and the closed-loop convergence of the temperature and the interface errors proven for the single-sided and the two-sided Stefan problems. Simulation shows the exponential-like trajectory convergence attained by the implementable smooth bounded control signals.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Equivariant Filter (EqF)
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Authors: Pieter van Goor;Tarek Hamel;Robert Mahony;
Pages: 3501 - 3512
Abstract: The kinematics of many systems encountered in robotics, mechatronics, and avionics are naturally posed on homogeneous spaces; i.e., their state lies in a smooth manifold equipped with a transitive Lie group symmetry. This article proposes a novel filter, the equivariant filter (EqF), by posing the observer state on the symmetry group, linearizing global error dynamics derived from the equivariance of the system, and applying EKF design principles. We show that equivariance of the system output can be exploited to reduce linearization error and improve filter performance. Simulation experiments of an example application show that the EqF significantly outperforms the EKF and that the reduced linearization error leads to a clear improvement in performance.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Identification of Diffusively Coupled Linear Networks Through Structured
Polynomial Models-
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Authors: E. M. M. Kivits;Paul M. J. Van den Hof;
Pages: 3513 - 3528
Abstract: Physical dynamic networks most commonly consist of interconnections of physical components that can be described by diffusive couplings. These diffusive couplings imply that the cause-effect relationships in the interconnections are symmetric, and therefore, physical dynamic networks can be represented by undirected graphs. This article shows how prediction error identification methods developed for linear time-invariant systems in polynomial form can be configured to consistently identify the parameters and the interconnection structure of diffusively coupled networks. Furthermore, a multistep least squares convex optimization algorithm is developed to solve the nonconvex optimization problem that results from the identification method.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Maximally Permissive Supervisors for Nonblocking Similarity Control of
Nondeterministic Discrete-Event Systems-
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Authors: Jinglun Li;Shigemasa Takai;
Pages: 3529 - 3544
Abstract: This article investigates a nonblocking similarity control problem for nondeterministic discrete-event systems, which is a problem of synthesizing a nonblocking supervisor such that the supervised system is simulated by the given specification. In this article, the state of the system is not required to be observable, and the event occurrence is allowed to be partially observed. We propose an algorithm that computes a nonblocking supervisor from a possibly blocking one by iteratively removing certain states. Then, we identify two key properties of input supervisors, named state-unmergedness and strong maximal permissiveness, which together guarantee the maximal permissiveness of output nonblocking supervisors. The algorithm is applied to a supervisor with these two properties to obtain a maximally permissive nonblocking supervisor. In addition, we show that a nonblocking supervisor is generated by the algorithm if and only if there exists a solution to the nonblocking similarity control problem.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Receding Horizon Control With Online Barrier Function Design Under Signal
Temporal Logic Specifications-
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Authors: Maria Charitidou;Dimos V. Dimarogonas;
Pages: 3545 - 3556
Abstract: Signal temporal logic (STL) has been found to be an expressive language for describing complex, time-constrained tasks in several robotic applications. Existing methods encode such specifications by either using integer constraints or by employing set invariance techniques. While in the first case this results in a mixed integer linear program (MILP), control problems, in the latter case, designer-specific choices may induce conservatism in the robot's performance and the satisfaction of the task. In this article, a continuous-time receding horizon control scheme (RHS) is proposed that exploits the tradeoff between task satisfaction and performance costs such as actuation and state costs, traditionally considered in RHS schemes. The satisfaction of the STL tasks is encoded using time-varying control barrier functions that are designed online, thus avoiding the integer expressions that are often used in literature. The recursive feasibility of the proposed scheme is guaranteed by the satisfaction of a time-varying terminal constraint that ensures the satisfaction of the task with predetermined robustness. The effectiveness of the method is illustrated in a multirobot simulation scenario.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Smoother Entropy for Active State Trajectory Estimation and Obfuscation in
POMDPs-
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Authors: Timothy L. Molloy;Girish N. Nair;
Pages: 3557 - 3572
Abstract: In this article, we study the problem of controlling a partially observed Markov decision process (POMDP) to either aid or hinder the estimation of its state trajectory. We encode the estimation objectives via the smoother entropy, which is the conditional entropy of the state trajectory given measurements and controls. Consideration of the smoother entropy contrasts with previous approaches that instead resort to marginal (or instantaneous) state entropies due to tractability concerns. By establishing novel expressions for the smoother entropy in terms of the POMDP belief state, we show that both the problems of minimizing and maximizing the smoother entropy in POMDPs can surprisingly be reformulated as belief-state Markov decision processes with concave cost and value functions. The significance of these reformulations is that they render the smoother entropy a tractable optimization objective, with structural properties amenable to the use of standard POMDP solution techniques for both active estimation and obfuscation. Simulations illustrate that optimization of the smoother entropy leads to superior trajectory estimation and obfuscation compared to alternative approaches.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
-
- Computation of Input Disturbance Sets for Constrained Output Reachability
-
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Authors: Sampath Kumar Mulagaleti;Alberto Bemporad;Mario Zanon;
Pages: 3573 - 3580
Abstract: Linear models with additive unknown-but-bounded input disturbances are extensively used to model uncertainty in robust control system design. Typically, the disturbance set is either assumed to be known a priori or estimated from data through set-membership identification. However, the problem of computing a suitable input disturbance set in case the set of possible output values is assigned a priori has received relatively little attention. This problem arises in many contexts, such as in supervisory control, actuator design, decentralized control, and others. In this article, we propose a method to compute input disturbance sets (and the corresponding set of states) such that the resulting set of outputs matches as closely as possible a given set of outputs, while additionally satisfying strict (inner or outer) inclusion constraints. We formulate the problem as an optimization problem by relying on the concept of robust invariance. The effectiveness of the approach is demonstrated in numerical examples that illustrate how to solve safe reference set and input constraint set computation problems.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- The Model Matching Problem for Max-Plus Linear Systems: A Geometric
Approach-
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Authors: Davide Animobono;David Scaradozzi;Elena Zattoni;Anna Maria Perdon;Giuseppe Conte;
Pages: 3581 - 3587
Abstract: Linear systems over the max-plus algebra provide a suitable formalism to model discrete-event systems where synchronization, without competition, is involved. In this article, we consider a formulation of the model matching problem for systems of such class, in which the output of a given system, called the plant, is forced, by a suitable input, to track exactly that of a given model. A necessary and sufficient condition for its solvability is obtained by making a suitable use of geometric methods in the framework of systems over the max-plus algebra.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Rendezvous Control Design for the Generalized Cucker–Smale Model on
Riemannian Manifolds-
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Authors: Xiaoyu Li;Yuhu Wu;Jiandong Zhu;
Pages: 3588 - 3595
Abstract: In this article, we consider a rendezvous problem for the generalized Cucker–Smale model, which is a double-integrator multiagent system, on complete Riemannian manifolds. With the help of the covariant derivative, parallel transport, and logarithm map on the Riemannian manifold, we design a rendezvous feedback law that enables all agents to converge at a given target in the Riemannian manifold, under some a priori conditions. Furthermore, we consider three concrete complete Riemannian manifolds, such as the unit circle, unit sphere, and hyperboloid, and present the explicit feedback laws for rendezvous on them by calculating the corresponding covariant derivatives, parallel transports, and logarithm maps. Meanwhile, numerical examples are given for the manifolds as mentioned above to verify and illustrate the theoretical results.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
-
- $H_{infty+}$
+Filtering+via+a+High-Rate+Network+With+the+FlexRay+Protocol&rft.title=IEEE+Transactions+on+Automatic+Control&rft.issn=0018-9286&rft.date=2023&rft.volume=68&rft.spage=3596&rft.epage=3603&rft.aulast=Wei;&rft.aufirst=Shuai&rft.au=Shuai+Liu;Zidong+Wang;Licheng+Wang;Guoliang+Wei;">Finite-Horizon $H_{infty }$ Filtering via a High-Rate Network With the
FlexRay Protocol-
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Authors: Shuai Liu;Zidong Wang;Licheng Wang;Guoliang Wei;
Pages: 3596 - 3603
Abstract: This article addresses the finite-horizon $H_{infty }$ filtering problem for a class of discrete time-varying nonlinear systems over high-rate networks whose signal exchanges are scheduled by the FlexRay protocol. To improve the efficiency of the data transmission, a high-rate network is deployed for the measurement signals to be broadcasted from the sensors to the filter. The FlexRay protocol is embedded into the high-rate network to orchestrate the transmission rule of the signals with different attributes, thereby further enhancing the transmission flexibility. On the basis of the round-robin and try-once-discard protocols, a novel FlexRay-protocol-based measurement model is proposed by using certain data holding strategies. A sufficient condition is provided to guarantee that the filtering error dynamics meets the desirable disturbance attenuation level against exogenous disturbances over a finite horizon. The parameterized form of the filter gain is attained by the solutions to some matrix inequalities. Numerical simulation is carried out to substantiate the proposed filter design algorithm.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Disturbance Observer-Based Boundary Control for an Antistable Stochastic
Heat Equation With Unknown Disturbance-
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Authors: Ze-Hao Wu;Hua-Cheng Zhou;Feiqi Deng;Bao-Zhu Guo;
Pages: 3604 - 3611
Abstract: In this article, a novel control strategy namely disturbance observer-based control is first applied to stabilization and disturbance rejection for an antistable stochastic heat equation with Neumann boundary actuation and unknown boundary external disturbance generated by an exogenous system. A disturbance observer-based boundary control is designed based on the backstepping approach and estimation/cancellation strategy, where the unknown disturbance is estimated in real time by a disturbance observer and rejected in the closed loop, while the in-domain multiplicative noise whose intensity is within a known finite interval is attenuated. It is shown that the resulting closed-loop system is exponentially stable in the sense of both mean square and almost surely. A numerical example is demonstrated to validate the effectiveness of the proposed control approach.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
-
- Strong Left Inversion of Linear Systems and Input Reconstruction
-
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Authors: Michael Di Loreto;Damien Eberard;
Pages: 3612 - 3617
Abstract: Left inversion of linear time-invariant systems aims at identifying the input acting on a system, for the zero initial state, from partial information on the input and the state. In the present contribution, we propose to generalize such left inversion for linear systems in various directions that take arbitrary initial state into consideration to address both exact and asymptotic input reconstructions. Necessary and sufficient algebraic conditions are given to achieve such strong left inversion properties. Complete characterizations of introduced concepts in terms of system zeros are provided. Relationship between inversion and input reconstruction is therefore investigated, with emphasis on causal realization. Conditions for input observer existence are proposed, and a constructive causal design for an asymptotically convergent input observer is presented.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
-
- Approximate Optimal Trajectory Tracking With Sparse Bellman Error
Extrapolation-
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Authors: Max L. Greene;Patryk Deptula;Scott Nivison;Warren E. Dixon;
Pages: 3618 - 3624
Abstract: This article provides an approximate online adaptive solution to the infinite-horizon optimal tracking problem for control-affine continuous-time nonlinear systems with uncertain drift dynamics. A model-based approximate dynamic programming (ADP) approach, which is facilitated using a concurrent learning-based system identifier, approximates the optimal value function. To reduce the computational complexity of model-based ADP, the state space is segmented into user-defined segments (i.e., regions). Off-policy trajectories are selected within each segment to facilitate learning of the value function weight estimates; this process is called Bellman error (BE) extrapolation. Within certain segments of the state space, sparse neural networks are used to reduce the computational expense of BE extrapolation. Discontinuities occur in the weight update laws since different groupings of extrapolated BE trajectories are active in certain regions of the state space. A Lyapunov-like stability analysis is presented to prove boundedness of the overall system in the presence of discontinuities. Simulation results are included to demonstrate the performance and validity of the developed method. The simulation results demonstrate that using the sparse, switched BE extrapolation method developed in this article reduces the computation time by 85.6% when compared to the traditional BE extrapolation method.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
-
- Adaptive Event-Triggered Control for Nonlinear Systems With Asymmetric
State Constraints: A Prescribed-Time Approach-
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Authors: Ziwei Wang;Hak-Keung Lam;Yao Guo;Bo Xiao;Yanan Li;Xiaojie Su;Eric M. Yeatman;Etienne Burdet;
Pages: 3625 - 3632
Abstract: Finite/fixed-time control yields a promising tool to optimize a system's settling time, but lacks the ability to separately define the settling time and the convergence domain (known as practically prescribed-time stability, PPTS). We provide a sufficient condition for PPTS based on a new piecewise exponential function, which decouples the settling time and convergence domain into separately user-defined parameters. We propose an adaptive event-triggered prescribed-time control scheme for nonlinear systems with asymmetric output constraints, using an exponential-type barrier Lyapunov function. We show that this PPTS control scheme can guarantee tracking error convergence performance, while restricting the output state according to the prescribed asymmetric constraints. Compared with traditional finite/fixed-time control, the proposed methodology yields separately user-defined settling time and convergence domain without the prior information on disturbance. Moreover, asymmetric state constraints can be handled in the control structure through bias state transformation, which offers an intuitive analysis technique for general constraint issues. Simulation and experiment results on a heterogeneous teleoperation system demonstrate the merits of the proposed control scheme.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
-
- Distributed Gradient Tracking for Unbalanced Optimization With Different
Constraint Sets-
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Authors: Songsong Cheng;Shu Liang;Yuan Fan;Yiguang Hong;
Pages: 3633 - 3640
Abstract: Gradient tracking methods have become popular for distributed optimization in recent years, partially because they achieve linear convergence using only a constant step-size for strongly convex optimization. In this article, we construct a counterexample on constrained optimization to show that direct extension of gradient tracking by using projections cannot guarantee the correctness. Then, we propose projected gradient tracking algorithms with diminishing step-sizes rather than a constant one for distributed strongly convex optimization with different constraint sets and unbalanced graphs. Our basic algorithm can achieve $O(ln T/{T})$ convergence rate. Moreover, we design an epoch iteration scheme and improve the convergence rate as $O(1/{T})$.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
-
- Value of Information in Feedback Control: Global Optimality
-
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Authors: Touraj Soleymani;John S. Baras;Sandra Hirche;Karl H. Johansson;
Pages: 3641 - 3647
Abstract: The rate-regulation tradeoff, defined between two objective functions, one penalizing the packet rate and one the regulation cost, can express the fundamental performance bound of networked control systems. However, the characterization of the set of globally optimal solutions in this tradeoff for multidimensional Gauss–Markov processes has been an open problem. In this article, we characterize a policy profile that belongs to this set without imposing any restrictions on the information structure or the policy structure. We prove that such a policy profile consists of a symmetric threshold triggering policy based on the value of information and a certainty-equivalent control policy based on a non-Gaussian linear estimator. These policies are deterministic and can be designed separately. Besides, we provide a global optimality analysis for the value of information $mathbf{{VoI}}_{{boldsymbol{k}}}$, a semantic metric that emerges from the rate-regulation tradeoff as the difference between the benefit and the cost of a data packet. We prove that it is globally optimal that a data packet containing sensory information at time ${boldsymbol{k}}$ be transmitted to the controller only if $mathbf{{VoI}}_{{boldsymbol{k}}}$ becomes nonnegative. These findings have important implications in the areas of communication and control.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Nonlinear PI“D”-Type Control of Flexible Joint Robots by Using Motor
Position Measurements Is Globally Asymptotically Stable-
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Authors: Jerónimo Moyrón;Javier Moreno–Valenzuela;Jesús Sandoval;
Pages: 3648 - 3655
Abstract: An important subject that arises in the position control of robot manipulators is the local or global asymptotic stability of the closed-loop system equilibrium point, especially when an integral action is added to the control loop. For rigid joint robot manipulators, global nonlinear proportional-integral-derivative (PID) controllers have been introduced few years ago. However, for the case of flexible joint robot manipulators, the design and analysis of such nonlinear PID laws is much more challenging. Only local asymptotic stability results have been reported. Thus, a novel global regulator for flexible joint robots is presented in this document. The proposed controller considers a nonlinear integral action and it requires only motor position measurements because an estimator subsystem is used to replace the motor velocity measurements. In other words, a nonlinear proportional–integral–“derivative” (PI“D”)-type controller is introduced. According to the closed-loop system analysis, conditions on the controller gains are established. Thus, the global asymptotic stability is concluded. Finally, experimental results on a two degrees-of-freedom serial flexible joint robot are shown and discussed.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
-
- Decentralized Circular Formation Control of Nonholonomic Mobile Robots
Under a Directed Sensor Graph-
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Authors: Xiao Yu;Rong Su;
Pages: 3656 - 3663
Abstract: This article investigates the circular formation control problem of multiple unicycle-type mobile robots under a directed sensor graph. The topology of the sensor graph among all robots is described by a directed graph containing a spanning tree, and the node denoting the center is only required to be globally reachable in the sensor graph. A dynamic control law is developed such that the multi-robot systems with speed constraint are able to globally converge to a circular formation prescribed by a stationary center, a radius, and a spacing configuration. Remarkably, the proposed control law does not rely on any communication, and only requires each robot to use local measurements with respect to its neighbors based on its local coordinate frame, which makes it feasible to implement this control law in a decentralized manner. The global asymptotic stability of the closed-loop multi-robot system is established by small-gain theorem of which the small-gain condition is guaranteed by a low gain parameter in the designed observer.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
-
- Prescribed-Time Tracking Control of MIMO Nonlinear Systems With
Nonvanishing Uncertainties-
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Authors: Hefu Ye;Yongduan Song;
Pages: 3664 - 3671
Abstract: It is highly desirable yet challenging to achieve zero-error tracking within a given short time period for uncertain multi-input–multi-output (MIMO) nonlinear systems. Previous results are primarily state-regulation oriented and are valid only for single-input single-output linear systems or nonlinear systems in normal-form. This note presents a tracking control solution for high-order MIMO nonlinear systems in strict-feedback-like form. The proposed control is able to achieve precise tracking within the prescribed time irrespective of initial conditions in the presence of mismatched uncertainties and nonvanishing disturbances.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
-
- An Online Kullback–Leibler Divergence-Based Stealthy Attack Against
Cyber-Physical Systems-
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Authors: Qirui Zhang;Kun Liu;André M. H. Teixeira;Yuzhe Li;Senchun Chai;Yuanqing Xia;
Pages: 3672 - 3679
Abstract: This article investigates the design of online stealthy attacks with the aim of moving the system's state to the desired target. Different from the design of offline attacks, which is only based on the system's model, to design the online attack, the attacker also estimates the system's state with the intercepted data at each instant and computes the optimal attack accordingly. To ensure stealthiness, the Kullback–Leibler divergence between the innovations with and without attacks at each instant should be smaller than a threshold. We show that the attacker should solve a convex optimization problem at each instant to compute the mean and covariance of the attack. The feasibility of the attack policy is also discussed. Furthermore, for the strictly stealthy case with zero threshold, the analytical expression of the unique optimal attack is given. Finally, a numerical example of the longitudinal flight control system is adopted to illustrate the effectiveness of the proposed attack.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
-
- Designing Distributed Impulsive Controller for Networked Singularly
Perturbed Systems-
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Authors: Wangli He;Kun Liang;Feng Qian;Guanrong Chen;
Pages: 3680 - 3686
Abstract: This article develops a novel synthesis approach for the synchronization of a network of singularly perturbed systems (SPSs) with a small singular perturbation parameter $varepsilon$ via distributed impulsive control. First, a decoupling method in the setting of directed networks is employed to decompose networked SPSs related to complex eigenvalues of the Laplacian matrix. Then, based on an improved piecewise continuous Lyapunov function, an $varepsilon$-dependent synchronization criterion is established. The relationship among the impulse interval, the impulse gain matrix, and $varepsilon$ is revealed. By employing the newly obtained synchronization criterion, some sufficient conditions on the existence of an $varepsilon$-dependent impulse gain matrix are derived. Finally, an example is simulated to verify the effectiveness of the theoretical results.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
-
- To Filter or Not to Filter' Impact on Stability of Delay-Difference and
Neutral Equations With Multiple Delays-
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Authors: Wim Michiels;
Pages: 3687 - 3693
Abstract: For control systems where the closed-loop system description is governed by linear delay-differential equations of neutral type, it is known that stability may be fragile, in the sense of sensitive to infinitesimal perturbations to parameters in the system model or arbitrarily small errors in the implementation of the controller. A natural approach to resolve this problem of ill-posedness and to break down the underlying instability mechanisms, rooted in characteristic roots moving from the left plane to the right one via the point at infinity, consists of including a low-pass filter in the control loop, provided the inclusion preserves stability. Independently of the particular control problem, the addition of a low-pass filter essentially boils down to a “regularization” of delay-difference equations and delay equations of neutral type in terms of parametrized delay equations of retarded type, where the parameter can be interpreted as the inverse of the filter's cut-off frequency. In this article, the stability properties of these parametrized delay equations are analyzed in a general, multidelay setting, with focus on the transition to the original delay-difference or neutral equations. It is illustrated that the spectral abscissa may not be continuous at the transition, which may impact stability. Hence, conditions for preservation of stability in terms of a robustified stability indicator called filtered spectral abscissa are presented, for which mathematical characterizations and a computationally tractable expression are provided. The application of a proportional-derivative (PD) controller to a time-delay system with relative degree one is used to motivate the structure of the equations studied throughout this article, and to explicate the implications of the presented results on control design, discussed in the last section.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
-
- Discrete-Time Switching Systems as Difference Inclusions: Deducing
Converse Lyapunov Results for the Former From Those for the Latter-
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Authors: Rafal Goebel;
Pages: 3694 - 3697
Abstract: Nonlinear discrete-time switching systems under mode-dependent switching and dwell-time constraints are modeled by difference inclusions. Novel proofs of converse Lyapunov results are obtained for the switching systems as consequences of a converse Lyapunov result for a difference inclusion.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Nonminimality of the Realizations and Possessing State Matrices With
Integer Elements in Linear Discrete-Time Controllers-
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Authors: Mohammad Saleh Tavazoei;
Pages: 3698 - 3703
Abstract: It is known that discrete-time controllers, whose state matrices have no noninteger element, are beneficial in homomorphic-based encrypted control systems. Nevertheless, it has been recently shown that possessing state matrices with integer elements usually yields unstable discrete-time controllers. In this article, we investigate the problem from a nonminimality perspective. It is shown that nonminimal realizations, in comparison to minimal ones, can theoretically provide a wider framework to obtain controllers having state matrices with integer elements. However, in the case of dealing with bounded-input bounded-output (BIBO) stable controllers, this framework cannot preserve internal stability. But, benefiting from the introduced framework, a class of unstable controllers is introduced, which can be realized by state-space forms having state matrices with integer elements. Numerical examples are presented to verify the usefulness of the introduced framework in the realization of unstable controllers with integer state matrices.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
-
- Optimal Tracking for Periodic Linear Hybrid Systems
-
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Authors: Corrado Possieri;
Pages: 3704 - 3711
Abstract: This article provides a comprehensive characterization of the quadratic optimal tracking problem for hybrid systems with linear dynamics undergoing periodic time-driven jumps. Solutions to such a problem are proposed for both the finite horizon and the periodic cases. Furthermore, it is shown that if the reference signals are not known in advance, then the best control strategy to deal with the worst case reference signals is to simply minimize the (scaled) outputs. Finally, the derived optimal solutions are used to solve two relevant control problems, which are the reconstruction of vector fields from noisy measurements of the corresponding flows and the estimation of the time derivatives of a periodic, sampled, and noisy signal.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Concurrent Receding Horizon Control and Estimation Against Stealthy
Attacks-
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Authors: Filippos Fotiadis;Kyriakos. G. Vamvoudakis;
Pages: 3712 - 3719
Abstract: In this article, we consider a game-theoretic framework for cyber-physical systems, where a defender develops a mitigation strategy against an intelligent attacker who exploits the system's uncertainty to remain undetected. The goal of the defender is to optimize a performance cost constructed specifically to account for robustness against stealthy attacks so that the system is regulated. Conversely, the goal of the attacker is to disrupt the system's performance by leveraging its significant information advantage against the defender. Both players implement their policies in a moving horizon fashion, according to the principles of receding horizon control. However, because the defender has no access to the full state of the system, it concurrently employs receding horizon estimation to overcome this limitation. Rigorous theoretical analysis shows that such a concurrent policy can guarantee closed-loop boundedness, despite the stealthy attacks and the information disadvantage. Simulations verify and clarify these findings.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
-
- On Optimizing the Conditional Value-at-Risk of a Maximum Cost for
Risk-Averse Safety Analysis-
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Authors: Margaret P. Chapman;Michael Fauß;Kevin M. Smith;
Pages: 3720 - 3727
Abstract: The popularity of Conditional Value-at-Risk (CVaR), a risk functional from finance, has been growing in the control systems community due to its intuitive interpretation and axiomatic foundation. We consider a nonstandard optimal control problem in which the goal is to minimize the CVaR of a maximum random cost subject to a Borel-space Markov decision process. The objective represents the maximum departure from a desired operating region averaged over a given fraction of the worst cases. This problem provides a safety criterion for a stochastic system that is informed by both the probability and severity of the potential consequences of the system’s behavior. In contrast, existing safety analysis frameworks apply stagewise risk constraints or assess the probability of constraint violation without quantifying the potential severity of the violation. To the best of our knowledge, the problem of interest has not been solved. To solve the problem, we propose and study a family of stochastic dynamic programs on an augmented state space. We prove that the optimal CVaR of a maximum random cost enjoys an equivalent representation in terms of the solutions to these dynamic programs under appropriate assumptions. For each dynamic program, we show the existence of an optimal policy that depends on the dynamics of an augmented state under the assumptions. In a numerical example, we illustrate how our safety analysis framework is useful for assessing the severity of combined sewer overflows under precipitation uncertainty.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- On 1-D PDE-Based Cardiovascular Flow Bottleneck Modeling and Analysis: A
Vehicular Traffic Flow-Inspired Approach-
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Authors: Nikolaos Bekiaris-Liberis;
Pages: 3728 - 3735
Abstract: We illustrate the potential of partial differential equation (PDE)-based traffic flow control in cardiovascular flow analysis, monitoring, and control, presenting a PDE-based control-oriented formulation, for one-dimensional (1-D) blood flow dynamics in the presence of stenosis. This is achieved adopting an approach for modeling and analysis that relies on the potential correspondence of 1-D blood flow dynamics in the presence of stenosis, with 1-D traffic flow dynamics in the presence of bottleneck. We reveal such correspondence in relation to the respective (for the two flow types), speed dynamics and a (consistent with them) fundamental diagram-based reduction; bottleneck dynamic effects description and resulting boundary conditions; and free-flow/congested regimes characterization.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Distributed Online Aggregative Optimization for Dynamic Multirobot
Coordination-
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Authors: Guido Carnevale;Andrea Camisa;Giuseppe Notarstefano;
Pages: 3736 - 3743
Abstract: This article focuses on an online version of the emerging distributed constrained aggregative optimization framework, which is particularly suited for applications arising in cooperative robotics. Agents in a network want to minimize the sum of local cost functions, each one depending both on a local optimization variable, subject to a local constraint, and on an aggregated version of all the variables (e.g., the mean). We focus on a challenging online scenario in which the cost, the aggregation functions, and the constraints can all change over time, thus enlarging the class of captured applications. Inspired by an existing scheme, we propose a distributed algorithm with constant step size, named projected aggregative tracking, to solve the online optimization problem. We prove that the dynamic regret is bounded by a constant term and a term related to time variations. Moreover, in the static case (i.e., with constant cost and constraints), the solution estimates are proved to converge with a linear rate to the optimal solution. Finally, numerical examples show the efficacy of the proposed approach on a robotic surveillance scenario.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Abstracting the Traffic of Nonlinear Event-Triggered Control Systems
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Authors: Giannis Delimpaltadakis;Manuel Mazo;
Pages: 3744 - 3751
Abstract: Scheduling communication traffic in networks of event-triggered control (ETC) systems is challenging, as their sampling times are unknown, hindering application of ETC in networks. In previous work, finite-state abstractions were created, capturing the sampling behavior of linear time-invariant (LTI) ETC systems with quadratic triggering functions. Offering an infinite-horizon look to ETC systems’ sampling patterns, such abstractions can be used for scheduling of ETC traffic. Here, we significantly extend this framework, by abstracting perturbed uncertain nonlinear ETC systems with general triggering functions. To construct an ETC system’s abstraction: 1) the state space is partitioned into regions; 2) for each region, an interval is determined, containing all intersampling times of points in the region; and 3) the abstraction’s transitions are determined through reachability analysis. To determine intervals and transitions, we devise algorithms based on reachability analysis. For partitioning, we propose an approach based on isochronous manifolds, resulting into tighter intervals and providing control over them, thus containing the abstraction’s nondeterminism. Simulations showcase our developments.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Improving the Feasibility of Moment-Based Safety Analysis for Stochastic
Dynamics-
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Authors: Peter Du;Katherine Driggs-Campbell;Roy Dong;
Pages: 3752 - 3759
Abstract: Given a dynamical system modeled via stochastic differential equations (SDEs), we evaluate the safety of the system through its exit-time moments. Using appropriate semidefinite positive matrix constraints, an SDP moment-based approach can be used to compute moments of the exit time. However, the approach is impeded when analyzing higher dimensional physical systems as the dynamics are limited to polynomials. Computational scalability is also poor as the dimensionality of the state grows, largely due to the combinatorial growth of the optimization program. We propose methods to make feasible the safety analysis of higher dimensional physical systems. The restriction to polynomial dynamics is lifted by using state augmentation, which allows one to generate the optimization for a broader class of nonlinear stochastic systems. We then reformulate the constraints to mitigate the computational limitations associated with an increase in state dimensionality. We employ our methods on two example processes to characterize their safety via exit times and show the ability to handle multidimensional systems that were previously unsupported by the existing SDP method of moments.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Adaptive Tracking Control With Global Performance for Output-Constrained
MIMO Nonlinear Systems-
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Authors: Linghuan Kong;Wei He;Zhijie Liu;Xinbo Yu;Carlos Silvestre;
Pages: 3760 - 3767
Abstract: In this article, a novel adaptive tracking control technique is developed for multiple-input-multiple-output nonlinear systems with model uncertainty and under output constraints occurring in a limited time interval (OCOLT). The OCOLT, which is a type of constraints occurring sometime after (rather than the beginning of) system operation and with limited duration, can be found in many practical systems and has not been effectively addressed in the literature until now. By designing a new shift function and with the aid of barrier functions, the constrained system is transformed into an unconstrained one. A new disturbance observer is then designed to estimate unknown disturbances. The resultant control method is able to not only address the OCOLT, but also deal with the constraint-free output case and the infinite-time constrained one (i.e., constraints existing for all $tgeq 0$) without the need to revise the control structure. Finally, the effectiveness of the proposed technique is assessed in simulation.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Robust Output Feedback Control Design in the Presence of Sporadic
Measurements-
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Authors: Roberto Merco;Francesco Ferrante;Ricardo G. Sanfelice;Pierluigi Pisu;
Pages: 3768 - 3775
Abstract: Output feedback control design for linear time-invariant systems in the presence of sporadic measurements and exogenous perturbations is addressed. To cope with the sporadic availability of measurements of the output, a hybrid dynamic output feedback controller equipped with a holding device whose state is reset when a new measurement is available is designed. The closed-loop system, resulting from the interconnection of the controller and the plant, is augmented with a timer variable triggering the arrival of new measurements and its properties are analyzed using hybrid system tools. Building upon Lyapunov theory for hybrid systems, sufficient conditions for internal and $mathcal {L}_{2}$ input-to-output stability are proposed. A linear matrix inequalities-based design methodology for the codesign of the gains of the controller and the parameters of the holding device is presented. The effectiveness of the proposed design approach is showcased in a numerical example.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- On Liveness Enforcement of Distributed Petri Net Systems
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Authors: Daniel Clavel;Cristian Mahulea;Manuel Silva;
Pages: 3776 - 3782
Abstract: In this article, we consider the liveness enforcement problem in a class of Petri nets (PNs) modeling distributed systems. They are called synchronized sequential processes. The presented design algorithm is based on the construction of a control PN, an abstraction of the relations of the T-semiflows, and buffers of the original nonstructurally live PN. The control PN evolves in parallel with the system, avoiding the firing of transitions that may lead the system to nonliveness. Four algorithms are presented, one allowing for the computation of the control PN and three ensuring its liveness.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Classical Control System Analysis Over Lossy Networks: An Easy-to-Use
Nyquist Plot Approach-
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Authors: Luís H. C. Ferreira;Fernando H. D. Guaracy;
Pages: 3783 - 3789
Abstract: This article presents an approach based on the Nyquist plot to analyze the mean-square stability of a networked control system in which data transmission is subject to the occurrence of packet losses. This result is obtained by translating well-known linear matrix inequality (LMI) conditions for mean-square stability to conditions that take the form of upper bounds on the $mathcal {H}_{infty }$ norms of the sensitivity and complementary sensitivity transfer matrices. Although the results obtained provide only sufficient conditions, the proposed approach allows us to inspect if the stochastic feedback system is mean-square stable by conveniently using classical Nyquist plots. A numerical example is given to illustrate the ease of use of the proposed tool.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Event-Based Finite-Time Control for Nonlinear Multiagent Systems With
Asymptotic Tracking-
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Authors: Yongming Li;Yuan-Xin Li;Shaocheng Tong;
Pages: 3790 - 3797
Abstract: In this article, an adaptive neural finite-time event-triggered consensus tracking problem is studied for nonlinear multiagent systems (MASs) under directed graphs. First, the unknown nonlinear functions of MASs can be approximated by neural networks. Then, a distributed adaptive event-triggered control scheme is proposed via command filter and backstepping technique. The newly designed control scheme cannot only circumvent the problem of the explosion of complexity, but also remove the singularity issue typical of conventional backstepping technique. In the meanwhile, an event-triggered mechanism with a dynamic threshold is devised to reduce the waste of network resources. Moreover, by using a novel finite-time stability criterion, it can be proved that the closed-loop system is finite-time stable and the consensus tracking errors can reach zero as time approaches to infinity. Finally, a numerical example is given to validate the feasibility of the proposed scheme.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Stabilization of Triangular Nonlinear Systems With Multiplicative
Stochastic State Sensing Noise-
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Authors: Wuquan Li;Miroslav Krstic;
Pages: 3798 - 3805
Abstract: We present new state feedback control designs for lower/upper triangular nonlinear systems with multiplicative stochastic sensor uncertainty. For lower triangular nonlinear systems with small sensor noise, we develop a novel control design where the control gains are suitably constructed to simultaneously dominate the nonlinear functions and sensor noise of sufficiently small multiplicative gain. For upper triangular nonlinear systems, we propose a new low-gain domination design, the advantage of which is that it can effectively deal with the sensor noise with arbitrarily large intensities. These two designs can both ensure that the closed-loop system has an almost surely unique global solution; the origin of the closed-loop system is mean-square stable, and the states can be regulated to zero almost surely. Finally, two simulation examples are given to illustrate the designs.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Robust Nonlinear MPC With Variable Prediction Horizon: An Adaptive
Event-Triggered Approach-
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Authors: Peng-Biao Wang;Xue-Mei Ren;Dong-Dong Zheng;
Pages: 3806 - 3813
Abstract: This article investigates the event-triggered model predictive control (ETMPC) problem for nonlinear systems with the bounded disturbance. First, a novel adaptive event-triggered mechanism without Zeno behaviors, in which the triggering threshold can constantly be adjusted with the change of the system state, is proposed for computational load reduction. Then, an adaptive prediction horizon update strategy is proposed to further reduce the computational complexity of the optimization problem at each triggering instant. Moreover, a dual-mode ETMPC algorithm is developed, and sufficient conditions on the algorithm feasibility and the system robust stability are provided. Through a simulation example, the results show that the proposed scheme can use fewer computational resources and a shorter calculation time for solving the optimization problem while ensuring satisfactory system performances than the existing ones.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Stability and Wardrop Equilibria of Noncooperative Routing With
Time-Varying Load-
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Authors: Alessandro Giuseppi;Antonio Pietrabissa;
Pages: 3814 - 3821
Abstract: Noncooperative or selfish routing problems emerge in several applications of network control theory. Considering a multicommodity setting subject to time-varying traffic demands, this article studies the convergence properties of a family of noncooperative routing control laws, originally developed in the literature for constant traffic demands. By employing results from hybrid systems theory and set stability, this article identifies the minimum time between bounded load variations to assure the convergence of the controlled system toward a set of approximated Wardrop equilibria. Numerical simulations validate the results on a test scenario.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Computationally Efficient Robust Model Predictive Control for Uncertain
System Using Causal State-Feedback Parameterization-
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Authors: Anastasis Georgiou;Furqan Tahir;Imad M. Jaimoukha;Simos A. Evangelou;
Pages: 3822 - 3829
Abstract: This article investigates the problem of robust model predictive control (RMPC) of linear-time-invariant discrete-time systems subject to structured uncertainty and bounded disturbances. Typically, the constrained RMPC problem with state-feedback parameterizations is nonlinear (and nonconvex) with a prohibitively high computational burden for online implementation. To remedy this, a novel approach is proposed to linearize the state-feedback RMPC problem, with minimal conservatism, through the use of semidefinite relaxation techniques. The proposed algorithm computes the state-feedback gain and perturbation online by solving a linear matrix inequality optimization that, in comparison to other schemes in the literature is shown to have a substantially reduced computational burden without adversely affecting the tracking performance of the controller. Additionally, an offline strategy that provides initial feasibility on the RMPC problem is presented. The effectiveness of the proposed scheme is demonstrated through numerical examples from the literature.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- A Warm-Start Strategy in Interior Point Methods for Shrinking Horizon
Model Predictive Control With Variable Discretization Step-
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Authors: Ziyou Zhang;Qianchuan Zhao;Fa-An Dai;
Pages: 3830 - 3837
Abstract: In this article, we present a warm-start point algorithm in interior point methods for shrinking horizon model predictive control with a variable discretization step. In the algorithm, a convex combination of components of the earlier optimal solution is used to construct an interpolation point, and we use the convex combination of the modified interpolation point and the cold-start point to obtain a warm-start point. We prove that the worst-case iteration complexity of our strategy is better than that of the cold-start. In the numerical experiment of fuel-optimal planetary powered-descent guidance problems, our strategy reduces the number of iterations of second-order cone programming by about 80% with the number of samples available in practical applications.
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Expand Your Network, Get Rewarded
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Pages: 3838 - 3838
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- Introducing IEEE Collabratec
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Pages: 3839 - 3839
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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- TechRxiv: Share Your Preprint Research with the World!
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Pages: 3840 - 3840
PubDate: June 2023
Issue No: Vol. 68, No. 6 (2023)
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