{"title":"Safety Verification of Stochastic Systems: A Set-Erosion Approach","authors":"Zishun Liu;Saber Jafarpour;Yongxin Chen","doi":"10.1109/LCSYS.2024.3518394","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3518394","url":null,"abstract":"We study the safety verification problem for discrete-time stochastic systems. We propose an approach for safety verification termed set-erosion strategy that verifies the safety of a stochastic system on a safe set through the safety of its associated deterministic system on an eroded subset. The amount of erosion is captured by the probabilistic bound on the distance between stochastic trajectories and their associated deterministic counterpart. Building on recent development of stochastic analysis, we establish a sharp probabilistic bound on this distance. Combining this bound with the set-erosion strategy, we establish a general framework for the safety verification of stochastic systems. Our method is versatile and can work effectively with any deterministic safety verification techniques. We exemplify our method by incorporating barrier functions designed for deterministic safety verification, obtaining barrier certificates much tighter than existing results. Numerical experiments are conducted to demonstrate the efficacy and superiority of our method.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"2859-2864"},"PeriodicalIF":2.4,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142880413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Traffic Density Control for Heterogeneous Highway Systems With Input Constraints","authors":"Arash Rahmanidehkordi;Amir H. Ghasemi","doi":"10.1109/LCSYS.2024.3516073","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3516073","url":null,"abstract":"This letter introduces a traffic management algorithm for heterogeneous highway corridors consisting of both human-driven vehicles (HVs) and autonomous vehicles (AVs). The traffic flow dynamics are modeled using the heterogeneous METANET model, with variable speed control employed to maintain desired vehicle densities and reduce congestion. To generate speed control commands, we developed a hybrid framework that combines feedback linearization (FL) and model predictive control (MPC), treating the traffic system as an over-actuated, constrained nonlinear system. The FL component linearizes the nonlinear dynamics, while the MPC component handles constraints by generating virtual control inputs that ensure control limits are respected. To address the over-actuated nature of the system, we introduce a novel constraint mapping algorithm within the MPC that links virtual control input constraints to the actual control commands. Additionally, we propose a real-time reference density generation method that accounts for both AVs and HVs to mitigate congestion. Numerical simulations were conducted for two scenarios: controlling only AVs and controlling both AVs and HVs. The results demonstrate that the proposed FL-MPC framework effectively reduces congestion, even when speed control is applied exclusively to AVs.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"2787-2792"},"PeriodicalIF":2.4,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142858882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reduced Sample Complexity in Scenario-Based Control System Design via Constraint Scaling","authors":"Jaeseok Choi;Anand Deo;Constantino Lagoa;Anirudh Subramanyam","doi":"10.1109/LCSYS.2024.3515861","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3515861","url":null,"abstract":"The scenario approach is widely used in robust control system design and chance-constrained optimization, maintaining convexity without requiring assumptions about the probability distribution of uncertain parameters. However, the approach can demand large sample sizes, making it intractable for safety-critical applications that require very low levels of constraint violation. To address this challenge, we propose a novel yet simple constraint scaling method, inspired by large deviations theory. Under mild nonparametric conditions on the underlying probability distribution, we show that our method yields an exponential reduction in sample size requirements for bilinear constraints with low violation levels compared to the classical approach, thereby significantly improving computational tractability. Numerical experiments on robust pole assignment problems support our theoretical findings.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"2793-2798"},"PeriodicalIF":2.4,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142858886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Trade-Off Between Efficiency and Unpredictability in Stochastic Robotic Surveillance","authors":"Weizhen Wang;Jianping He;Xiaoming Duan","doi":"10.1109/LCSYS.2024.3515858","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3515858","url":null,"abstract":"We study the inherent trade-off in Markov chain-based surveillance strategies between the efficiency, as measured by Kemeny’s constant, and unpredictability, as measured by the entropy rate. We first formulate a multi-objective optimization problem to account for these two criteria and demonstrate the intrinsic contradiction between them, emphasizing the need for a trade-off through the concept of Pareto optimality. We then employ the \u0000<inline-formula> <tex-math>$varepsilon $ </tex-math></inline-formula>\u0000-constraint method to approximate the Pareto curve and illustrate its concavity and strict monotonicity. Due to the lack of a natural order, the points along the Pareto curve are noncomparable and we introduce two additional metrics—the distance to an ideal point and the mixing rate—to discriminate over different Pareto optimal solutions. We demonstrate that the optimal Markov chain minimizing the distance to an ideal point can be identified through convex optimization. While for optimizing the mixing rate over the Pareto curve, we first analyze several tractable examples to establish some intuitions and then propose a bisection-based heuristic algorithm.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"2829-2834"},"PeriodicalIF":2.4,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142858892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multi-Agent Reinforcement Learning in Non-Cooperative Stochastic Games Using Large Language Models","authors":"Shayan Meshkat Alsadat;Zhe Xu","doi":"10.1109/LCSYS.2024.3515879","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3515879","url":null,"abstract":"We study the use of large language models (LLMs) to integrate high-level knowledge in stochastic games using reinforcement learning with reward machines to encode non-Markovian and Markovian reward functions. In non-cooperative games, one challenge is to provide agents with knowledge about the task efficiently to speed up the convergence to an optimal policy. We aim to provide this knowledge in the form of deterministic finite automata (DFA) generated by LLMs (LLM-generated DFA). Additionally, we use reward machines (RMs) to encode the temporal structure of the game and the non-Markovian or Markovian reward functions. Our proposed algorithm, LLM-generated DFA for Multi-agent Reinforcement Learning with Reward Machines for Stochastic Games (StochQ-RM), can learn an equivalent reward machine to the ground truth reward machine (specified task) in the environment using the LLM-generated DFA. Additionally, we propose DFA-based q-learning with reward machines (DBQRM) to find the best responses for each agent using Nash equilibrium in stochastic games. Despite the fact that the LLMs are known to hallucinate, we show that our method is robust and guaranteed to converge to an optimal policy. Furthermore, we study the performance of our proposed method in three case studies.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"2757-2762"},"PeriodicalIF":2.4,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142858883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Proximal Gradient Dynamics: Monotonicity, Exponential Convergence, and Applications","authors":"Anand Gokhale;Alexander Davydov;Francesco Bullo","doi":"10.1109/LCSYS.2024.3516632","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3516632","url":null,"abstract":"In this letter we study the proximal gradient dynamics. This recently-proposed continuous-time dynamics solves optimization problems whose cost functions are separable into a nonsmooth convex and a smooth component. First, we show that the cost function decreases monotonically along the trajectories of the proximal gradient dynamics. We then introduce a new condition that guarantees exponential convergence of the cost function to its optimal value, and show that this condition implies the proximal Polyak-Łojasiewicz condition. We also show that the proximal Polyak-Łojasiewicz condition guarantees exponential convergence of the cost function. Moreover, we extend these results to time-varying optimization problems, providing bounds for equilibrium tracking. Finally, we discuss applications of these findings, including the LASSO problem, certain matrix based problems and a numerical experiment on a feed-forward neural network.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"2853-2858"},"PeriodicalIF":2.4,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142880452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Port-Hamiltonian-Based Geometric Control for Rigid Body Platoons With Mesh Stability Guarantee","authors":"Zihao Song;Panos J. Antsaklis;Hai Lin","doi":"10.1109/LCSYS.2024.3516672","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3516672","url":null,"abstract":"Rigid body platoons are widely applied in many scenarios, such as planar vehicular platoons, satellite networks, and aerial/underwater navigation formations. Like string stability, mesh stability is adopted in these higher dimensional platoons to capture the non-increasing tracking errors over the networks. In this letter, we extend the traditional vehicular platooning control to higher dimensional rigid body scenarios with mesh stability concerns. The main challenges stem from the inherent underactuation of rigid body dynamics, the nonlinearity introduced by the \u0000<inline-formula> <tex-math>$SOtextit {(}3textit {)}$ </tex-math></inline-formula>\u0000-based rotations, and the maintenance of mesh stability for all formations. To this end, we first apply the notion of \u0000<inline-formula> <tex-math>$l_{2}$ </tex-math></inline-formula>\u0000 weak mesh stability to capture the effect of propagation of errors over the network. Then, by assuming all the followers have access to the leader’s information, we propose a novel and constructive rigid body platooning control method based on the port-Hamiltonian framework, which also guarantees the \u0000<inline-formula> <tex-math>$l_{2}$ </tex-math></inline-formula>\u0000 weak mesh stability. This designed controller is further refined for the case when each follower only knows the neighboring information. Finally, the effectiveness of the proposed methods is verified via numerical simulations.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"2805-2810"},"PeriodicalIF":2.4,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142858891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Characterization of Passivizing Input-Output Transformations of Nonlinear MIMO Systems","authors":"Miel Sharf;Daniel Zelazo","doi":"10.1109/LCSYS.2024.3513238","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3513238","url":null,"abstract":"This letter provides a characterization of linear passivizing input-output transformations for MIMO systems with known passivity indices. Building on recent results for SISO systems, we show that any transformation mapping an I/O \u0000<inline-formula> <tex-math>$({rho },~{nu })$ </tex-math></inline-formula>\u0000-passive MIMO system to an I/O \u0000<inline-formula> <tex-math>$(rho ^{*},nu ^{star })$ </tex-math></inline-formula>\u0000-passive system can be expressed as the product of three matrices - two depending on the original and desired passivity indices, and a matrix satisfying a matrix inequality. This parameterization enables formulation of optimal passivation problems that we explore as an application example.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"2733-2738"},"PeriodicalIF":2.4,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142821292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sample Complexity Bounds for Linear System Identification From a Finite Set","authors":"Nicolas Chatzikiriakos;Andrea Iannelli","doi":"10.1109/LCSYS.2024.3514995","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3514995","url":null,"abstract":"This letter considers a finite sample perspective on the problem of identifying an LTI system from a finite set of possible systems using trajectory data. To this end, we use the maximum likelihood estimator to identify the true system and provide an upper bound for its sample complexity. Crucially, the derived bound does not rely on a potentially restrictive stability assumption. Additionally, we leverage tools from information theory to provide a lower bound to the sample complexity that holds independently of the used estimator. The derived sample complexity bounds are analyzed analytically and numerically.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"2751-2756"},"PeriodicalIF":2.4,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142858922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal Constrained Stabilization of Stochastic Time-Delay Systems","authors":"Zhuo-Rui Pan;Wenbang Wang;Wei Ren;Xi-Ming Sun","doi":"10.1109/LCSYS.2024.3514702","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3514702","url":null,"abstract":"Physical systems in the real world are usually constrained due to different considerations. These constraints are closely related to the system safety and stability. In this letter we investigate the optimal stabilization control problem of stochastic time-delay systems under safety constraints. We first follow the Razumikhin approach to propose stochastic control Lyapunov and barrier functions, which result in the closed-form controllers for the stabilization and safety control individually. Next, based on the modification of the quadratic programming, an optimization problem is established to address the stabilization control under safe constraints. The optimal controller is derived explicitly in a switching form to tradeoff the stabilization and safety requirements. Finally, a numerical example is presented to illustrate the proposed control strategy.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"2775-2780"},"PeriodicalIF":2.4,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142858924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}