Pub Date : 2025-04-26DOI: 10.1016/j.automatica.2025.112345
Hongbo Zhu , Minane Joel Villier Amuri , Jinzhong Shen , Xueyang Li
Outliers can contaminate the communication and measurement processes of many sensor network systems, which may be induced by environmental disturbances, model uncertainties, sensor faults or errors, subnetwork faults or malicious cyberattacks. Once the distributed set-membership filter (DSMF) is used into such sensor network systems with outliers for distributed state estimation, the estimation performance can be seriously degraded in each sensor node. To address this problem, this article proposes a mean-shift-based trust set and zonotope extraction mechanism to modify the zonotopic DSMF toward building resilience and robustness against outliers. The proposed mechanism is capable of sifting out the outlier-contaminated local corrected zonotopes, and a sufficient condition for the full effectiveness of it is given and proved. Based on the proposed mechanism, the mean-shift-based outliers-robust zonotopic DSMF (MSRDSMF) is derived for estimating the state of a sensor network system in a distributed way. Simulation experiment results demonstrate the practical validity and superiority of the MSRDSMF in effectively suppressing the effects of outliers.
{"title":"Mean-shift-based robust distributed set-membership fusion filtering for sensor network systems with outliers","authors":"Hongbo Zhu , Minane Joel Villier Amuri , Jinzhong Shen , Xueyang Li","doi":"10.1016/j.automatica.2025.112345","DOIUrl":"10.1016/j.automatica.2025.112345","url":null,"abstract":"<div><div>Outliers can contaminate the communication and measurement processes of many sensor network systems, which may be induced by environmental disturbances, model uncertainties, sensor faults or errors, subnetwork faults or malicious cyberattacks. Once the distributed set-membership filter (DSMF) is used into such sensor network systems with outliers for distributed state estimation, the estimation performance can be seriously degraded in each sensor node. To address this problem, this article proposes a mean-shift-based trust set and zonotope extraction mechanism to modify the zonotopic DSMF toward building resilience and robustness against outliers. The proposed mechanism is capable of sifting out the outlier-contaminated local corrected zonotopes, and a sufficient condition for the full effectiveness of it is given and proved. Based on the proposed mechanism, the mean-shift-based outliers-robust zonotopic DSMF (MSRDSMF) is derived for estimating the state of a sensor network system in a distributed way. Simulation experiment results demonstrate the practical validity and superiority of the MSRDSMF in effectively suppressing the effects of outliers.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"177 ","pages":"Article 112345"},"PeriodicalIF":4.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-26DOI: 10.1016/j.automatica.2025.112336
Najmeh Javanmardi , Pablo Borja , Mohammad Javad Yazdanpanah , Jacquelien M.A. Scherpen
This paper addresses the stabilization and trajectory-tracking problems for two classes of weakly coupled electromechanical systems. To this end, we formulate an energy-based model for these systems within the port-Hamiltonian framework. Then, we employ Lyapunov theory and the notion of contractive systems to develop control approaches in the port-Hamiltonian framework. Remarkably, these control methods eliminate the need to solve partial differential equations or implement any change of coordinates and are endowed with a physical interpretation. We also investigate the effect of coupled damping on the transient performance and convergence rate of the closed-loop system. Finally, the applicability of the proposed approaches is illustrated in two applications of electromechanical systems through simulations.
{"title":"Energy-based control approaches for weakly coupled electromechanical systems","authors":"Najmeh Javanmardi , Pablo Borja , Mohammad Javad Yazdanpanah , Jacquelien M.A. Scherpen","doi":"10.1016/j.automatica.2025.112336","DOIUrl":"10.1016/j.automatica.2025.112336","url":null,"abstract":"<div><div>This paper addresses the stabilization and trajectory-tracking problems for two classes of weakly coupled electromechanical systems. To this end, we formulate an energy-based model for these systems within the port-Hamiltonian framework. Then, we employ Lyapunov theory and the notion of contractive systems to develop control approaches in the port-Hamiltonian framework. Remarkably, these control methods eliminate the need to solve partial differential equations or implement any change of coordinates and are endowed with a physical interpretation. We also investigate the effect of coupled damping on the transient performance and convergence rate of the closed-loop system. Finally, the applicability of the proposed approaches is illustrated in two applications of electromechanical systems through simulations.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"177 ","pages":"Article 112336"},"PeriodicalIF":4.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-26DOI: 10.1016/j.automatica.2025.112340
Paul Wijnbergen , Mark Jeeninga , Redmer de Haan , Erjen Lefeber
The formation of platoons, where groups of vehicles follow each other at close distances, has the potential to increase road capacity. In this paper, a decentralized control approach is presented that extends the well-known constant headway vehicle following approach to the two-dimensional case, i.e., lateral control is included in addition to the longitudinal control. The presented control scheme employs a direct vehicle-following approach where each vehicle in the platoon is responsible for following the directly preceding vehicle according to a nonlinear spacing policy. The proposed spacing policy is motivated by an approximation of a delay-based spacing policy and results in a generalization of the constant-headway spacing policy to the two-dimensional case. By input–output linearization, necessary and sufficient conditions for the tracking of the nonlinear spacing policy are obtained, which motivate the synthesis of the lateral and longitudinal controllers of each vehicle in the platoon. By deriving an internal state representation of the follower vehicle and showing input-to-state stability, the internal dynamics for each leader–follower subsystem are shown to be well-behaved. Furthermore, the spacing policy results in string-stable behavior of the platoon when driving in the longitudinal direction. The results are illustrated by a simulation.
{"title":"Longitudinal and lateral control of vehicle platoons: A unifying framework to prevent corner cutting","authors":"Paul Wijnbergen , Mark Jeeninga , Redmer de Haan , Erjen Lefeber","doi":"10.1016/j.automatica.2025.112340","DOIUrl":"10.1016/j.automatica.2025.112340","url":null,"abstract":"<div><div>The formation of platoons, where groups of vehicles follow each other at close distances, has the potential to increase road capacity. In this paper, a decentralized control approach is presented that extends the well-known constant headway vehicle following approach to the two-dimensional case, <em>i.e.</em>, lateral control is included in addition to the longitudinal control. The presented control scheme employs a direct vehicle-following approach where each vehicle in the platoon is responsible for following the directly preceding vehicle according to a nonlinear spacing policy. The proposed spacing policy is motivated by an approximation of a delay-based spacing policy and results in a generalization of the constant-headway spacing policy to the two-dimensional case. By input–output linearization, necessary and sufficient conditions for the tracking of the nonlinear spacing policy are obtained, which motivate the synthesis of the lateral and longitudinal controllers of each vehicle in the platoon. By deriving an internal state representation of the follower vehicle and showing input-to-state stability, the internal dynamics for each leader–follower subsystem are shown to be well-behaved. Furthermore, the spacing policy results in string-stable behavior of the platoon when driving in the longitudinal direction. The results are illustrated by a simulation.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"177 ","pages":"Article 112340"},"PeriodicalIF":4.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-26DOI: 10.1016/j.automatica.2025.112343
Maiying Zhong , Xiaoqiang Zhu , Shuai Liu , Qing-Long Han , Donghua Zhou
This paper investigates the problem of filtering for a class of nonlinear discrete time systems under a dynamic event-triggered scheme. First, a new general form of event-triggered filters is considered so that the filtering error system achieves full decoupling from the so-called event-triggered transmission error, which is the major concern of filtering performance degradation caused by an event-triggering mechanism. Moreover, the design of the event-triggered filter and event-triggering mechanism can be carried out independently. Second, the event-triggered nonlinear filtering is formulated as a problem of indefinite quadratic form minimum, and a Krein space-based approach is proposed for the design of the event-triggered filter. Based on the first-order Taylor approximation, sufficient and necessary conditions for the existence of a dynamic event-triggered filter are derived by employing Krein space projection, and a feasible solution is given in terms of Riccati recursions for guaranteeing the prescribed performance. Third, an algorithm with time-update and event-update recursions is also provided to perform the dynamic event-triggered nonlinear filtering. It is shown that the proposed Krein space-based approach is computational attractive and easy to implement. Finally, a three-tank system is considered as an illustrative example to demonstrate the effectiveness of the proposed approach.
{"title":"Krein space-based approach to dynamic event-triggered H∞ filtering for a class of nonlinear discrete time systems","authors":"Maiying Zhong , Xiaoqiang Zhu , Shuai Liu , Qing-Long Han , Donghua Zhou","doi":"10.1016/j.automatica.2025.112343","DOIUrl":"10.1016/j.automatica.2025.112343","url":null,"abstract":"<div><div>This paper investigates the problem of <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> filtering for a class of nonlinear discrete time systems under a dynamic event-triggered scheme. First, a new general form of event-triggered filters is considered so that the filtering error system achieves full decoupling from the so-called event-triggered transmission error, which is the major concern of <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> filtering performance degradation caused by an event-triggering mechanism. Moreover, the design of the event-triggered <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> filter and event-triggering mechanism can be carried out independently. Second, the event-triggered <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> nonlinear filtering is formulated as a problem of indefinite quadratic form minimum, and a Krein space-based approach is proposed for the design of the event-triggered <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> filter. Based on the first-order Taylor approximation, sufficient and necessary conditions for the existence of a dynamic event-triggered <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> filter are derived by employing Krein space projection, and a feasible solution is given in terms of Riccati recursions for guaranteeing the prescribed <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance. Third, an algorithm with time-update and event-update recursions is also provided to perform the dynamic event-triggered <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> nonlinear filtering. It is shown that the proposed Krein space-based approach is computational attractive and easy to implement. Finally, a three-tank system is considered as an illustrative example to demonstrate the effectiveness of the proposed approach.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"177 ","pages":"Article 112343"},"PeriodicalIF":4.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-26DOI: 10.1016/j.automatica.2025.112320
Haoran Li, Yuan-Hua Ni
This paper focuses on the learning of Kalman gain of a finite-horizon Kalman filter with unknown noise covariance through the policy optimization method. Firstly, we reformulate the finite-horizon Kalman filter as an optimization problem featuring a doubly-summed objective function Secondly, we establish the global linear convergence of exact gradient descent method in the scenario where the model parameters are all known. Thirdly, we propose a batch gradient descent algorithm to solve the optimization problem. Finally, we provide the global linear convergence and sample complexity of batch gradient descent for the scenario where the noise covariance matrices are unknown.
{"title":"Policy optimization of finite-horizon Kalman filter with unknown noise covariance","authors":"Haoran Li, Yuan-Hua Ni","doi":"10.1016/j.automatica.2025.112320","DOIUrl":"10.1016/j.automatica.2025.112320","url":null,"abstract":"<div><div>This paper focuses on the learning of Kalman gain of a finite-horizon Kalman filter with unknown noise covariance through the policy optimization method. Firstly, we reformulate the finite-horizon Kalman filter as an optimization problem featuring a doubly-summed objective function Secondly, we establish the global linear convergence of exact gradient descent method in the scenario where the model parameters are all known. Thirdly, we propose a batch gradient descent algorithm to solve the optimization problem. Finally, we provide the global linear convergence and sample complexity of batch gradient descent for the scenario where the noise covariance matrices are unknown.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"177 ","pages":"Article 112320"},"PeriodicalIF":4.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-26DOI: 10.1016/j.automatica.2025.112347
Yuhan Xie , Sanbo Ding , Nannan Rong
Set-membership estimation over open sensor networks is a current research hotspot. It remains a risk of data leakage under highly open network channels. This paper focuses on establishing set-membership estimator design strategy under a privacy-preserving framework. Firstly, with the aid of state decomposition methods, a new group of set-membership estimators with privacy-preserving are originally established. Wherein the real measurement is divided into two parts for information interaction and performance compensation respectively. The proposed estimator structure contributes to the security of private data by confusing eavesdroppers. Secondly, a sufficient condition is established to guarantee that the ellipsoidal estimation sets are updated properly. Compared with the existing results on set-membership estimation, the developed one is less conservative. Thirdly, a rigorous theoretical analysis is proposed to justify that the proposed estimator is sufficiently robust to confuse eavesdroppers. Lastly, a simulation example is given to evaluate the estimation and privacy-preserving performance of the proposed technique.
{"title":"Set-membership estimator design with privacy-preserving for sensor networks: A state-decomposition-based approach","authors":"Yuhan Xie , Sanbo Ding , Nannan Rong","doi":"10.1016/j.automatica.2025.112347","DOIUrl":"10.1016/j.automatica.2025.112347","url":null,"abstract":"<div><div>Set-membership estimation over open sensor networks is a current research hotspot. It remains a risk of data leakage under highly open network channels. This paper focuses on establishing set-membership estimator design strategy under a privacy-preserving framework. Firstly, with the aid of state decomposition methods, a new group of set-membership estimators with privacy-preserving are originally established. Wherein the real measurement is divided into two parts for information interaction and performance compensation respectively. The proposed estimator structure contributes to the security of private data by confusing eavesdroppers. Secondly, a sufficient condition is established to guarantee that the ellipsoidal estimation sets are updated properly. Compared with the existing results on set-membership estimation, the developed one is less conservative. Thirdly, a rigorous theoretical analysis is proposed to justify that the proposed estimator is sufficiently robust to confuse eavesdroppers. Lastly, a simulation example is given to evaluate the estimation and privacy-preserving performance of the proposed technique.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"177 ","pages":"Article 112347"},"PeriodicalIF":4.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-26DOI: 10.1016/j.automatica.2025.112338
Antai Xie , Xinlei Yi , Xiaofan Wang , Ming Cao , Xiaoqiang Ren
This paper studies the privacy-preserving distributed optimization problem under limited communication, where each agent aims to keep its cost function private while minimizing the sum of all agents’ cost functions. To this end, we propose two differentially private distributed algorithms under compressed communication. We show that the proposed algorithms achieve sublinear convergence for smooth (possibly nonconvex) cost functions and linear convergence when the global cost function additionally satisfies the Polyak–Łojasiewicz condition, even for a general class of compressors with bounded relative compression error. Furthermore, we rigorously prove that the proposed algorithms ensure -differential privacy. Unlike methods in the literature, the analysis of privacy under the proposed algorithms do not rely on the specific forms of compressors. Simulations are presented to demonstrate the effectiveness of our proposed approach.
{"title":"Differentially private and communication-efficient distributed nonconvex optimization algorithms","authors":"Antai Xie , Xinlei Yi , Xiaofan Wang , Ming Cao , Xiaoqiang Ren","doi":"10.1016/j.automatica.2025.112338","DOIUrl":"10.1016/j.automatica.2025.112338","url":null,"abstract":"<div><div>This paper studies the privacy-preserving distributed optimization problem under limited communication, where each agent aims to keep its cost function private while minimizing the sum of all agents’ cost functions. To this end, we propose two differentially private distributed algorithms under compressed communication. We show that the proposed algorithms achieve sublinear convergence for smooth (possibly nonconvex) cost functions and linear convergence when the global cost function additionally satisfies the Polyak–Łojasiewicz condition, even for a general class of compressors with bounded relative compression error. Furthermore, we rigorously prove that the proposed algorithms ensure <span><math><mi>ϵ</mi></math></span>-differential privacy. Unlike methods in the literature, the analysis of privacy under the proposed algorithms do not rely on the specific forms of compressors. Simulations are presented to demonstrate the effectiveness of our proposed approach.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"177 ","pages":"Article 112338"},"PeriodicalIF":4.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-25DOI: 10.1016/j.automatica.2025.112344
Ruochen Tai , Liyong Lin , Rong Su
This work investigates the security verification problem against covert learning attackers. These are attackers that do not know the supervisor model and thus may require passive learning by collecting observations of the system’s runs. From the attacker’s point of view, any supervisor consistent with the set of observations may have been deployed; thus, a successful attacker needs to remain covert and inflict damage against every supervisor consistent with the set of observations. In such a setting, a supervisor is said to be secure if no covert learning attacker can be successful. We then consider two different setups for the security verification. In the first setup, the attacker can only observe plant events. It is shown that the security verification in this setup can be reduced to verifying the existence of an attacker that is covert and damage-reachable against every supervisor that is consistent with the monitor language (without an explicit tracking of control commands). This is then solved by extending the existing observation-assisted covert attacker synthesis algorithm to the case where the set of observations is a regular set captured by a finite-state automaton. In the second setup, the attacker can observe both plant events and control commands. For this setup, we construct a new structure called unique monitor-embedded bipartite supervisor and prove that the security verification problem can be reduced to checking the existence of an attacker that is covert and damage-reachable against the unique monitor-embedded bipartite supervisor, which can be solved by invoking the existing covert attacker synthesis algorithm against a given supervisor whose model is known to the attacker.
{"title":"Security verification against covert learning attackers","authors":"Ruochen Tai , Liyong Lin , Rong Su","doi":"10.1016/j.automatica.2025.112344","DOIUrl":"10.1016/j.automatica.2025.112344","url":null,"abstract":"<div><div>This work investigates the security verification problem against covert learning attackers. These are attackers that do not know the supervisor model and thus may require passive learning by collecting observations of the system’s runs. From the attacker’s point of view, any supervisor consistent with the set of observations may have been deployed; thus, a successful attacker needs to remain covert and inflict damage against every supervisor consistent with the set of observations. In such a setting, a supervisor is said to be secure if no covert learning attacker can be successful. We then consider two different setups for the security verification. In the first setup, the attacker can only observe plant events. It is shown that the security verification in this setup can be reduced to verifying the existence of an attacker that is covert and damage-reachable against every supervisor that is consistent with the monitor language (without an explicit tracking of control commands). This is then solved by extending the existing observation-assisted covert attacker synthesis algorithm to the case where the set of observations is a regular set captured by a finite-state automaton. In the second setup, the attacker can observe both plant events and control commands. For this setup, we construct a new structure called unique monitor-embedded bipartite supervisor and prove that the security verification problem can be reduced to checking the existence of an attacker that is covert and damage-reachable against the unique monitor-embedded bipartite supervisor, which can be solved by invoking the existing covert attacker synthesis algorithm against a given supervisor whose model is known to the attacker.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"177 ","pages":"Article 112344"},"PeriodicalIF":4.8,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-24DOI: 10.1016/j.automatica.2025.112330
Hongji Ma , Chenchen Mou , Daniel W.C. Ho
This paper addresses the solvability of linear mean-field (MF) forward–backward stochastic difference equations (FBSEs) associated with discrete-time MF linear quadratic (LQ) optimal control problems. First of all, the relationships are investigated among the concerned equations and three different types of FBSEs arising from the available literature. It is found that the various formulations of FBSEs can be cast into a unified paradigm. Furthermore, through the solvability of two coupled difference Riccati equations, a necessary and sufficient condition is presented for the well-posedness of a general class of fully coupled linear MF-FBSEs in a finite horizon. Finally, based on stabilizability and detectability, a sufficient condition is proposed for an infinite-horizon MF-FBSE to admit an adapted solution, which can be explicitly characterized via the stabilizing solution of two coupled algebraic Riccati equations. As applications of the concerned MF-FBSEs, open-loop solvability is studied for finite- and infinite-horizon MF-LQ optimal control problems, respectively.
{"title":"Well-posedness of mean-field forward–backward stochastic difference equations and applications to optimal control","authors":"Hongji Ma , Chenchen Mou , Daniel W.C. Ho","doi":"10.1016/j.automatica.2025.112330","DOIUrl":"10.1016/j.automatica.2025.112330","url":null,"abstract":"<div><div>This paper addresses the solvability of linear mean-field (MF) forward–backward stochastic difference equations (FBS<span><math><mi>Δ</mi></math></span>Es) associated with discrete-time MF linear quadratic (LQ) optimal control problems. First of all, the relationships are investigated among the concerned equations and three different types of FBS<span><math><mi>Δ</mi></math></span>Es arising from the available literature. It is found that the various formulations of FBS<span><math><mi>Δ</mi></math></span>Es can be cast into a unified paradigm. Furthermore, through the solvability of two coupled difference Riccati equations, a necessary and sufficient condition is presented for the well-posedness of a general class of fully coupled linear MF-FBS<span><math><mi>Δ</mi></math></span>Es in a finite horizon. Finally, based on stabilizability and detectability, a sufficient condition is proposed for an infinite-horizon MF-FBS<span><math><mi>Δ</mi></math></span>E to admit an adapted solution, which can be explicitly characterized via the stabilizing solution of two coupled algebraic Riccati equations. As applications of the concerned MF-FBS<span><math><mi>Δ</mi></math></span>Es, open-loop solvability is studied for finite- and infinite-horizon MF-LQ optimal control problems, respectively.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"177 ","pages":"Article 112330"},"PeriodicalIF":4.8,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-23DOI: 10.1016/j.automatica.2025.112318
Junyu Zhang , Xianping Guo , Li Xia
This paper investigates a finite-horizon two-player zero-sum risk-sensitive stochastic game in continuous-time Markov chains with Borel state and action spaces. The model accommodates unbounded reward rates, transition rates, and terminal reward functions, while permitting history-dependent policies. The risk metric is the exponential utility function. Under appropriate conditions, we establish the existence of a solution to the corresponding Shapley equation (SE) through an approximation technique. Using the SE and an extension of Dynkin’s formula, we prove the existence of saddle-point equilibrium and demonstrate that the stochastic game’s value is the unique solution to the SE. Furthermore, we develop a value iteration algorithm for approximating the stochastic game’s value, with convergence guaranteed by a specialized contraction operator within our risk-sensitive stochastic game framework. Finally, we illustrate our main findings through an example.
{"title":"Zero-sum risk-sensitive continuous-time stochastic games with unbounded reward and transition rates in Borel spaces","authors":"Junyu Zhang , Xianping Guo , Li Xia","doi":"10.1016/j.automatica.2025.112318","DOIUrl":"10.1016/j.automatica.2025.112318","url":null,"abstract":"<div><div>This paper investigates a finite-horizon two-player zero-sum risk-sensitive stochastic game in continuous-time Markov chains with Borel state and action spaces. The model accommodates unbounded reward rates, transition rates, and terminal reward functions, while permitting history-dependent policies. The risk metric is the exponential utility function. Under appropriate conditions, we establish the existence of a solution to the corresponding Shapley equation (SE) through an approximation technique. Using the SE and an extension of Dynkin’s formula, we prove the existence of saddle-point equilibrium and demonstrate that the stochastic game’s value is the unique solution to the SE. Furthermore, we develop a value iteration algorithm for approximating the stochastic game’s value, with convergence guaranteed by a specialized contraction operator within our risk-sensitive stochastic game framework. Finally, we illustrate our main findings through an example.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"177 ","pages":"Article 112318"},"PeriodicalIF":4.8,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143864613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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