Pub Date : 2025-02-01DOI: 10.1016/j.sysconle.2024.105994
Li Tang, Feixia Liu
This paper investigates the output feedback containment control problem of multi-agent systems (MASs) with multiple leaders described by partial differential equations (PDEs). In contrast to MASs modeled by ODEs, the PDEs system studied in this paper considers additional spatial variables, which leads to traditional ODEs control design methods inapplicable, then the design of observer based adaptive distributed protocols is more challenging. Considering that leaders may be task-driven, the control inputs of the leaders are non-zero and time-varying. Through the introduction of nonlinear terms in the containment controller to eliminate the influence of leader control inputs, the paper ultimately achieves bounded tracking errors and containment errors for agents under undirected graph topologies. Finally, the designed control scheme is validated through examples.
本文研究了由偏微分方程（PDEs）描述的多领导者多代理系统（MASs）的输出反馈控制问题。与用偏微分方程建模的 MAS 相比，本文研究的偏微分方程系统考虑了额外的空间变量，这导致传统的偏微分方程控制设计方法不适用，那么基于观测器的自适应分布式协议的设计就更具挑战性。考虑到领导者可能是任务驱动的，领导者的控制输入是非零和时变的。通过在遏制控制器中引入非线性项来消除领导者控制输入的影响，本文最终实现了无向图拓扑下代理的有界跟踪误差和遏制误差。最后，本文通过实例验证了所设计的控制方案。
{"title":"Adaptive output feedback containment control for parabolic PDE multi-agent systems","authors":"Li Tang, Feixia Liu","doi":"10.1016/j.sysconle.2024.105994","DOIUrl":"10.1016/j.sysconle.2024.105994","url":null,"abstract":"<div><div>This paper investigates the output feedback containment control problem of multi-agent systems (MASs) with multiple leaders described by partial differential equations (PDEs). In contrast to MASs modeled by ODEs, the PDEs system studied in this paper considers additional spatial variables, which leads to traditional ODEs control design methods inapplicable, then the design of observer based adaptive distributed protocols is more challenging. Considering that leaders may be task-driven, the control inputs of the leaders are non-zero and time-varying. Through the introduction of nonlinear terms in the containment controller to eliminate the influence of leader control inputs, the paper ultimately achieves bounded tracking errors and containment errors for agents under undirected graph topologies. Finally, the designed control scheme is validated through examples.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"196 ","pages":"Article 105994"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143183652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-02-01DOI: 10.1016/j.sysconle.2024.106018
Mohsen Amiri, Mehdi Hosseinzadeh
Model Predictive Control (MPC) is widely used to achieve performance objectives, while enforcing operational and safety constraints. Despite its high performance, MPC often demands significant computational resources, making it challenging to implement in systems with limited computing capacity. A recent approach to address this challenge is to use the Robust-to-Early Termination (REAP) strategy. At any time instant, REAP converts the MPC problem into the evolution of a virtual dynamical system whose trajectory converges to the optimal solution, and provides guaranteed sub-optimal and feasible solution whenever its evolution is terminated due to limited computational power. REAP has been introduced as a continuous-time scheme and its theoretical properties have been derived under the assumption that it performs all the computations in continuous time. However, REAP should be practically implemented in discrete-time. This paper focuses on the discrete-time implementation of REAP, exploring conditions under which anytime feasibility and convergence properties are maintained when the computations are performed in discrete time. The proposed methodology is validated and evaluated through extensive simulation and experimental studies.
{"title":"Practical considerations for implementing robust-to-early termination model predictive control","authors":"Mohsen Amiri, Mehdi Hosseinzadeh","doi":"10.1016/j.sysconle.2024.106018","DOIUrl":"10.1016/j.sysconle.2024.106018","url":null,"abstract":"<div><div>Model Predictive Control (MPC) is widely used to achieve performance objectives, while enforcing operational and safety constraints. Despite its high performance, MPC often demands significant computational resources, making it challenging to implement in systems with limited computing capacity. A recent approach to address this challenge is to use the Robust-to-Early Termination (REAP) strategy. At any time instant, REAP converts the MPC problem into the evolution of a virtual dynamical system whose trajectory converges to the optimal solution, and provides guaranteed sub-optimal and feasible solution whenever its evolution is terminated due to limited computational power. REAP has been introduced as a continuous-time scheme and its theoretical properties have been derived under the assumption that it performs all the computations in continuous time. However, REAP should be practically implemented in discrete-time. This paper focuses on the discrete-time implementation of REAP, exploring conditions under which anytime feasibility and convergence properties are maintained when the computations are performed in discrete time. The proposed methodology is validated and evaluated through extensive simulation and experimental studies.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"196 ","pages":"Article 106018"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143182057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-02-01DOI: 10.1016/j.sysconle.2024.106016
José E. Márquez-Prado , Onésimo Hernández-Lerma , Héctor Jasso-Fuentes
We give conditions for a class of continuous-time deterministic and stochastic optimal control problems to have myopic optimal strategies, that is, optimal controls obtained by solving optimization problems independent of the state trajectory. We show how these sufficient conditions are the same for the deterministic and stochastic cases, which means that the certainty equivalence principle is satisfied. Moreover, for the infinite-horizon time-homogeneous case, myopic optimal strategies are obtained by solving a single optimization problem; hence, optimal controls are constant functions.
{"title":"Myopic optimal strategies for a class of continuous-time deterministic and stochastic control problems","authors":"José E. Márquez-Prado , Onésimo Hernández-Lerma , Héctor Jasso-Fuentes","doi":"10.1016/j.sysconle.2024.106016","DOIUrl":"10.1016/j.sysconle.2024.106016","url":null,"abstract":"<div><div>We give conditions for a class of continuous-time deterministic and stochastic optimal control problems to have <em>myopic optimal strategies</em>, that is, optimal controls obtained by solving optimization problems independent of the state trajectory. We show how these sufficient conditions are the same for the deterministic and stochastic cases, which means that the <em>certainty equivalence principle</em> is satisfied. Moreover, for the infinite-horizon time-homogeneous case, myopic optimal strategies are obtained by solving a single optimization problem; hence, optimal controls are constant functions.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"196 ","pages":"Article 106016"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143183649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.sysconle.2024.106014
Yuminghao Xiao, Tianbing Xia, Hongdong Wang
In this paper, we develop a formal safety verification method based on analytic probabilistic reachability computation, which can estimate the probability of controlled non-deterministic systems entering unsafe states subject to disturbances. Specifically, we employ stochastic differential equations (SDEs) to describe the dynamics of the system and resort to a regularized indicator function to express the collision probability between the state trajectory of the system and unsafe states. We proceed to formulate this collision probability as the viscosity solution to a second-order variational-inequality and provide a rigorous proof for such a novel interpretation. Moreover, we discuss the ENO-Godunov scheme for solving the deduced variational-inequality, which obviates the need for Monte-Carlo simulations and the optimality condition along a complex boundary. The developed framework offers a structured approach to identify potential risks in safety critical systems and maintains a user-friendly implementation. Lastly, we demonstrate the above application in a safety verification problem related to maritime navigation.
{"title":"Formal safety verification of non-deterministic systems based on probabilistic reachability computation","authors":"Yuminghao Xiao, Tianbing Xia, Hongdong Wang","doi":"10.1016/j.sysconle.2024.106014","DOIUrl":"10.1016/j.sysconle.2024.106014","url":null,"abstract":"<div><div>In this paper, we develop a formal safety verification method based on analytic probabilistic reachability computation, which can estimate the probability of controlled non-deterministic systems entering unsafe states subject to disturbances. Specifically, we employ stochastic differential equations (SDEs) to describe the dynamics of the system and resort to a regularized indicator function to express the collision probability between the state trajectory of the system and unsafe states. We proceed to formulate this collision probability as the viscosity solution to a second-order variational-inequality and provide a rigorous proof for such a novel interpretation. Moreover, we discuss the ENO-Godunov scheme for solving the deduced variational-inequality, which obviates the need for Monte-Carlo simulations and the optimality condition along a complex boundary. The developed framework offers a structured approach to identify potential risks in safety critical systems and maintains a user-friendly implementation. Lastly, we demonstrate the above application in a safety verification problem related to maritime navigation.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"196 ","pages":"Article 106014"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143182972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-02-01DOI: 10.1016/j.sysconle.2024.105982
Jukka-Pekka Humaloja, Nikolaos Bekiaris-Liberis
We provide two methods for computation of continuum backstepping kernels that arise in control of continua (ensembles) of linear hyperbolic PDEs and which can approximate backstepping kernels arising in control of a large-scale, PDE system counterpart (with computational complexity that does not grow with the number of state components of the large-scale system). In the first method, we provide explicit formulae for the solution to the continuum kernels PDEs, employing a (triple) power series representation of the continuum kernel and establishing its convergence properties. In this case, we also provide means for reducing computational complexity by properly truncating the power series (in the powers of the ensemble variable). In the second method, we identify a class of systems for which the solution to the continuum (and hence, also an approximate solution to the respective large-scale) kernel equations can be constructed in closed form. We also present numerical examples to illustrate computational efficiency/accuracy of the approaches, as well as to validate the stabilization properties of the approximate control kernels, constructed based on the continuum.
{"title":"On computation of approximate solutions to large-scale backstepping kernel equations via continuum approximation","authors":"Jukka-Pekka Humaloja, Nikolaos Bekiaris-Liberis","doi":"10.1016/j.sysconle.2024.105982","DOIUrl":"10.1016/j.sysconle.2024.105982","url":null,"abstract":"<div><div>We provide two methods for computation of continuum backstepping kernels that arise in control of continua (ensembles) of linear hyperbolic PDEs and which can approximate backstepping kernels arising in control of a large-scale, PDE system counterpart (with computational complexity that does not grow with the number of state components of the large-scale system). In the first method, we provide explicit formulae for the solution to the continuum kernels PDEs, employing a (triple) power series representation of the continuum kernel and establishing its convergence properties. In this case, we also provide means for reducing computational complexity by properly truncating the power series (in the powers of the ensemble variable). In the second method, we identify a class of systems for which the solution to the continuum (and hence, also an approximate solution to the respective large-scale) kernel equations can be constructed in closed form. We also present numerical examples to illustrate computational efficiency/accuracy of the approaches, as well as to validate the stabilization properties of the approximate control kernels, constructed based on the continuum.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"196 ","pages":"Article 105982"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143182995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-02-01DOI: 10.1016/j.sysconle.2024.105992
Muhammad Zaki Almuzakki , Bayu Jayawardhana , Aneel Tanwani , Antonis I. Vakis
This paper studies stabilization of linear time-invariant (LTI) systems when control actions can only be realized in finitely many directions where it is possible to actuate uniformly or logarithmically extended positive scaling factors in each direction. Furthermore, a nearest-action selection approach is used to map the continuous measurements to a realizable action where we show that the approach satisfies a weak sector condition for multiple-input multiple-output (MIMO) systems. Using the notion of input-to-state stability, under some assumptions imposed on the transfer function of the system, we show that the closed-loop system converges to the target ball exponentially fast. Moreover, when logarithmic extension for the scaling factors is realizable, the closed-loop system is able to achieve asymptotic stability instead of only practical stability. Finally, we present an example of the application that confirms our analysis.
{"title":"Exponential stabilization of linear systems using nearest-action control with countable input set","authors":"Muhammad Zaki Almuzakki , Bayu Jayawardhana , Aneel Tanwani , Antonis I. Vakis","doi":"10.1016/j.sysconle.2024.105992","DOIUrl":"10.1016/j.sysconle.2024.105992","url":null,"abstract":"<div><div>This paper studies stabilization of linear time-invariant (LTI) systems when control actions can only be realized in <em>finitely</em> many directions where it is possible to actuate uniformly or logarithmically extended positive scaling factors in each direction. Furthermore, a nearest-action selection approach is used to map the continuous measurements to a realizable action where we show that the approach satisfies a <em>weak</em> sector condition for multiple-input multiple-output (MIMO) systems. Using the notion of input-to-state stability, under some assumptions imposed on the transfer function of the system, we show that the closed-loop system converges to the target ball exponentially fast. Moreover, when logarithmic extension for the scaling factors is realizable, the closed-loop system is able to achieve asymptotic stability instead of only practical stability. Finally, we present an example of the application that confirms our analysis.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"196 ","pages":"Article 105992"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143182999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-02-01DOI: 10.1016/j.sysconle.2025.106024
Jovan Stefanovski
This paper addresses the singular linear–quadratic (LQ) control problem, considering cases with or without impulses in the state, and with or without stability. The optimal controller obtained includes a derivative of the state. The assumptions made are system stabilizability and the left-invertibility of the plant transfer matrix. Necessary and sufficient conditions for stability and the impulse-freeness of the optimal state are provided. These conditions are related to the absence of invariant zeros on the imaginary axis, and at infinity with orders greater than one, as well as to strong detectability. When these conditions are not met, the subspace ensuring that the optimal state is impulse-free, if the initial state belongs to that subspace, is determined. Additionally, a suboptimal yet practically realizable controller is presented, along with an explicit expression for the difference between the cost functional values corresponding to the suboptimal and optimal controllers. Illustrative examples are included.
{"title":"Impulsive and impulse-free PD solutions of singular LQ control","authors":"Jovan Stefanovski","doi":"10.1016/j.sysconle.2025.106024","DOIUrl":"10.1016/j.sysconle.2025.106024","url":null,"abstract":"<div><div>This paper addresses the singular linear–quadratic (LQ) control problem, considering cases with or without impulses in the state, and with or without stability. The optimal controller obtained includes a derivative of the state. The assumptions made are system stabilizability and the left-invertibility of the plant transfer matrix. Necessary and sufficient conditions for stability and the impulse-freeness of the optimal state are provided. These conditions are related to the absence of invariant zeros on the imaginary axis, and at infinity with orders greater than one, as well as to strong<span><math><msup><mrow></mrow><mrow><mo>∗</mo></mrow></msup></math></span> detectability. When these conditions are not met, the subspace ensuring that the optimal state is impulse-free, if the initial state belongs to that subspace, is determined. Additionally, a suboptimal yet practically realizable controller is presented, along with an explicit expression for the difference between the cost functional values corresponding to the suboptimal and optimal controllers. Illustrative examples are included.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"196 ","pages":"Article 106024"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143182440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-02-01DOI: 10.1016/j.sysconle.2024.105989
Shixian Luo , Xin Chen , Feiqi Deng , Yan Jiang
This paper focuses on the characterization of moment detectability and almost sure detectability for linear stochastic impulsive systems. The concepts and characterizations of the th moment detectability and almost sure detectability are first introduced. Two expanded systems, the state-expanded stochastic system and the moment equation, are established by utilizing the generalized -representation technique. A series of geometric and algebraic conditions for the th moment detectability of the linear stochastic impulsive systems are established by analyzing the 2nd moment detectability of the state-expanded system and the complete detectability of the moment equation. Subsequently, by introducing a strictly positive-definite quasi-periodic composite polynomial Lyapunov candidate, almost sure detectability criteria are framed in terms of linear matrix inequalities, showing that almost sure detectability is less conservative than moment detectability. Finally, two numerical examples with comparisons are provided to illustrate the proposed theoretical results.
{"title":"Detectability of linear stochastic impulsive systems with state-dependent noises","authors":"Shixian Luo , Xin Chen , Feiqi Deng , Yan Jiang","doi":"10.1016/j.sysconle.2024.105989","DOIUrl":"10.1016/j.sysconle.2024.105989","url":null,"abstract":"<div><div>This paper focuses on the characterization of moment detectability and almost sure detectability for linear stochastic impulsive systems. The concepts and characterizations of the <span><math><mrow><mn>2</mn><mi>p</mi></mrow></math></span>th moment detectability and almost sure detectability are first introduced. Two expanded systems, the state-expanded stochastic system and the moment equation, are established by utilizing the generalized <span><math><mi>H</mi></math></span>-representation technique. A series of geometric and algebraic conditions for the <span><math><mrow><mn>2</mn><mi>p</mi></mrow></math></span>th moment detectability of the linear stochastic impulsive systems are established by analyzing the 2nd moment detectability of the state-expanded system and the complete detectability of the moment equation. Subsequently, by introducing a strictly positive-definite quasi-periodic composite polynomial Lyapunov candidate, almost sure detectability criteria are framed in terms of linear matrix inequalities, showing that almost sure detectability is less conservative than moment detectability. Finally, two numerical examples with comparisons are provided to illustrate the proposed theoretical results.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"196 ","pages":"Article 105989"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143183644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-02-01DOI: 10.1016/j.sysconle.2024.106002
Yanyun Li , Junping Li
This paper concentrates on the minimal hitting probability of continuous-time controlled Markov systems (CTCMSs) with countable state and finite admissible action spaces. The existence of an optimal policy is first proved. In particular, for a special and important case of controlled branching processes (CBPs), it is proved that the minimal hitting probability is the unique solution to an improved optimal system of equations. Furthermore, a novel and precise improved-policy iteration algorithm of an optimal policy and the minimal hitting probability (minimal extinction probability) is presented for CBPs.
{"title":"The minimal hitting probability of continuous-time controlled Markov systems with countable states","authors":"Yanyun Li , Junping Li","doi":"10.1016/j.sysconle.2024.106002","DOIUrl":"10.1016/j.sysconle.2024.106002","url":null,"abstract":"<div><div>This paper concentrates on the minimal hitting probability of continuous-time controlled Markov systems (CTCMSs) with countable state and finite admissible action spaces. The existence of an optimal policy is first proved. In particular, for a special and important case of controlled branching processes (CBPs), it is proved that the minimal hitting probability is the unique solution to an improved optimal system of equations. Furthermore, a novel and precise improved-policy iteration algorithm of an optimal policy and the minimal hitting probability (minimal extinction probability) is presented for CBPs.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"196 ","pages":"Article 106002"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143182987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-02-01DOI: 10.1016/j.sysconle.2024.105993
Xing Chen , Xiaoyue Li , Chenggui Yuan
Since response lags are essential in the feedback loops and are required by most physical systems, it is more appropriate to stabilize McKean–Vlasov stochastic differential equations (MV-SDEs) with common noise through the implementation of delay feedback control mechanisms. The aim of this paper is to design delay feedback control functions such that the controlled system is bounded in infinite horizon and further exponentially stable in the mean square. The designed controller, which depends only on the system state is easier to implement than that in Wu et al. (2022) which was designed to depend on both system state and measure. The existence and uniqueness of the global solution of the controlled system is proved. The Itô formula in both state and measure is derived. The proposed delay feedback control strategies are rendered viable for effective stabilization of MV-SDEs with common noise. Furthermore, the moment Lyapunov exponent, which is intricately linked to the time delays, is meticulously estimated.
{"title":"The delay feedback control for the McKean–Vlasov stochastic differential equations with common noise","authors":"Xing Chen , Xiaoyue Li , Chenggui Yuan","doi":"10.1016/j.sysconle.2024.105993","DOIUrl":"10.1016/j.sysconle.2024.105993","url":null,"abstract":"<div><div>Since response lags are essential in the feedback loops and are required by most physical systems, it is more appropriate to stabilize McKean–Vlasov stochastic differential equations (MV-SDEs) with common noise through the implementation of delay feedback control mechanisms. The aim of this paper is to design delay feedback control functions such that the controlled system is bounded in infinite horizon and further exponentially stable in the mean square. The designed controller, which depends only on the system state is easier to implement than that in Wu et al. (2022) which was designed to depend on both system state and measure. The existence and uniqueness of the global solution of the controlled system is proved. The Itô formula in both state and measure is derived. The proposed delay feedback control strategies are rendered viable for effective stabilization of MV-SDEs with common noise. Furthermore, the moment Lyapunov exponent, which is intricately linked to the time delays, is meticulously estimated.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"196 ","pages":"Article 105993"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143183242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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