{"title":"Feedback linear quadratic Nash equilibrium for discrete-time Markov jump linear systems","authors":"","doi":"10.1016/j.sysconle.2024.105893","DOIUrl":null,"url":null,"abstract":"<div><p>This paper deals with the infinite horizon feedback LQ Nash equilibrium for discrete-time Markov jump linear systems (MJLS), which are linear systems subject to random variations that follow a Markov chain. We present necessary and sufficient conditions based on a set of coupled algebraic Riccati-like equations for the existence of a feedback LQ Nash equilibrium. To guarantee that the solution of these coupled equations are mean square stabilizing solutions some conditions written in terms of the observability/ detectability of the system modes are presented. The paper concludes with an illustrative example in the context of failure-prone robotic systems.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167691124001816","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper deals with the infinite horizon feedback LQ Nash equilibrium for discrete-time Markov jump linear systems (MJLS), which are linear systems subject to random variations that follow a Markov chain. We present necessary and sufficient conditions based on a set of coupled algebraic Riccati-like equations for the existence of a feedback LQ Nash equilibrium. To guarantee that the solution of these coupled equations are mean square stabilizing solutions some conditions written in terms of the observability/ detectability of the system modes are presented. The paper concludes with an illustrative example in the context of failure-prone robotic systems.
期刊介绍：
Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.
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