Feedback linear quadratic Nash equilibrium for discrete-time Markov jump linear systems

IF 2.1 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters Pub Date : 2024-08-06 DOI:10.1016/j.sysconle.2024.105893

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.

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离散时马尔可夫跃迁线性系统的反馈线性二次纳什均衡

本文讨论离散时间马尔可夫跃迁线性系统（MJLS）的无限视界反馈 LQ 纳什均衡，MJLS 是受马尔可夫链随机变化影响的线性系统。我们基于一组类似里卡提的代数耦合方程，提出了反馈 LQ 纳什均衡存在的必要条件和充分条件。为了保证这些耦合方程的解是均方稳定解，我们提出了一些以系统模式的可观测性/可探测性为基础的条件。论文最后以易失效机器人系统为例进行了说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Systems & Control Letters 工程技术-运筹学与管理科学

CiteScore

4.60

自引率

3.80%

发文量

144

审稿时长

6 months

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.