Reachable set synthesis of nonlinear heterogeneous multi-agent systems with Markov switching topologies

IF 4.2 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS
Zhihao Shen, Liang Zhang, Ning Zhao
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引用次数: 0

Abstract

This study addresses the problem of reachable set synthesis for nonlinear leaderless heterogeneous multi-agent systems (NLHMASs) under Markov switching topologies. Currently, there exists a paucity of relevant studies on NLHMASs under Markov switching topologies. However, the communication topologies of NLHMASs plays a crucial role in their collaboration, and Markov switching topologies capture the randomness of communication more effectively than fixed topologies. Motivated by this gap, the NLHMASs under Markov switching topologies are considered in this paper, and a consensus protocol in the form of proportional derivative state feedback is designed. Then, by applying Lyapunov functional theory, sufficient conditions described in the form of linear matrix inequalities (LMIs) are derived to guarantee that the reachable set of the systems is bounded by a compact ellipsoid. To increase the feasibility of solutions for LMIs in the sufficient conditions, the free-weighting matrix method is used. However, the introduction of the free-weighting matrix leads to a problem of matrix coupling. To solve this problem effectively, the gains are obtained by using the matrix transformation technique. The validity of the theoretical results is finally verified by a numerical example and practical verification.
马尔可夫切换拓扑非线性异构多智能体系统的可达集综合
研究了马尔可夫切换拓扑下非线性无领导异构多智能体系统(NLHMASs)的可达集综合问题。目前,关于马尔可夫切换拓扑下NLHMASs的相关研究较少。然而,NLHMASs的通信拓扑在其协作中起着至关重要的作用,并且马尔可夫切换拓扑比固定拓扑更有效地捕获了通信的随机性。在此基础上,本文考虑了马尔可夫切换拓扑下的NLHMASs,设计了比例导数状态反馈形式的共识协议。然后,应用Lyapunov泛函理论,导出了以线性矩阵不等式(lmi)形式描述的系统的可达集以紧椭球为界的充分条件。为了提高lmi在充分条件下解的可行性,采用了自由加权矩阵法。然而,自由加权矩阵的引入导致了矩阵耦合问题。为了有效地解决这一问题,利用矩阵变换技术获得了增益。最后通过数值算例和实际验证验证了理论结果的有效性。
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
CiteScore
7.30
自引率
14.60%
发文量
586
审稿时长
6.9 months
期刊介绍: The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.
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