Distributed Containment Control of Multi-Agent Linear Systems

WEN Guanghui; HU Guoqiang; ZUO Zhiqiang; CAO Jinde; YU Wenwu

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Distributed Containment Control of Multi-Agent Linear Systems

WEN Guanghui 1, HU Guoqiang 2, ZUO Zhiqiang 3, CAO Jinde 1, YU Wenwu 1

1. Department of Mathematics, Southeast University,Nanjing 210096, China

2. School of Electrical and Electronic Engineering, Nanyang Technological University,639798, Singapore

3. Department of Automation,Tianjin University, Tianjin 300072,China

*Correspondence author

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Funding: Australian ResearchCouncil (ARC) Discovery Scheme （No.DP130104765）

Opened online:25 November 2014

Accepted by: none

Citation: WEN Guanghui, HU Guoqiang, ZUO Zhiqiang.Distributed Containment Control of Multi-Agent Linear Systems[OL]. [25 November 2014] http://en.paper.edu.cn/en_releasepaper/content/4613517

In this paper, the distributed containment control problem is studied for a class of multi-agent systems with linear node dynamics and directed communication topology.A kind of distributedcontrol protocol based only on the relative outputs of neighboringagents is first designed and utilized. Under the assumptions that each dynamical agent is stabilizable and detectable, and for each followerthere exists at least one leader that has a directed path to thatfollower, it is theoretically proved that containment in the closed-loop multi-agent systemcan be guaranteed if the coupling strength between neighboring agents is larger than a threshold value $xi_{0}$, which depends on the eigenvalues of the Laplacian matrix $L$ associated with the communication topology. The convergence rate of containment in multi-agent systems is also discussed. However, the designed protocols fail to achieve containment if some agents can not obtain the exact values of the nonzero eigenvalues of Laplacian matrix $L$. To deal with this challenging case, a favorable self-adaptive containment protocol is further constructed and employed.

Keywords:Distributed control, containment control, multi-agent system, adaptive control.

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