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Research Papers

Consensus and Consensualization of High-Order Swarm Systems With Time Delays and External Disturbances

[+] Author and Article Information
Jianxiang Xi1

Department of Automation,  Tsinghua University, Beijing 100084, P. R. Chinaxijx07@mails.tsinghua.edu.cn

Zongying Shi

Department of Automation,  Tsinghua University, Beijing 100084, P. R. China

Yisheng Zhong

Department of Automation and TNList,  Tsinghua University, Beijing 100084, P. R. China

1

Also at: High-Tech Institute of Xi’an, Xi’an 710025, P. R. China.

J. Dyn. Sys., Meas., Control 134(4), 041011 (May 07, 2012) (7 pages) doi:10.1115/1.4006221 History: Received February 26, 2011; Revised February 05, 2012; Published May 04, 2012; Online May 07, 2012

By using dynamic output feedback consensus protocols, consensus analysis, and design, problems for swarm systems with external disturbances and time-varying delays are dealt with. First, two subspaces, namely, a consensus subspace and a complement consensus subspace, are defined. Based on the state projection onto the two subspaces, L2-consensus and L2-consensualization problems are introduced. Then, a necessary and sufficient condition for consensus is presented and an explicit expression of the consensus function is given. Especially, it is shown that the time-varying delay does not influence the consensus function. Finally, in terms of linear matrix inequalities, sufficient conditions for L2-consensus and L2-consensualization are presented, respectively, which possess less calculation complexity, since they are independent of the number of agents, and numerical simulations are shown to demonstrate theoretical results.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Undirected interaction topology

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Figure 2

State trajectories of the swarm system with ϖ(t)≡0

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Figure 3

State trajectories of the swarm system with a nonzero ϖ(t)

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Figure 4

Energy trajectories of vC¯(t) and ϖ(t)

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