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Robust consensus control for a class of multi-agent systems via distributed PID algorithm and weighted edge dynamics

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  • Shi, Chong-Xiao
  • Yang, Guang-Hong

Abstract

This paper studies the robust proportional-integral-derivative (PID) consensus control for a class of linear multi-agent systems (MASs) with external disturbances. Different from the existing results, both the consensus analysis and the transient performance characteristics for high-order linear MASs are considered. Based on a factorization of Laplacian matrix, the initial MAS is firstly transformed into the so-called weighted edge dynamics, and then a design equivalence between the proposed PID consensus controller and the corresponding stabilizing controller for such weighted edge dynamics is presented via some graph theory results. Furthermore, by combining Lyapunov theory and Barbalat’s Lemma, it is proved that both the stabilization of weighted edge dynamics and the consensus of MAS can be guaranteed even in the presence of external disturbances. In particular, some relationships between the transient time performance of weighted edge dynamics and the PID design parameters are given. Finally, some numerical examples on LC oscillator network are provided to illustrate the validity of theoretical results.

Suggested Citation

  • Shi, Chong-Xiao & Yang, Guang-Hong, 2018. "Robust consensus control for a class of multi-agent systems via distributed PID algorithm and weighted edge dynamics," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 73-88.
    • Handle: RePEc:eee:apmaco:v:316:y:2018:i:c:p:73-88
    DOI: 10.1016/j.amc.2017.07.069
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    References listed on IDEAS

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    1. Song, Xiaona & Men, Yunzhe & Zhou, Jianping & Zhao, Junjie & Shen, Hao, 2017. "Event-triggered H∞ control for networked discrete-time Markov jump systems with repeated scalar nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 123-132.
    2. Song, Xinmin & Duan, Zhenhua & Park, Ju H., 2016. "Linear optimal estimation for discrete-time systems with measurement-delay and packet dropping," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 115-124.
    3. Zhao, Huanyu & Park, Ju H. & Zhang, Yulin, 2014. "Couple-group consensus for second-order multi-agent systems with fixed and stochastic switching topologies," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 595-605.
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    Cited by:

    1. Yang, Nana & Li, Junmin & Chen, Jiaxi, 2020. "Fully distributed hybrid adaptive learning consensus protocols for a class of non-linearly parameterized multi-agent systems," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    2. Liu, Xinrui & Zhang, Mingchao & Xie, Xiangpeng & Zhao, Liang & Sun, Qiuye, 2022. "Consensus-based energy management of multi-microgrid: An improved SoC-based power coordinated control method," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    3. Xingcheng Pu & Chaowen Xiong & Lianghao Ji & Longlong Zhao, 2019. "Weighted Couple-Group Consensus Analysis of Heterogeneous Multiagent Systems with Cooperative-Competitive Interactions and Time Delays," Complexity, Hindawi, vol. 2019, pages 1-13, March.
    4. Liu, Yan & Mei, Jingling & Li, Wenxue, 2018. "Stochastic stabilization problem of complex networks without strong connectedness," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 304-315.

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