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Distributed finite-time containment control for second-order nonlinear multi-agent systems

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  • He, Xiaoyan
  • Wang, Qingyun
  • Yu, Wenwu

Abstract

This paper considers the finite-time containment control problem for a class of second-order nonlinear multi-agent systems with external disturbances under the directed topology graph. The considered nonlinear systems are composed of multiple dynamic leaders, and they have only a subset of the followers with their accessing to the leaders. Firstly, by using the one-hop neighbors’ information, a second-order finite-time distributed observer estimator protocol is constructed to achieve accurate estimation of the weighted average of the velocities and positions of the leaders. Furthermore, it is proved that the proposed estimator protocol can guarantee accurate estimation of the weighted average of the velocities and positions of the leaders in the finite-time. Then, we design a new continuous nonlinear control protocol by means of the nonsingular terminal sliding mode. It is shown that by using proposed control protocol, the states of the followers can converge to the convex hull spanned by those of the leaders in the finite-time. In addition, the finite convergence time can be also explicitly estimated. Finally, the effectiveness of the obtained theoretical results is illustrated by the numerical simulation.

Suggested Citation

  • He, Xiaoyan & Wang, Qingyun & Yu, Wenwu, 2015. "Distributed finite-time containment control for second-order nonlinear multi-agent systems," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 509-521.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:509-521
    DOI: 10.1016/j.amc.2015.06.101
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    References listed on IDEAS

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    1. He, Xiaoyan & Wang, Qingyun & Yu, Wenwu, 2015. "Finite-time distributed cooperative attitude tracking control for multiple rigid spacecraft," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 724-734.
    2. Iain D. Couzin & Jens Krause & Nigel R. Franks & Simon A. Levin, 2005. "Effective leadership and decision-making in animal groups on the move," Nature, Nature, vol. 433(7025), pages 513-516, February.
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    Cited by:

    1. He, Xiaoyan & Wang, Qingyun, 2017. "Distributed finite-time leaderless consensus control for double-integrator multi-agent systems with external disturbances," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 65-76.
    2. He, Xiaoyan & Hao, Yuqing & Wang, Qingyun, 2019. "Leaderless finite-time consensus for second-order Lipschitz nonlinear multi-agent systems with settling time estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 280-289.
    3. Zhang, Meijie & Yang, Xinsong & Xiang, Zhengrong & Liu, Xiaoyang, 2023. "Consensus of nonlinear MAS via double nonidentical mode-dependent event-triggered switching control," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    4. Li, Zanhua & Chen, Xiangyong & Ding, Shihong & Liu, Yang & Qiu, Jianlong, 2020. "TCP/AWM network congestion algorithm with funnel control and arbitrary setting time," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    5. Ruichi Ren & Zhenbing Luo & Kaiyu Qin & Boxian Lin & Mengji Shi, 2025. "Robust Fixed-Time Containment Tracking of Multi-Agent Systems with Unknown External Disturbances," Mathematics, MDPI, vol. 13(3), pages 1-19, January.
    6. Liu, Yifan & Su, Housheng, 2019. "Containment control of second-order multi-agent systems via intermittent sampled position data communication," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    7. Du, Yingxue & Wang, Yijing & Zuo, Zhiqiang & Zhang, Wentao, 2022. "Event-triggered bipartite consensus for multi-agent systems subject to multiplicative and additive noises," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    8. Zhao, Lin & Jia, Yingmin & Yu, Jinpeng & Du, Junping, 2017. "H∞ sliding mode based scaled consensus control for linear multi-agent systems with disturbances," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 375-389.

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