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Leader-following consensus problem with a varying-velocity leader and time-varying delays

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  • Peng, Ke
  • Yang, Yupu

Abstract

In this paper, we study a leader-following consensus problem for a multi-agent system with a varying-velocity leader and time-varying delays. Here, the interaction graph among the followers is switching and balanced. At first, we propose a neighbor-based rule for every agent to track a leader whose states may not be measured. In addition, we consider the convergence analysis of this multi-agent system under two different conditions: the connection between the followers and the leader is time-invariant and time-varying. For the first case, a novel decomposition method is introduced to facilitate the convergence analysis. By utilizing a Lyapunov–Krasovskii functional, we obtain sufficient conditions for uniformly ultimately boundedness of the tracking errors. Finally, two simulations are also presented to illustrate our theoretical results.

Suggested Citation

  • Peng, Ke & Yang, Yupu, 2009. "Leader-following consensus problem with a varying-velocity leader and time-varying delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(2), pages 193-208.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:2:p:193-208
    DOI: 10.1016/j.physa.2008.10.009
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    Citations

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    Cited by:

    1. Xi, Jianxiang & Shi, Zongying & Zhong, Yisheng, 2012. "Admissible consensus and consensualization of high-order linear time-invariant singular swarm systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5839-5849.
    2. Masroor, Suhaib & Peng, Chen, 2022. "An agent based observer model of the networked DC drives for speed coordination," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    3. Xi, Jianxiang & Yao, Zhicheng & Wang, Zhong & Liu, Guangbin & Zhong, Yisheng, 2014. "Admissible L2 consensus for singular time-delayed swarm systems with external disturbances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 165-176.
    4. Wu, Jinying & Xi, Jianxiang & Yang, Xiaogang & Liu, Guangbin, 2015. "Uniqueness of consensus functions for time-delayed swarm systems with time-varying topologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 781-787.
    5. Xi, Jianxiang & Cai, Ning & Zhong, Yisheng, 2010. "Consensus problems for high-order linear time-invariant swarm systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5619-5627.
    6. Li, Yongfu & Li, Kezhi & Zheng, Taixiong & Hu, Xiangdong & Feng, Huizong & Li, Yinguo, 2016. "Evaluating the performance of vehicular platoon control under different network topologies of initial states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 359-368.
    7. Rudy Cepeda-Gomez, 2016. "Finding the exact delay bound for consensus of linear multi-agent systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(11), pages 2598-2606, August.
    8. Rudy Cepeda-Gomez & Nejat Olgac, 2016. "Stability of formation control using a consensus protocol under directed communications with two time delays and delay scheduling," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(2), pages 433-449, January.
    9. M. Saburov & K. Saburov, 2016. "Reaching a consensus: a discrete nonlinear time-varying case," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2449-2457, July.
    10. Wu, Zhihai & Peng, Li & Xie, Linbo & Wen, Jiwei, 2013. "Stochastic bounded consensus tracking of leader–follower multi-agent systems with measurement noises based on sampled-data with small sampling delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 918-928.
    11. Xi, Jianxiang & Shi, Zongying & Zhong, Yisheng, 2011. "Consensus analysis and design for high-order linear swarm systems with time-varying delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4114-4123.
    12. Baojie Zheng & Xiaowu Mu, 2016. "Formation-containment control of second-order multi-agent systems with only sampled position data," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(15), pages 3609-3618, November.
    13. Guoguang Wen & Zhaoxia Peng & Ahmed Rahmani & Yongguang Yu, 2014. "Distributed leader-following consensus for second-order multi-agent systems with nonlinear inherent dynamics," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(9), pages 1892-1901, September.

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