中国物理B ›› 2009, Vol. 18 ›› Issue (8): 3355-3366.doi: 10.1088/1674-1056/18/8/040

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Nonlinear consensus protocols for multi-agent systems based on centre manifold reduction

关新平1, 李玉梅2   

  1. (1)Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China; (2)Institute of Mathematics and System Science, Xinjiang University, Urumuqi 830046, China
  • 收稿日期:2008-10-27 修回日期:2009-03-02 出版日期:2009-08-20 发布日期:2009-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 60525303) and the Natural Science Foundation of Hebei Province, China (Grant No 2006000270).

Nonlinear consensus protocols for multi-agent systems based on centre manifold reduction

Li Yu-Mei(李玉梅)a)† and Guan Xin-Ping(关新平)b)   

  1. a Institute of Mathematics and System Science, Xinjiang University, Urumuqi 830046, China; b Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China
  • Received:2008-10-27 Revised:2009-03-02 Online:2009-08-20 Published:2009-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 60525303) and the Natural Science Foundation of Hebei Province, China (Grant No 2006000270).

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摘要： Nonlinear consensus protocols for dynamic directed networks of multi-agent systems with fixed and switching topologies are investigated separately in this paper. Based on the centre manifold reduction technique, nonlinear consensus protocols are presented. We prove that a group of agents can reach a β-consensus, the value of which is the group decision value varying from the minimum and the maximum values of the initial states of the agents. Moreover, we derive the conditions to guarantee that all the agents reach a β--consensus on a desired group decision value. Finally, a simulation study concerning the vertical alignment manoeuvere of a team of unmanned air vehicles is performed. Simulation results show that the nonlinear consensus protocols proposed are more effective than the linear protocols for the formation control of the agents and they are an improvement over existing protocols.

Abstract: Nonlinear consensus protocols for dynamic directed networks of multi-agent systems with fixed and switching topologies are investigated separately in this paper. Based on the centre manifold reduction technique, nonlinear consensus protocols are presented. We prove that a group of agents can reach a $\beta$-consensus, the value of which is the group decision value varying from the minimum and the maximum values of the initial states of the agents. Moreover, we derive the conditions to guarantee that all the agents reach a $\beta$--consensus on a desired group decision value. Finally, a simulation study concerning the vertical alignment manoeuvere of a team of unmanned air vehicles is performed. Simulation results show that the nonlinear consensus protocols proposed are more effective than the linear protocols for the formation control of the agents and they are an improvement over existing protocols.

Key words: nonlinear consensus protocol, centre manifold reduction, multi-agent systems, switching topology

中图分类号:  (Telecommunications: signal transmission and processing; communication satellites)

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