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Consensus of high-order dynamic multi-agent systems with switching topology and time-varying delays

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Abstract

This paper studies the consensus problems for a group of agents with switching topology and time-varying communication delays, where the dynamics of agents is modeled as a high-order integrator. A linear distributed consensus protocol is proposed, which only depends on the agent’s own information and its neighbors’ partial information. By introducing a decomposition of the state vector and performing a state space transformation, the closed-loop dynamics of the multi-agent system is converted into two decoupled subsystems. Based on the decoupled subsystems, some sufficient conditions for the convergence to consensus are established, which provide the upper bounds on the admissible communication delays. Also, the explicit expression of the consensus state is derived. Moreover, the results on the consensus seeking of the group of high-order agents have been extended to a network of agents with dynamics modeled as a completely controllable linear time-invariant system. It is proved that the convergence to consensus of this network is equivalent to that of the group of high-order agents. Finally, some numerical examples are given to demonstrate the effectiveness of the main results.

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Authors and Affiliations

  1. Institute of Intelligent Engineering, Center for Systems and Control, College of Engineering, and Key Laboratory of Machine Perception (Ministry of Education), Peking University, Beijing, 100871, China

    Fangcui Jiang, Long Wang & Guangming Xie

Authors
  1. Fangcui Jiang
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  2. Long Wang
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  3. Guangming Xie
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Corresponding author

Correspondence to Fangcui Jiang.

Additional information

This work was supported by the National Natural Science Foundation of China (No.60674050, 60736022, 10972002, 60774089, 60704039).

Fangcui JIANG received the B.S. and M.S. degrees in Mathematics from Qufu Normal University, Qufu, China, in 2003 and 2006, respectively, and is currently pursuing the Ph.D. degree in Complex Systems at Peking University, Beijing, China. Her current research interests are in the fields of cooperative control and controllability of multi-agent systems, consensus problems, formation control, and swarm dynamics.

Long WANG was born in Xi’an, China in 1964. He received his B.E., M.E., and Ph.D. degrees in Dynamics and Control from Tsinghua University and Peking University in 1986, 1989, and 1992, respectively. He has held research positions at the University of Toronto, the University of Alberta, Canada, and the German Aerospace Center, Munich, Germany. He is currently Cheung Kong Chair Professor of Dynamics and Control, Director of Center for Systems and Control of Peking University. He is also Guest Professor of Wuhan University and Beihang University (Beijing University of Aeronautics and Astronautics), and Director of Center for Intelligent Aerospace Systems, Academy for Advanced Technology, Peking University. He serves as Vice-Chairman of Chinese Intelligent Aerospace Systems Committee, and Executive Chairman of the Department of Industrial Engineering and Management, Peking University. He is a panel member of the Division of Information Science, National Natural Science Foundation of China, and a member of IFAC (International Federation of Automatic Control) Technical Committee on Networked Systems. He is in the editorial boards of Science China, Progress in Natural Science, Journal of Intelligent Systems, Acta Automatica Sinica, Journal of Control Theory and Applications, Control and Decision, Information and Control, Journal of Applied Mathematics and Computation, Journal of Intelligent and Robotic Systems, International Journal of Mechanical Science and Engineering, etc. His research interests are in the fields of complex networked systems, information dynamics, collective intelligence, and bio-mimetic robotics.

Guangming XIE received his B.S. degree in Applied Mathematics and Computer Science and Technology, his M.E. degree in Control Theory and Control Engineering, and his Ph.D. degree in Control Theory and Control Engineering from Tsinghua University, Beijing, China in 1996, 1998 and 2001, respectively. Then he worked as a postdoctoral research fellow in the Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing, China from July 2001 to June 2003. In July 2003, he joined the Center as a lecturer. Now he is an associate professor of Dynamics and Control. He is also a guest professor of East China Jiaotong University. He is an editorial advisory board member of the International Journal of Advanced Robotic Systems and an editorial board member of the Open Operational Research Journal. His research interests include hybrid and switched systems, networked control systems, multiagent systems, multi-robot systems, and biomimetic robotics.

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Jiang, F., Wang, L. & Xie, G. Consensus of high-order dynamic multi-agent systems with switching topology and time-varying delays. J. Control Theory Appl. 8, 52–60 (2010). https://doi.org/10.1007/s11768-010-9184-x

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