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Containment control of continuous-time multi-agent systems with general linear dynamics under time-varying communication topologies

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Abstract

This paper devotes itself to the containment tracking problem of general linear high-order multiagent systems (MASs) under time-varying communications. For general linear MASs with time-varying weightunbalanced digraph, the containment control problem is difficult and challenging, because the Lyapunov method is not an effective approach in this case. Under the assumption that the graph topology uniformly and jointly has a directed spanning forest, we show that when the exponentially unstable mode associated with each agent’s self-dynamics is weak enough, the followers can asymptotically tend to the dynamical convex hull spanned by the leaders, i.e. the containment can be achieved. Moreover, the least convergence rate is explicitly specified. Simulations are also provided to demonstrate the effectiveness of our result.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan, 450001, China

    Zhe Yang & Xiao-wu Mu

  2. College of Science, Henan Institute of Engineering, Zhengzhou, Henan, 451191, China

    Kai Liu

Authors
  1. Zhe Yang
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  2. Xiao-wu Mu
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  3. Kai Liu
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Corresponding author

Correspondence to Xiao-wu Mu.

Additional information

Recommended by Associate Editor Choon Ki Ahn under the direction of Editor PooGyeon Park. This work is supported by The National Natural Science Foundation of China under grants 11571322.

Zhe Yang received her B.S. and M.S. degrees from the Department of Mathematics of Zhengzhou University in 2010 and 2012, respectively. Now she is a PhD candidate of School of Mathematics and Statistics of Zhengzhou University. Her research interests include nonlinear control theory, switched systems and network control systems.

Xiao-wu Mu received his B.S. and Ph.D. degrees from the Department of Mathematics of Peking University, in 1983 and 1991, respectively. Now he is a Professor of Zhengzhou University. His research interests include stochastic systems, hybrid systems, nonlinear control, network control systems.

Kai Liu was born in Henan Province, China, in 1984. He received the B.S. degree in computing science from School of Mathematics, Shandong University, Jinan, China, in 2005, and his M.E. and Ph.D. degrees in theory of control from Zhengzhou University, Zhengzhou, China, in 2008 and 2015, respectively. Since 2008, he has been with College of Science, Henan Institution of Engineering, Zhengzhou, China, where he is currently a lecturer. His current research interests include quantized control, limited data rate, networked control, and multi-agent system.

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Yang, Z., Mu, Xw. & Liu, K. Containment control of continuous-time multi-agent systems with general linear dynamics under time-varying communication topologies. Int. J. Control Autom. Syst. 15, 442–449 (2017). https://doi.org/10.1007/s12555-015-0205-x

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  • DOI: https://doi.org/10.1007/s12555-015-0205-x

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