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Cluster-delay consensus in first-order multi-agent systems with nonlinear dynamics

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Abstract

In this paper, a new concept of cluster-delay consensus is defined, which means that all agents in the same cluster reach identical consensus and that any two agents in the different clusters reach delay consensus simultaneously. In fact, cluster-delay consensus is a kind of dynamics between identical consensus and cluster consensus. And then, the problem of leader-following cluster-delay consensus in a nonlinear multi-agent system is investigated. By using graph theory, Lyapunov stability theory and matrix theory, a control protocol for cluster-delay consensus is given, which is based on intrinsic dynamics of each agent and the topology of multi-agent system. Finally, some numerical simulations are also given to verify the theoretical analysis.

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Acknowledgments

The authors would like to thank the anonymous reviewers for their comments. In particular, the reviewers read this paper very carefully and give very important advices that greatly helped the authors in revising this paper. This work was supported by the National Natural Science Foundation of China (No. 11562006), Guangxi Key Laboratory of Trusted Software (No. kx201417) and Outstanding Young Teachers Training in Higher Education Institutions of Guangxi (No. gxqg022014025).

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Authors and Affiliations

  1. School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, 541004, China

    Zhongjun Ma & Xiaomei Li

  2. Guangxi Key Laboratory of Trusted Software, Guilin University of Electronic Technology, Guilin, 541004, China

    Zhongjun Ma

  3. School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, 310012, China

    Yi Wang

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  1. Zhongjun Ma
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  2. Yi Wang
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  3. Xiaomei Li
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Correspondence to Yi Wang.

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Ma, Z., Wang, Y. & Li, X. Cluster-delay consensus in first-order multi-agent systems with nonlinear dynamics. Nonlinear Dyn 83, 1303–1310 (2016). https://doi.org/10.1007/s11071-015-2403-8

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  • DOI: https://doi.org/10.1007/s11071-015-2403-8

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