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Robust consensus of multi-agent systems with noise

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Abstract

The consensus problem of multi-agent systems has attracted wide attention from researchers in recent years, following the initial work of Jadbabaie et al. on the analysis of a simplified Vicsek model. While the original Vicsek model contains noise effects, almost all the existing theoretical results on consensus problem, however, do not take the noise effects into account. The purpose of this paper is to initiate a study of the consensus problems under noise disturbances. First, the class of multi-agent systems under study is transformed into a general time-varying system with noise. Then, for such a system, the equivalent relationships are established among (i) robust consensus, (ii) the positivity of the second smallest eigenvalue of a weighted Laplacian matrix, and (iii) the joint connectivity of the associated dynamical neighbor graphs. Finally, this basic equivalence result is shown to be applicable to several classes of concrete multi-agent models with noise.

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Authors and Affiliations

  1. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Lin Wang & ZhiXin Liu

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  1. Lin Wang
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  2. ZhiXin Liu
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Correspondence to Lin Wang.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 60821091, 60804043, 60574068), and the Knowledge Innovation Project of Chinese Academy of Sciences (Grant No. KJCX3-SYW-S01)

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Wang, L., Liu, Z. Robust consensus of multi-agent systems with noise. Sci. China Ser. F-Inf. Sci. 52, 824–834 (2009). https://doi.org/10.1007/s11432-009-0082-0

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  • DOI: https://doi.org/10.1007/s11432-009-0082-0

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