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Convergence of a Class of Multi-Agent Systems In Probabilistic Framework

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Abstract

Multi-agent systems arise from diverse fields in natural and artificial systems, and a basic problem is to understand how locally interacting agents lead to collective behaviors (e.g., synchronization) of the overall system. In this paper, we will consider a basic class of multi-agent systems that are described by a simplification of the well-known Vicsek model. This model looks simple, but the rigorous theoretical analysis is quite complicated, because there are strong nonlinear interactions among the agents in the model. In fact, most of the existing results on synchronization need to impose a certain connectivity condition on the global behaviors of the agents’ trajectories (or on the closed-loop dynamic neighborhood graphs), which are quite hard to verify in general. In this paper, by introducing a probabilistic framework to this problem, we will provide a complete and rigorous proof for the fact that the overall multi-agent system will synchronize with large probability as long as the number of agents is large enough. The proof is based on a detailed analysis of both the dynamical properties of the nonlinear system evolution and the asymptotic properties of the spectrum of random geometric graphs.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Gongguo Tang & Lei Guo

Authors
  1. Gongguo Tang
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  2. Lei Guo
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Correspondence to Lei Guo.

Additional information

The research is supported by National Natural Science Foundation of China under the Grants No. 60221301 and No. 60334040.

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Tang, G., Guo, L. Convergence of a Class of Multi-Agent Systems In Probabilistic Framework. Jrl Syst Sci & Complex 20, 173–197 (2007). https://doi.org/10.1007/s11424-007-9016-3

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  • DOI: https://doi.org/10.1007/s11424-007-9016-3

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