CONVERGENCE OF A CLASS OF MULTI-AGENT SYSTEMS IN PROBABILISTIC FRAMEWORK  

作　　者：Gongguo TANG Lei GUO 

机构地区：[1]Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China

出　　处：《Journal of Systems Science & Complexity》2007年第2期173-197,共25页系统科学与复杂性学报（英文版）

基　　金：The research is supported by National Natural Science Foundation of China under the Grants No. 60221301 and No. 60334040.Acknowledgement The authors would like to thank Prof. Feng TIAN and Dr. Mei LU for providing the proof of Lemma 6 in Appendix B. We would also like to thank Ms. Zhixin Liu for valuable discussions.

摘　　要：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.

关 键 词：CONNECTIVITY large deviation local interaction rules multi-agent systems random geometric graph spectral graph theory SYNCHRONIZATION Vicsek model 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]