Robust consensus of multi-agent systems with noise

作     者：WANG Lin LIU ZhiXin 

作者机构：Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China 

出 版 物：《Science in China(Series F)》 (中国科学（F辑英文版）)

年 卷 期：2009年第52卷第5期

页      面：824-834页

核心收录：

学科分类：0810[工学-信息与通信工程] 12[管理学] 0711[理学-系统科学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 0808[工学-电气工程] 07[理学] 081104[工学-模式识别与智能系统] 08[工学] 0835[工学-软件工程] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

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

主　　题：time-varying systems stochastic matrix robust consensus connectivity exponential stability Vicsek model 

摘      要：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.