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.
The collective behavior of a multi-agent system is the macroscopic phenomenon,such as swarm intelligence,flock...
HAN Jing1,WANG Lin2 1.Key Laboratory of Systems and Control,Institute of Systems Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,No.55,Zhong Guan Cun East Road,Beijing 100190,P.R.China2.Department of Automation,Shanghai Jiao Tong University,No.800,Dong Chuan Road,Shanghai 200240,P.R.China
Cooperation possesses a very significant role on the development of human being societies and animal colonies....
WANG Xin,HAN Jing Key Laboratory of Systems and Control,Institute of Systems Science Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China
