Consensus And Group Consensus Of Multi-agent Systems By Graph Filtering

The cooperative control of multi-agent systems has been an active research area due to its wide application in various fields such as mathematics,physics,biology,social sciences,information science,and control science.The theoretical results have been widely used by many areas such as unmanned aerial vehicle formation control,and urban traffic control,etc.Consensus problem is one of the fundamental problems in the research of multi-agent cooperative control,how to design the control algorithm to improve the convergence speed and the dynamic performance of the control system has been paid more and more attention by scholars.From the perspective of graph filtering,this thesis studies and solves the problems of fast consensus and group consensus of multi-agent system.The main research work and contents are as follows:1.This thesis studies the fast consensus problem of multi-agent systems by second-order graph filters and shows how to use the knowledge of the Laplacian spectrum to accelerate consensus.It is found that for some special graphs,under the consensus protocol corresponding to the second-order graph filter,more knowledge about the Laplacian spectrum has no advantage to improve the convergence rate.By analyzing the second-order graph filter,this thesis propose the conditions that enable to accelerate convergence,give the direct solution formula of the optimal two period control sequence,and obtain the corresponding explicit formula of the fastest convergence rate.Finally,several numerical simulations are presented to verify the efficiency of these results.2.This thesis studies the group consensus of multi-agent systems by graph filtering.For in-degree balanced graphs,sufficient and necessary conditions of the finite time group consensus and the asymptotic group consensus are given,respectively.And the exact convergence rate of the asymptotic group consensus is discussed.Furthermore,for the case of estimated graphs,two design methods of the periodic control protocol are proposed,and the optimal worst-case control sequence with the fastest convergence rate is obtained by using linear programming algorithm.Finally,numerical simulations are presented to verify the efficiency of theoretical results.