Research And Application On Consensus Of Multi-agent Systems

Multi-agent systems,one of the branches in complex network control system,have a very wide applications.The researches about them have become an important topic in many fields of the world.The research progress of multi-agent systems is paid close attention by many experts,such as control science,mathematics,informatics,physics,social science and so on.After decades of development,the theories about multi-agent systems have been a considerable foundation,but them have not yet formed a complete theoretical system.Recently,lots of achievements have been made in theoretical researches of multi-agent systems.But the theoretical system of the first order linear multi-agent systems,the foundation of multi-agent system theory,remains to be developed.In this paper,they are studied to the consistency of first order linear multi-agent systems,its applications,and the optimal design of network communication topology.Specifically,it is given to the condition of consensus in the first-order linear multi-agent system with continuous time-varying topology.And it is discussed to the condition that the first-order linear multi-agent system by external interference keep consensus with undirected connection communication topology.In addition,we study the consensus of the first order linear multi-agent systems with directed connection topology.Finally,it is obtained to the optimal design of communication topology with the consensus or the group consensus about the first order linear multi-agent systems.They are proposed to the concepts of interference controller,exponential controller,communication energy and control energy in order to extend the application for the first order linear multi-agent systems.The following results have been achieved.1.Multi-agent systems with piecewise continuous time-varying topology are studies.The agents are assumed to have identical first order linear dynamics.The underlying communication topology is piecewise continuous time-varying.We establish condi-tions under which the network is asymptotically stable meaning that its Laplacian matrix has limit with time.The primary conditions established are in terms of that the asymptotically stable communication topology is connected.When the commu-nication topology is directed connected,the consensus also depends on the absolute integrability of the elements in the difference matrix between Laplacian matrix and the limit matrix.The proposed results are also extended to the case of switching topology.2.The consensus for multi-agent systems with intervention in undirected interaction topology is proposed.They are given to the sufficient conditions and consensus value for the convergence of the system.Then,a valid intervention controller is designed for converging to the specified location.Finally,the consensus tracking algorithm is given for moving target.3.The consensus problem for multi-agent systems with intervention is considered.The sufficient condition of such systems is presented.For converged to the specified lo-cation,we provide a valid intervention controller based on exponential function with fast convergence and integrability.4.The relationship is studied between the consensus(group consistency)and the eigen-vectors of the eigenvalue 0 of Laplacian matrix for multi-agent systems.Then the design method is provided for interaction topology of multi-agent systems.Final-ly,the optimal design is given for interaction topology when the total energy of the system is minimum.This paper is based on graph theory,control theory,matrix theory and differential e-quation theory etc.Lots of simulation experiments show the correctness of the conclusions here.