Finite-time Consensus For Multi-agent Systems With Signed Graphs

Over the last few years,due to the rapid development of network science and control theory,multi-agent systems have attracted much attentions from many researchers of different fields,in which consensus problem has been a hot topic research.Consensus,as a basic collective behavior of multi-agent systems,means that all agents,through local couplings,agree upon a common quantity under certain networks,and the consensus protocol is the rules of the network’s internal information transmission.Finite-time consensus protocol as a class of consensus protocol,means that all agents of the multi-agent systems will reach agreement in finite time.Based on Lyapunov stability method,graph theory and homogeneity function tools,some theoretical results for finite-time consensus of multi-agent systems with antagonistic interactions are obtained,which were further verified by numerical simulations.The main work of this paper is listed as follows:In Chapter 1,current research significance and prospects of multi-agent systems are summarized.Then we analyse some finite-time consensus control of recent research results.Furthermore,we present the motivation and derivation of our main works in this paper.In Chapter 2,the fixed-time consensus problem of undirected multi-agent networks with antagonistic interactions is investigated.For a given undirected network topology structure,we design a class of fixed-time consensus protocols.According to Lyapunov stability theory and graph theory,we proved that all the agents of the multi-agent networks can achieve a fixed-time bipartite consensus,i.e.,the consensus values are the same in modulus but different in sign.Moreover,two numerical examples are provided to demonstrate the effectiveness of our proposed results.In Chapter 3,the finite-time consensus problem of detail-balanced multi-agent networks with antagonistic interactions is studied.Different from Chapter 2,the network topology structure consider here is directed or contains a spanning tree and satisfies the condition of detail-balanced.Pinning control situation is also considered in this chapter.Based on Lyapunov stability method,graph theory and homogeneity function tools,some sufficient conditions about finite-time bipartite consensus and pinning bipartite consensus are obtained.Finally,three numerical simulations are given to verify the reliability of the theoretical results.In Chapter 4,a brief conclusion is presented to end this dissertation,also the prospect for the work is made.