Research On Consensus Problems And Network Structure Effect For Multi-agent Systems

Many kinds of systems can be modeled by networks,so to speak,networked systems are ubiquitous in all domains of science and technology.It is for this reason that networked systems catch the eyes of researchers from various disciplines.In particular,the researches of complex systems and social networks have captured a great deal of concern from different research communities.Among them,multi-agent systems as a typical class of complex systems have become a hot topic certainly.In recent years,it has been developed rapidly to study consensus problems and structure effect for multi-agent systems.Recently,most researches of consensus problems have considered the communication weights which are non-negative.However,communication weights of the real network are not only positive but also negative(signed network).So,it is very important to research the consensus problems based on signed graph.Meanwhile,synchronization is a general and universal phenomenon in the network.Most synchronization researches focus on the single network,but most of the real networks are not isolated,but interrelated.Therefore,the synchronization research of coupled network is of great significance.In this dissertation,by using nonlinear control theory,graph theory and matrix analysis,consensus problems and structure effect for multi-agent systems are investigated further.The main work can be listed as follows:1)To study the nonlinear consensus problems under the network topology which is not connected.At first,the signed graph whose weights are positive or negative is imported.Then,the necessary conditions for the convergence of individuals' states to a common state are given.And compared with other consensus protocol,our protocol has two key features: one is that the constraint conditions of communication topology are weaker;the other is that the convergence rate of individuals' states is quicker.And finally,by using Gershgorin circle theorem,squeeze theorem,graph theory and matrix analysis to derive the necessary conditions for the convergence of individuals' states to a common value.And the numerical simulations are carried out to validate the theoretical analysis.2)To discuss the effect of network structure to the convergence speed of individuals' states.Firstly,under the condition that consensus protocol is same,we consider the effect of two kinds of networks which are acyclic networks and ring networks to the convergence rate of individuals' states.And then,we investigate the effect in the view of the node—node position and node number.At last,we demonstrate the effectiveness of our results by numerical simulations.3)To explore the synchronization properties of interconnected network based on the vital node,find simpler coupled networks whose synchronizability is same as the corresponding coupled fully-connected networks and the factors which have impact on synchronizability of the simpler coupled networks.The concepts of key node and simplest and equivalent network are firstly introduced.Then,the conclusion is given: the synchronizability of coupled fully-connected network is identical to its simplest and equivalent network.We strictly derive the eigenvalues of Laplace matrix and the synchronizability of coupled fullyconnected network and its simplest and equivalent networks through utilizing the master stability function approach.And then,we identify the general factors: node number,the number of inter-edges,intra-edge coupling strength and inter-edge coupling strength,which determine the synchronizability of the above coupled networks.Finally,theoretical analysis and numerical simulations are given to indicate the validity and effectiveness of our results.