Coherence Analysis Of Determinictic Recursive Networks

The consensus problems of multi-agent systems have attracted much attention,which have many potential applications in several aspects,such as sensor networks,spacecraft formation flying,and cooperative surveillance,aiming to design robust distributed consensus protocols to let the agents maintain consensus.Recently,the consensus analysis of the multi-agent systems in the presence of additional noise is a new topic to explore the influence of network topology on coherence,where the behavior of network coherence is characterized by the Laplacian spectrum.This dissertation chooses the deterministic recursive networks as the research objection,based on the topology construction of the recursive network rules,drives expressions of the coherence,mainly analyzes the impact of controlled parameters,the number of leaders and weight factor on coherence,and investigates the relationship between the topology and coherence of the recursive networks.The detailed work is as follows:The first chapter introduces the research background and development history of complex networks,and describes the deterministic recursive network model and the related knowledge of consensus dynamics.The second chapter proposes a family of deterministic recursive networks with controlled initial state,and obtains the relationship between Laplacian eigenvalues in two successive generations by the construction of network rules.Then,we obtain the firstand second-order coherence calculated by the sum and square sum of reciprocals of all nonzero Laplacian spectrum and analyze the effect of iterative parameters on coherence.Finally,the relationship between network consistency and Laplacian energy is discussed,the numerical results show that the first-and second-order network coherence respectively increase with Laplacian energy at linear and exponential rates,and it is indicate that the large number of Laplacian energy,the worse the consensus.Chapter 3 studies the coherence of the leader-follower recursive networks,selects the initial state node of the network as the leader,and discusses the influence of the coherence of the number of leaders.The explicit expression of the first-order coherence for the leader-follower networks is obtained by recursive algorithm of network.The leaderfollower coherence will be better with the larger number of leaders,but it shows that the first-order coherence without leaders is better than that with leaders.In the fourth chapter,we focus the influence of weighted recursive network on coherence,propose a method to calculate the coherence on weighted recursive networks,and obtain the expression of network coherence and the scalings of coherence with network size.The first-and second-order coherence show that the different consensus behaviors with the different of weighted values,and it is indicates that the large number of the weight,the better the coherence bears,along with the range of the weight factor(0,1].The fifth chapter includes the conclusion and the future studies.