Lag Synchronization Of Complex Networks And Pinning Control Consensus Of Multi-agent Systems

With rapid developments of social information,the studies of complex networks have attracted increasing attention and permeated into a lot of scientific branches including mathematics,physics,biology,computer etc.Synchronization and its control is a hot topic,which involves the interplay between topology and node dynamics.As synchronization of complex networks,the consensus in the control field is also an important research focus.They are related and different,e.g.,the scale of complex networks is big,while it is small in the multi-agent systems(e.g.,robots formation).Presently they have been the research front in the studies of complex networks and possessed applied background.This dissertation mainly studies lag synchronization of complex networks with unknown parameters and consensus of second-order nonlinear multi-agent systems with directed no-circuit topology.Our work is to propose a hybrid feedback control and a pinning-control scheme to realize lag synchronization and consensus.The detailed studies are as follows:The first chapter introduces the research background and current situation of complex networks,and the common models of complex networks,and gives the research methods of synchronization in complex network and consensus of multi-agent systems.The second chapter presents a hybrid feedback control to achieve lag synchronization of drive-response network with unknown parameters and disturbance.For the hybrid linear feedback controller and hybrid adaptive feedback controller,the network of criteria is obtained to achieve lag synchronization by the stability theory of Lyapunov function.Finally,a numerical example is used to verify the effectiveness of the theoretical results.When the network reaches the lag synchronization,the unknown parameters of the network are accurately identified.In the third chapter,we study the consensus of the nonlinear second-order multiagent systems.For second-order multi-agent systems with directed no-circuit topology,an efficient and convenient algorithm of pinning control is proposed by using properties of the M matrix.The pinned number of multi-agents is determined by whose out-degrees and in-degrees,and gets the conditions for consensus of second-order nonlinear multiagent systems at the same time.The numerical results verify the effectiveness of the control algorithm.The fourth chapter is a summary of this dissertation and the future the work.