Synchronization Of Neural Networks And Consensus Of Multi-agent Systems Problems

So far,one of the major topics of complex nonlinear dynamic systems is the investigation ofnot only periodic and aperiodic control but also its stability complex networks which have been received much attention from a lot of scholars both at home and abroad.This article mainly dis-cusses finite-times stability and its stabilization of nonlinear delayed systems,synchronization of neural networks with time-delayed under impulse and intermittent effects and consensus of multi-agent systems.Firstly,the theme purpose and meaning of the research are introduced.A survey is presented on dynamical behavior of neural networks,as well as the methods of study.The research status and significance of the periodic and aperiodic time-delayed synchronization are expounded.At the same time,the contents of the theme are put forward.In chapter 2,we mainly study the synchronization control problem of the undirected network and the intermittent control of the complex network with time-delayed distributed coupling.By means of the pinning control and adaptive feedback control mechanism,reduction to inequality method and Barbalat lemma,a synchronization criterion is set up on adaptive coupling weighted of the undirected dynamic networks.At the same time,by using inequality technique and analysis method,some novel criteria are established to the global exponential synchronization of neural networks and a feasible region of the control parameters for each neuron is also derived based on these criteria.In chapter 3,the issue of synchronization of the competitive neural networks(CNNs)with time-varying delays is investigated via impulses control.First,based on Lyapunov-Krasovski function method and the matrix inequality theory,a linear matrix inequality(LMI)criterion is presented for achieving synchronization of the CNNs.Moreover,an algebraic form sufficient criterion,which reflects the relation among the time delay,impulses feedback matrices,and impulsive interval,is proposed to guarantee exponentially synchronization of the CNNs with bounded time-varying delays.Finally,an example is given to illustrate the effectiveness of the results and feasibility of the schemes proposed.In chapter 4,we discuss a global exponential synchronization of competitive neural net-works(CNNs)via intermittent effect.By means of Lyapunov function and differential inequal-ities technique,some global exponential synchronization conditions are derived to guarantee intermittent control and some criteria are obtained.Additionally,a numerical simulation show the effectiveness of the derived results and the proposed scheme.In chapter 5,the consensus of the high-order multi-agent system is investigated for a class of restricted communication and nonlinear feed-forward behaviors.First,we propose an aperiodic interval control strategies that it different from previous work.Secondly,a low gain control protocol is proposed and derived a sufficient uniform condition of multi-agent system under the protocol by using analysis technique.Finally,some numerical examples are given to illustrate the feasibility of control scheme and the correctness of the theory.