Synchronization Analysis And Control Of Several Types Of Complex Dynamical Networks

Network,is not only the actual network in the traditional sense,but also the network of abstract meaning,and it can also be the network of the micro world.It can be said that the network is ubiquitous,and the network also represents a mainstream direction in the development of many research fields,so the research of complex network becomes more and more important.The research of complex networks has entered an epoch-making upsurge with the emergence of the "small-world" characteristics and the scale-free properities.In the past decade,the research of complex networks has attracted wide attention in various fields,including physics,mathematics,biological information,social management and other fields of engineering and engineering researchers.Network synchronization is an important dynamic characteristic of complex networks,widely used in many fields,such as secure communication,electronic circuit,biological system and so on.It has become an important subject in complex network research.In this thesis,based on the Lyapunov stability theory,the problems of asymptotic synchronization,bounded synchronization and finite-time synchronization are studied for several types of complex dynamic network models,and appropriate pinning control,adaptive control and discontinuous control strategies are designed.The main contents of this thesis include the following four aspects:1.A class of complex dynamic network is studied,which contains coupled time delay and state delay of nodes.A suitable pinning controller and an adaptive controller are designed,which make the considered delayed complex dynamic network achieve asymptotic synchronization.Meanwhile,the criteria of global asymptotic synchronization are given in the form of linear matrix inequalities for the delayed complex dynamic networks.According to the Lyapunov stability theory,the synchronization is theoretically proved.Finally,the numerical simulation shows the effectiveness of the algorithm.2.The bounded synchronization of a class of heterogeneous complex dynamic networks is investigated.Based on the state averages of nodes,a new definition of bounded synchronization is proposed for the heterogeneous complex dynamic networks,and it is proved theoretically that the new definition is equivalent to the other bounded synchronization definition.Under this new definition,a novel theorem of bounded synchronization is obtained for this kind of heterogeneous complex dynamic network by applying the bounded synchronous lemma and Lyapunov stability theory,and its bounded synchronous convergence domain can be estimated.Finally,the effectiveness and superiority of the algorithm are verified by simulation results.3.The ynchronization is considered for a class of output coupled complex dynamic networks with unknown parameters and output feedback.Based on the output feedback information and using the high order nonlinear term in the hypothesis of nonlinear function,a new distributed adaptive controller is designed to realize the state synchronization of network nodes.Moreover,it overcomes the influence of the unknown parameters of the nodes,thus ensuring the asymptotically synchronization of the complex dynamic network model.The final simulation experiments indicates the correctness and effectiveness of the conclusion of this chapter.4.The finite-time synchronization is studied for a class of linear coupled complex dynamic networks with uncertain interference term.By designing a group of discontinuous state feedback controllers,the considered heterogeneous complex dynamic network can achieve the finite-time synchronization.Meanwhile,by using Lyapunov function method and linear matrix inequality technique,the sufficient conditions are given to guarantee the finite-time synchronization of the heterogeneous complex dynamic network,and the conclusion is extended to the homogeneous node and the undisturbed case.In addition,the adaptive finite-time synchronization problem is further analyzed and discussed for the heterogeneous complex dynamic network.Theoretical analysis and numerical simulation experiments show the correctness and feasibility of the proposed method.