Study On Synchronization And Control Of Complex Networks System

With the complexity science and the rapid development of internet technology,all kinds of complex networks have emerged in the life of human society.Human life and production activities are increasingly dependent on a variety of complex network systems.The complex networks system has become one of the most important ways to describe complex systems,network formation mechanism and the evolution of diversity,which has attracted wide interest of researchers.At this time,a variety of complex network research has penetrated into the Internet,the world wide web(WWW),mathematics,physics,biological sciences,social sciences and computer science and engineering.The synchronization phenomenon of each node in the network system is one of the representative projects,which generally exists in all kinds of complex network systems,and it is related to the specific problems in many disciplines.Therefore,it is of great practical significance and theoretical value to study the synchronization control of complex network systems.In this paper,we do some research on the synchronization of the complex network of Markovian jump and the generalized complex network model.A com plex network system is often composed of a large number of nodes,to add a controller to all nodes is a very difficult thing.In order to reduce the number of controllers,it is natural to try to control some of the nodes.Taking this as a starting point,the main research work is summarized as follows.Firstly,a kind of synchronization method for complex network system under the action of pinning control is proposed.The appropriate controller is added in the part of the network.And the criterion of synchronization of the system is obtained.Secondly,the synchronization control problem of the generalized complex network system model with Markovian parameters is studied.By choosing appropriate control parameters,using the theory of stability analysis and inequality and other basic knowledge,the realization of such system synchronization criterion is obtained.This section does not only supplement the basic theory of complex network control,and further extend the synchronization theory of complex networks to general complex networks.Thirdly,the finite time synchronization of complex networks with mixed time delays is studied.In this chapter,the general state feedback controller is designed by using the Kronecker integral operation,which makes the system achieve synchronization in a finite time.At the same time,a new complex network model,namely the coupling matrix in Markov jump.Increase the complexity of the system,is the result of more practical significance,more in line with the actual situation.Finally,finite time synchronization of complex network system with Mark ovian jump is studied.In this complex network model,the complex net work model with Markovian switching is discussed.The sufficient conditions for the system to achieve the synchronization state of the system are obtained.Finally,an example is given to verify the correctness of the conclusion.