Study On Synchronization Control Of Stochastic Complex Networks

Recently,with the more and more extensive application of complex network,it has attracted the attention of physics,mathematics,biology and other fields.In various dynamic behaviors of complex networks,the synchronization has always been the focus of attention,that is,the states of all nodes in the network approach the same trajectory.Synchronization appears in every corner of our lives,such as the phenomenon of synchronization on the Internet,the synchronous transmission of digital or analog signals over communication networks,and the synchronization associated with biological neural networks.In addition,it is inevitable to consider the influence of stochastic interference on the complex network when studying the synchronization of complex networks.Therefore,how to solve the synchronization control problem of stochastic complex networks is significance and challenging for us.In this paper,the study of synchronous control will be carried out by selecting suitable control methods for two types of stochastic complex network systems,which are outlined as follows:1 ? For complex networks subject to stochastic coupling,the problem of guaranteed cost finite time synchronization control is studied.Firstly,we design a continuous and without sign function controller,so that the system can not only achieve synchronization in limited time,but also conquer the chattering phenomenon in most results.Secondly,the synchronization criterion of synchronization error system is given by using stochastic analysis technology,Lyapunov stability theory as well as linear matrix inequality(LMI).Then,the upper bound on convergence time and the optimal guaranteed cost function are gained.Finally,the validity of the results is verified by a simulation example.2?For stochastic complex networks with unknown nonlinear coupling strength and derivative coupling,the adaptive synchronization control is discussed.Firstly,to deal with the problem of non-linear coupling strength,we obtain a set of T-S fuzzy complex networks with constant coupling strength based on the Takagi-Sugeno(T-S)fuzzy interpolation method;Then,we design a T-S fuzzy adaptive controller for achieve the T-S fuzzy complex networks;Secondly,a new Lyapunov function,which related to the derivative coupling matrix and derivative coupling strength is constructed.Through the stochastic analysis technology and Lyapunov stability theory,a sufficient condition is given to ensure that the mean square exponential stability is realized for the synchronization error system.Finally,the validity of the results is verified by a simulation example.