Adaptive Heterogeneous Synchronization And Control For Interdependent Networks With Noise

With the discovery of the characteristics of small-world and scale-free for the complex networks,complex networks have obtained vigorous development over the past two decades.Synchronization,as a typical type of nonlinear phenomenon in our lives,has become an important research direction for the dynamics of complex networks.However,most of the previous researches focused on the single networks,and the research for networks of networks,especially the interdependent networks,is still in its infancy.Moreover,the presence of noise increases the difficulty of the synchronization and control of the networks.Therefore,in this paper,we investigate the synchronization and control problem of interdependent networks with noise.The main research contents and innovations are as follows.(1)The local adaptive H_?heterogeneous synchronization is investigated for interdependent networks with noise.The network considered consisting of two sub-networks,which are“one-by-one”inter-coupled.The unknown but bounded nonlinear functions exist both in the intra-coupling and inter-coupling between two sub-networks.Based on the Lyapunov stability theory,linear matrix inequality(LMI),adaptive and H_?control technique,the sufficient conditions are established to lead the sub-networks of the interdependent networks with noise to heterogeneous synchronization,respectively.Theconditionsproposedguaranteerobust asymptotically synchronization for networks with noise as well as achieving a prescribed robust H_?performance level.(2)When the noise in the above network is stochastic disturbances,based on It?formula,stochastic Lyapunov stability theory,adaptive control and linear matrix inequality,we analyze and explore the mean-square asymptotically heterogeneous synchronization for the interdependent networks.With the stochastic disturbances,using suitable adaptive controllers,the sufficient conditions are proposed to achieve the mean heterogeneous synchronization of two sub-networks with their isolated systems,respectively.These conditions are simple and easy to achieve.Finally,the numerical simulations prove the effectiveness and feasibility of the methods put forward in this paper.