Event-triggered Consensus And Generalized Synchronization For Directed Interdependent Networks

In real life,there exist interdependent networks composed of a large number of interrelated and interdependent nodes.Compared with a single network,interdependent networks have nodes with different characteristics and structures with different scales.So far,the synchronization or consistency of a network has always been a hot issue in the science field of complex network.For the synchronization and control of interdependent networks,how to effectively reduce the number of executions of control tasks while ensure a certain closed-loop system performance has always been a significant question.Under the framework of event-triggered control strategy,we mainly investigate the following two aspects in this paper.(1)Based on event-triggered control strategy,the heterogeneous consensus of directed interdependent networks is discussed.Two types of networks consisting of two subnets are considered.One is that there is no intra-coupling connection in the subnets,and the other is that there are coupling relationships in the subnets.According to Lyapunov stability theory,a new event-triggered control protocol is designed in this paper,as well as the event-triggered threshold,and some sufficient conditions for heterogeneous synchronization are put forward,which will decrease the updating number of the controllers and guarantee the asymptotic heterogeneous consensus between the directed interdependent network and the equilibrium points of the isolated node systems of the two subnets.In addition,we analyze that there is no Zeno phenomenon during event-driven control process of the network.(2)Furthermore,based on the event-driven control strategy,combined with the auxiliary system method,the generalized synchronization problem of the directed interdependent network is studied.Firstly,a directed interdependent network is used as a response network,and an auxiliary network with the same structure but with different initial values as a response network is constructed.By applying appropriate event-driven controllers to the response network and the auxiliary network,separately,the asymptotically complete synchronization of the response network and the auxiliary network is realized.Then,using the idea of the auxiliary system method,some sufficient conditions of generalized synchronization between each node and its neighbor nodes in the interdependent network are presented.Similarly,we prove that the Zeno phenomenon does not exist in the network in the process of generalized synchronization of event-driven control.Finally,numerical simulations verify the effectiveness and feasibility of the proposed theories.