Impulsive Synchronization Analysis Of Several Heterogeneous Complex Networks

In this thesis,the impulsive synchronization problem of several kinds of heterogeneous complex networks is studied,including heterogeneous Lur’e networks,heterogeneous coupled neural networks and heterogeneous multi-layer neural networks.Several kinds of impulsive controller are designed by combining event-triggering mechanism and adaptive mechanism.By using stability theory and differential equation theory,several sufficient criteria for network synchronization are obtained.The specific research contents are as follows:(1)Synchronization of heterogeneous Lur’e networks with parametric disturbances is studied.By introducing a leader,the feedback impulsive control and the pinning impulsive control are proposed,and the criteria of exponential quasi-synchronization of heterogeneous Lur’e networks are derived.Considering the measurement error and parameter fluctuation in reality,heterogeneous Lur’e network models with uncertain parameters in linear and nonlinear dynamic cases are established.In addition,the design of impulsive control is extended from homogeneous network to heterogeneous network by applying average impulsive interval and average impulsive gain.(2)Synchronization of heterogeneous coupled neural networks is studied.Combined with the advantages of event-triggering mechanism,a hybrid impulsive control strategy is designed,which can effectively avoid the drawbacks of high cost and low efficiency under continuous control.At the same time,synchronous event-triggering impulsive strategy and asynchronous event-triggering impulsive strategy are proposed from the viewpoint of how control strategies use nodal information.Synchronous event-triggering impulsive strategy requires all nodes in the network to sample information synchronously,while in the asynchronous control,each node has its own sampling instants.The corresponding event-trigger function is designed for each node to achieve the corresponding control goal.Based on the stability theory,several criteria for quasi-synchronization of heterogeneous coupled neural networks are given.(3)The synchronization problem of heterogeneous multi-layer neural networks is studied.Based on the classification of multi-layer networks in existing literatures,a class of heterogeneous multilayer neural network model is constructed in this thesis.On the basis of the hybrid impulsive controller proposed in the previous chapter,an adaptive control strategy is further designed for the pinning strength to ensure the dynamical adjustment of the control strategy.By using stability theory and comparison theorem of differential equations,sufficient criteria for quasisynchronization of several networks are given.Besides,the convergence rates and upper bounds of synchronization errors are also given.