Synchronization Of Drive-response Dynamical Networks With Event-based Pinning Control

With the application of drive-response synchronization being manifest in image encryption,secure communications,and others,it is essential to design efficient control strategies to reduce control cost.This thesis thus probes into the synchronization of driveresponse dynamical networks with nonlinear nodal dynamics using event-based pinning control.To lay a solid foundation for the study,fundamental topics such as complex networks,neural networks,and drive-response synchronization are deeply reviewed.Further significant mathematical concepts used in the study are also presented.Such concepts include graph theory,matrix theory,linear and nonlinear systems,time-variant systems,pinning control,and the Zeno phenomenon.In achieving the objective of the thesis,sufficient criteria for synchronization are obtained using a novel differential inequality despite the changeable pinning strength,revealing the critical function of the time average of the smallest eigenvalue of an augmented matrix.A well-crafted triggering condition is used to update the control signal to minimize the cost of control.In the meantime,the Zeno phenomenon has been successfully excluded.Therefore,the main theorem is used to investigate a variety of pinning strategies,including pinning control with periodic intermittency,nonlinear pinning strength,and switching pinned node set.Even with a disconnected underlying topology,drive-response synchronization is still possible under the proposed strategies,an exciting discovery.Finally,numerical examples of networked nonlinear oscillators and coupled Hopfield neural networks are given for demonstration purposes.