Event-Triggered Synchronization Control Of Complex Dynamical Networks

The study of complex systems has always been a hot topic in the field of control science,and the study of complex networks has attracted extensive attention from researchers in mathematics,physics and other fields.If each node is composed of a dynamic system,such a complex networks is called complex dynamical networks.For complex dynamical networks,time delays are also inevitable,signal transmission is usually accompanied by time delay,which results in the oscillation phenomenon.Accordingly,it is of great significance to fully consider the influence of time delay in complex dynamical networks.In recent years,the research on asymptotically stability and synchronization control of complex dynamical networks is a key topic,and considerable achievements have been made.Since the main idea of synchronization control of complex dynamical networks is to achieve the synchronization of all the states of the network nodes with the states of isolate node by adding controllers,it is necessary to introduce appropriate control methods into the synchronization control of complex dynamical networks.By utilizing Lyapunov stability theory,this paper studies the synchronization control of complex dynamical networks based on event triggering mechanism.The main works can be summarized into the following three aspects:Firstly,for a class of discrete-time complex dynamical networks based on two-channel dynamic event-triggered schemes,the problem of output feedback synchronization control is studied.A sufficient condition is derived via the Lyapunov-Krasovskii functional approach to ensure that the asymptotic convergence of synchronization errors and estimation errors.Meanwhile,the explicit forms of control gain and estimation gain are presented based on the solutions to certain matrix inequalities.Finally,the feasibility of the theoretical results is verified by numerical simulation results.Secondly,the issue of quasi-synchronization for complex dynamical networks with the two-channel dynamic event-triggered mechanism and quantification is investigated.By designing time-delay dependent controller,using the method of Linear Matrix Inequalities method and Lyapunov stability theory and constructing proper Lyapunov-Krasovskii functional,sufficient conditions are derived such that the synchronization error dynamic is exponentially ultimately bounded.Subsequently,a set of the desired observers and synchronization controllers are designed by solving a linear matrix inequality.Finally,the circuit realisations for the proposed dynamic event-triggered synchronization control approach are given to demonstrate the feasibility of the theoretical results.Thirdly,by utilizing the pinning control method,Young's inequality method,Linear Matrix Inequalities approach and Lyapunov stability theory,sufficient conditions are derived for complex dynamical networks with hybrid time delay achieve prescribed performance synchronization.Finally,numerical examples are used to verify the validity and superiority of the pinning control approach.