Synchronization Analysis And Control Of Nonlinear Complex Networks With Time-delay And Actuator Saturation

Complex networks are everywhere.The synchronization of complex networks is one of the most important topics in complex network dynamics.In many engineering systems,actuator saturation is unavoidable due to physical limitations.Actuator saturation is a kind of strong nonlinear,which will affect the dynamic performance of the system and even destroy the stability of the system.Therefore,it is of great theoretical significance and practical value to study the synchronization of complex networks with actuator saturation constraints.This paper is devoted to studying the synchronization problem of nonlinear complex networks with time delay with actuator saturation constraints.Intermittent control strategy,dynamic event triggering control strategy and impulse control strategy are proposed respectively.Lyapunov stability theory,time-delay system analysis method,switching system method,impulse control method,comparison principle and linear matrix inequality technique are used to study the synchronization problem of time-delay nonlinear complex networks with output constraints.The specific content of this paper is as follows:The first chapter mainly introduces the research background and current research status of synchronization problem in homogeneous and heterogeneous complex networks,and expounds the related research progress of actuator saturation.In addition,this chapter also describes the relevant background knowledge of time-delay systems.At the end of this chapter,the main work and innovation of this paper are introduced.The second chapter mainly introduces some basic theoretical knowledge needed in the study of complex network synchronization with actuator saturation,including the actuator saturation theory and relevant important lemma,which provides necessary preparation for obtaining the results of the paper.In Chapter 3,the exponential synchronization problem of time-delay coupling networks constrained by input saturation is studied under intermittent control strategy.In the communication process,because of the existence of external interference,the data signal transmission process is interrupted.In order to save communication resources and reduce driving burden,intermittent control strategy is adopted.Firstly,the actuator constrained by input saturation is expressed as a set of convex combinations of matrices.Then,by using Lyapunov function,Halanay differential inequality and switching system method,sufficient conditions for exponential synchronization of the time-delay coupling network are derived.On this basis,the shape reference set is used to optimize the invariant set,and the maximum estimate of the attraction domain is obtained.In Chapter 4,the event triggering exponential synchronization of complex networks with actuator saturation is discussed.Considering the waste of communication resources caused by periodic sampling control,in order to further save communication resources,a controller based on dynamic event triggering is designed.It uses the dynamic event trigger function to determine when the event is triggered.By constructing a suitable Lyapunov function,combining saturation control theory,stability theory and some analytical techniques,the exponential synchronization criterion of nonlinear complex networks with time delay constrained by input saturation is derived.Furthermore,it is proved that the proposed event triggering mechanism does not exist Zeno phenomenon.In Chapter 5,the quasi-synchronization problem of heterogeneous complex networks with actuator saturation pulse control is considered.In this chapter,we consider the introduction of saturation-constrained pulse control mechanism on heterogeneous nonlinear time-delay complex networks,express the heterogeneous part as a bounded quantity,and then use the comparison principle to obtain a small error boundary,thus obtaining sufficient conditions for the heterogeneous complex networks to achieve leader-follower quasisynchronization.On this basis,the design problem of controller gain is transformed into some optimization problems,so as to maximize the range of attraction domain under the specified attenuation rate.Finally,the validity of the theory is verified by numerical simulation.