Synchronization And Parameter Identification Of Complex Dynamical Networks

In this dissertation,synchronization and parameter identification of complex dynamical networks are studied by applying linear matrix inequalities,feedback control,adaptive control and parametric adaptive control.According to linear stability theory,Lyapunov stability theory,LaSalle invariance principle and contraction mapping theorem,some sufficient conditions for achieving synchronization and parameter identification of complex networks are obtained respectively.Firstly,synchronization of discrete dynamical networks with both non-delayed and delayed couplings are discussed.Networks with invariable and variable topology are studied respectively.Sufficient conditions of synchronization are derived by using the linear matrix inequalities.Secondly,parameter identification of complex networks with delayed coupling is investigated.Delay identification of complex networks with nonlinear delayed coupling,including simple delay and multi-delays,are considered respectively.By designing some network estimators,some sufficient conditions of parameter identification are given.And complex networks with community structure and multi-delays are also addressed.Then,topology identification of complex dynamical networks is studied.Network estimators are designed with feedback control and adaptive control,and some sufficient conditions for achieving identification are derived by applying the LaSalle invarianee principle,Lyapunov stability theory and the contraction mapping theorem.Finally,topology monitoring of growing networks is studied.For continuoustime growing networks,their network monitors are designed by adaptive feedback control, and sufficient conditions for realizing topology monitoring are presented based on LaSalle invariance principle and Lyapunov stability theory.For discrete-time growing networks, based on contraction mapping theorem,sufficient conditions for their topology monitoring are also given.Numerical examples are given to show the efficiency of the above methods and theoretical results.Chapter 6 summarizes this dissertation and lists some problems for further research.