The Research On Adaptive Synchronization Control Of Complex Dynamical Networks

Complexity and complex systems are the important topics in the21st century. Complexnetworks are presently significant tools and methods to describe and understand the complexsystem, which highly summarize the complex system as the networks consisting of manyinteracting individuals or nodes. Complex networks have been used widely in different sci-entific fields, such as sociology, biological sciences computer sciences, physics, engineeringand so on, which have become a brilliant research topic of complexity science field. Syn-chronization is widespread in the various kinds of complicated network systems, and whichis a typical collective behavior in complex networks and one of the most important dynam-ic characteristics of complex networks as well. The research on the nonlinear dynamics areused as theoretical basis and tools for studying synchronization of complex networks. Syn-chronization control of complex dynamical networks is a key link of research and applicationof complex networks, and has great potential applications in secure communication, networkcongestion control, the generation of harmonic oscillator, multi-agent consensus, and so forth.Synchronization control method of complex dynamical networks is mainly divided into twokinds: one is to improve the network synchronization capability by changing the properties ofthe network itself, such as topology structure, coupling strength etc; another is to use controlmethod which is a representative of control theory, mainly including variable feedback con-trol method, adaptive control method, impulse control method, pinning control method, slidecontrol method, drive-response synchronization method.This paper studies the synchronization control of complex dynamical networks. Somenetwork models are mainly studied, such as time-varying complex networks, dynamic net-works with time-varying delayed, nonlinearly coupled complex networks with stochastic per-turbations, dynamic networks with nonlinear derivative coupled, delayed complex networkswith uncertain system parameters and the fractional-order complex chaotic dynamical net-works etc. Based on Lyapunov stability theory, stochastic differential equation theory, matrixtheory, control theory, we use adaptive control methods to study the synchronization controlproblems of these complex dynamics networks, and obtain some criteria to realize complete-ly synchronization, projection synchronization. Numerical simulations are given to illustratethe effectiveness of the results. This paper is composed of seven chapters. In chapter1, weintroduced the background briefly and study progress of complex networks and synchroniza-tion control. Main results and ideas were given from Chapter2to Chapter6. Some existingproblems as well as the future research were pointed out in Chapter7. The main contributionsof this dissertation are summarized as follows:1. Based on the Lyapunov stability theory, the adaptive control and the learning con- trol method, the complex dynamic network system with time-varying coupling strength isinvestigated. The appropriate adaptive learning controller is designed to achieve the globalsynchronization and average synchronization of the network proposed. Numerical simulationresults are performed to verify the validity of the presented method.2. Projective synchronization in a time-varying dynamical network is considered, wherethe nodes are not necessarily partially linear and the scale factors may be different from eachother. Based on stability theorem, appropriate nonlinear adaptive controller are designed, wederive synchronization criteria for the projective synchronization. Finally, the neutral-typetime-varying coupling complex dynamic networks is studied, We use adaptive strategies toachieve synchronization of networks. Corresponding theoretical proofs and numerical simu-lations demonstrate the validity of the presented schemes.3. The problem of the time-varying coupling time-varying delayed complex dynamicnetwork synchronization control is investigated. The coupling strength and coupling delayof the studied model are time-varying. Using adaptive control method and feedback control,we design some suitable controllers, the synchronization of complex dynamic network withdelayed and non-delayed coupling is realized. Theoretical proof is given by structured aLyapunov-Krasovskii functional. The simulation examples further illustrate the theoreticalresults is effective.4. Using the adaptive control method, the non-fragile synchronization problem of time-varying complex dynamic network is investigated. Considering the network time-varyinguncertain factors such as synchronous track, topological information, we assume that the cou-pling configured matrix of network is bounded, the disturbance of internal coupling matrix isbounded in norm, using the Lyapunov stability method, the linear matrix inequality (LMIs)condition to achieve non-fragile synchronization of time-varying complex dynamic networkis obtained. The results of the numerical simulations are compatible with the theoretical anal-ysis.5. We study synchronization control of time-varying coupled complex dynamical net-works with random disturbance. In this chapter, we consider the identical nodes and hetero-geneous nodes complex dynamic network with external perturbations, respectively. Some newsynchronization criteria are obtained by stochastic differential equation theory and feedbackcontrol method. Theoretical analysis and numerical simulations have verified the effectivenessof the proposed scheme.6. Synchronization of the fractional-order complex dynamical networks is considered.Based on the stability theory of fractional-order systems, the fractional-order adaptive con-trollers are designed to realize synchronization of the fractional-order dynamical networkswith identical nodes, and a sufficient synchronization criteria is obtained.