Research On Synchronization Control Of Complex Dynamic Networks With Multi-links

With the development of the networking of human society,the researches of complex networks theory have penetrated into many fields such as information science,computer science,engineering science and even social science.The theory and application of synchronization have also involved information technology,engineering technology,biological technology,human social relations,etc.Therefore,the research on synchronization control of complex dynamic networks with multi-links has an irreplaceable scientific significance and great application value in human life.In this dissertation,we study the finite-time synchronization control problem for complex multi-links dynamical networks with perturbations under two different situations,i.e.the constant time delay and the time-varying delay.Through the adaptive controller,matrix inequality techniques,the finite-time stability theory and Lyapunov stability criterion,this paper presents two finite time synchronization criteria under the circumstances of the constant time delay and the time-varying delay.And the finite time synchronization criteria can ensure the synchronization of complex multi-links dynamical networks with perturbations.Finally,numerical simulation examples are given to demonstrate the correctness and the effectiveness of our theoretical results.This thesis is composed of five parts,which are listed below.The first part of this dissertation mainly introduces the research background,the development history and the research significance of complex networks and complex multi-links networks,as well as the development of synchronization control at home and abroad.Then we analyze and discuss the problems that still exist in complex dynamic networks with multi-links.Finally,it briefly illustrates the main research content and the structure of this dissertation.The second part elaborates on the basic knowledge of complex network synchronization control.First of all,we introduce several main network model categories of complex networks.Then we present the control technologies of complex systems in detail,and introduce different control methods as well as applicable scenarios.We also introduce the types of synchronization and the stability theory in detail,and describe the synchronization type of this thesis.At last,we elaborate the preparatory knowledge such as the hypothesis and the lemma used in this dissertation.In the third part,a finite time synchronization control strategy is proposed for complex multi-links networks with constant time delay and perturbations.Due to the shortcoming that the nonlinear approximation linearization of the system is not accurate enough in the traditional control method,a nonlinear adaptive controller is proposed for the non-linearity of complex multi-links networks in this dissertation.It can ensure that the complex networks with multi-links achieve the synchronization within a finite time.And simulation experiments are to given to verify the correctness and the effectiveness of the proposed synchronization control criterion.In the fourth part,we establish a complex multi-links network model with time-varying delay and perturbations.Using the adaptive controller and the matrix inequality technique,this dissertation proposes a finite time synchronization criterion of complex multi-links network with time-varying delay and perturbations.At the same time,this finite time synchronization control strategy is strictly deduced through the stochastic process differential theory,the Lyapunov function and its stability theory.Finally,we use the simulation programming tools to verify the feasibility and the correctness of the synchronization criterion based on the basic sub-network types of different properties such as the B-A scale-free networks,the W-S small world networks and the E-R random networks.The fifth part summarizes this dissertation,and introduces the future research work combined with the current researches results of this paper.