Synchronization Of Partially Coupled Dynamical Networks With Impulses

Complex dynamical networks are recently attracting considerable interest as important models for social networks and industrial networks. According to the real-world background, most of net-works in our life can be described as complex dynamical networks in which each individual is regarded as a vertex of the network and interacted with each other. The recent decades have witnessed the great development of researches on the study of complex dynamical networks. Synchronization is fundamental concept in control theory, and they have attracted much concern from many researchers. Researches on these topics are not only of important theoretical values but also of widely practical applications. This thesis studies the synchronization of partial coupling dynamical networks under the influence of impulse. The main work of this thesis is listed as follows:The first chapter summarizes the recent research development of complex networks. Then, we analyse some synchronization and impulsive control of recent research results. Furthermore, we give the motivation and derivation of the main work in this paper.The second chapter presents an analytical study of outer synchronization in partially coupled dynamical networks. In fact, there usually exist communication constraints between connected nodes. The connections among any pairs of nodes have multiple channels to deliver the corresponding states. In many real cases, only part of the channels of the connections can work normally and moreover the valid channels for distinct connections can be different. Therefore, this chapter considers complex dynamical networks with partial coupling. Based on the regrouping method, we propose a pinning impulsive control scheme which is used to guarantee outer synchronization of drive-response partially coupled networks, and further a more flexible impulsive control law is derived by using the concept of average impulsive interval. Finally, two numerical examples, including a small world network, are given to illustrate the efficiency of the proposed approaches, and moreover the synchronization region is clearly plotted.The third chapter discusses quasi-synchronization problem in an array of heterogeneous partially coupling dynamical networks. The real networks often contain different types of objects and links, and it can be modeled with heterogeneous networks, which includes more comprehensive interaction between the objects. Therefore, this chapter considers the heterogeneous network model on the basis of the second chapter, and considers more general heterogeneous impulses. At first, by means of the time-varying Lyapunov function and the comparison principle, sufficient quasi-synchronization criteria are derived such that the proposed heterogeneous partially coupling dynamical networks with heterogeneous impulses can be synchronized within a nonzero error bound and developed in terms of average impulsive interval. Then, by take a specific matrix function P(t), we obtain some lower-dimensional inequalities, which are easier to verify. Moreover, we propose the design method of controllers under a given error bound and an optimization problem for the error bound are given. Finally, a numerical example is provided to illustrate the efficiency of the obtained results.Finally, the forth chapter summarizes the main results of this dissertation. Some possible future work concerning this issue are discussed.