Switching Intermittent Control Studies Of Complex Networks

Complex dynamical networks have drawn increasing attention ever since the typical models of small-world and scale-free networks were put forward in the 1990s. Models of complex dynamical networks have been widely utilized to our daily life. Especially, synchronization of complex networks can be applied not only to explain natural phenomenon, but also to the fields of secure communication, image process-ing and automatic control, and so on. However, synchronization can not be realized by itself in many cases, and hence some continuous or discontinuous control methods have been widely investigated. In this paper, we mainly introduce a discontinuous control method of intermittent control including semi-periodically intermittent con-trol strategy and aperiodically intermittent control scheme, which generalize and enhance the traditional periodically intermittent control approach. Furthermore, switched complex networks are very important hybrid dynamical networks which availably applied to model many networks demonstrating switched topologies such as network control systems, power electronics, flight control systems, etc. In this paper, the mathematical model of switched complex networks is established and a logical switching rule is determined. By applying intermittent control strategy and the mode-dependent average dwell time (MDADT) approach, we investigate synchronization issue for switched complex networks and design an effective inter-mittent feedback controller. The main content of this paper is arranged as follows:The first chapter is divided into three parts. First of all, the research back-ground and the present research situations of intermittent control strategy and switched complex dynamical networks are introduced. Furthermore, on this basis, we introduced the research significance and main contents of this paper. Finally, to derive the desired result successfully, some fundamental definitions and lemmas are introduced in the preliminary knowledge part.In the second chapter, we study the synchronization problem for switched com-plex networks with delayed coupling via semi-periodically intermittent control tech-nique and a mode-dependent average dwell time method. First of all, the mathemat-ical model of switched complex networks is established, and the networks switch a-mong a finite number of subnetworks in accordance with a switching rule. Moreover, by applying multiple Lyapunov function (MLF) method and the mode-dependent average dwell time (MDADT) approach, less conservative synchronization criteri-a are derived based on a sequence of solvable linear matrix inequalities (LMIs). Especially, the conventional synchronization conditions are improved by using semi-periodically intermittent control and MDADT approach. Finally, we present a nu-merical simulation example. By designing the logical switching rules of the switching signal and combining the theoretical synchronization condition of switched complex networks, the network achieve exponential synchronization quickly with the passage of time under semi-periodically intermittent control.In the third chapter, we investigate the asymptotical synchronization for di-rected dynamical networks with time-varying delay via aperiodically intermittent control and the adaptive pinning strategy. First of all, the model of complex dy-namical network with directed structure is established and corresponding adaptive aperiodically intermittent feedback controller is also designed. Further, based on Lyapunov function method and linear matrix inequality analysis technique, asymp-totical synchronization criteria are derived by applying aperiodically intermittent control, which is demonstrated to be more feasible and less conservative comparing with the periodic scheme. The adaptive algorithm for control gains of the adaptive control scheme is designed and the minimum number of pinning nodes is present-ed. Finally, numerical simulations are provided to illustrate the effectiveness of our theoretical results.Finally, the fourth chapter summarizes the research work of this dissertation and provides some trends of future research.