Feedback Control And Synchronization Of Complex Networks

This dissertation investigates feedback control and synchronization of a general n-dimensional non-autonomous chaotic system and a large class of complex networks. By studying the intrinsic property of the nonlinear function of chaotic system, some simple yet generic criteria for determining chaos control and synchronization of chaotic dynamical systems and complex networks are derived. The research method used in this dissertation is that: firstly, a special nonlinear function are constructed by separating the linear and nonlinear terms from the chaotic system and further explore the intrinsic property of this nonlinear function; secondly, we investigate the feedback control and synchronization of coupled chaotic systems and its applications by introducing respectively the delayed feedback signals, the linear feedback signals and the nonlinear feedback signals; finally, we study the feedback control and synchronization of a general class of complex networks and reveal the intrinsic relations between synchronization of networks and the dynamic behavior of the nodes composed of the network. Based on the Lyapunov-Krasovskii functional method and Lyapunov function approach as well as the linear matrix inequalities (LMIs), etc., we prove the correctness of control schemes and approaches developed here. We further verify the effectiveness and feasibility of the proposed techniques by numerical simulations of Matlab and Simulink in computer.This dissertation is divided into five chapters.The first chapter introduces the main works done and the concepts as well as the main lemmas in the thesis.Chapter two, we investigate the feedback control and synchronization of a general n-dimensional non-autonomous chaotic system.Chapter three, we study adaptive synchronization to a general n-dimensional non-autonomous chaotic system and its applications using respectively linear feedback signals and nonlinear feedback signals.Chapter four, consider the feedback control and its applications of a general complex network.Chapter five, some results in the thesis are concluded and looking forward to the research direction in the future. In this paper, we not only generalize the results of linear feedback control in recent literature to a general n-dimensional non-autonomous chaotic system, but also study the feedback control and synchronization between non-autonomous chaotic systems by general nonlinear feedback signals. Due to the techniques developed here based on the intrinsic property of the chaotic system itself, they have more reliability and better effects than the approaches reported so far in the literature for the feedback control of coupled chaotic systems.