On Controlling Chaotic Dynamical Systems

The subject of controlling chaotic dynamical systems has recently received a large amount of attention due to its great prospects for applications. This dissertation, which is composed of five parts, focuses on the methods of controlling chaotic dynamical systems.The work in part I investigates the methods of constructing a class of chaotic maps in the sense of Li and Yorke. Two simple analytical methods of constructing continuous maps with certain specific periodic points, which may exhibit chaos in the sense of Li and Yorke, are presented using the Lagrange and Newton's divided difference interpolation polynomial formulas. The dynamics in a extensive class of discrete dynamical systems is investigated and consequently May, Chang and Hu's works had been extended to the general case. Asymptotic property of chaotic maps is studied. A conjecture and open problems relevant to the Gaussian primitive property and chaotic maps are also presented.Part II of this dissertation investigates some controllability of chaotic systems. Stability criterion of open-loop and closed loop control scheme for chaotic systems is discussed. Some ambiguous points in the discussion of controllability of chaotic systems are clarified.Part III investigates the control of discrete-time chaotic systems. A class of controller for discrete-time chaotic system is presented. The objective of the controller is to drive the system to its initially unstable periodic points(or fixed points). Base on the continuity of eigenvalues, an iterative method of choosing the parameters of controller is presented. Feedback control of a class of nonlinear delay maps, including linear and nonlinear feedback, is analyzed.Part IV investigates the analytical methods of constructing generalized chaos synchronization systems. A simple analytical method of constructing generalized chaos synchronization discrete-time systems is proposed. Then a secure communication...