Chaos Synchronization, Parameter Identification And Application In Secure Communication

The concept of synchronization chaos is to make two chaotic systems oscillate in a synchronized manner, wherein the chaotic motion is now developed so as the two systems are in step during the course of time. The development of chaos synchronizaton not only brings satisfied solutions for the old problems of nonlinear dynamics, control and synchronization, but also brings new ideas and new techniques. Since drive-response synchronization was first found by Pecora and Carroll in early 1990s, synchronization of chaotic systems has attracted significant interests due to its potential application in many areas of science and technology such as communication, electronics, optics, chemistry and biology. It has become the hotspots of recent research. The thesis mainly deals with chaos synchronization, parameter identification and applicaion in secure communication, which is one of challenging researches in nonlinear sciences. The main work and contributions of the present thesis are as follows:(1)Based on theory of stability of linear discreet system, the Hénon chaotic system tracking control of reference signal is investigated and the problem of synchronization is discussed. The Hénon chaotic system tracking control and synchronization are realized. At the same time the new concept of chaotic synchronization of diverse structure is given; Furthermore based on optimal control theory, synchronization of chaotic system is investigated. Through integral and differential disposal of synchronized error system, problems of synchronization are transferred as problems of the least performace index, synchronization controller is given and diverse structure chaos synchronization and self-synchronization are realized.(2)The problems of synchronization and parameter identification for a class of time-delay chaotic systems with different time-delay number is disscussed. Based on Lyapunov stability theory synchronization controller and parameter identification controller are constructed. New concept of self-time-delay chaos synchronization is first given. Furthermore,self-time-delay chaos synchronization of Lorenz chaotic system which have two different time-delay are investigated. Synchronization controller is designed for the realization of self-time-delay chaos synchronization of Lorenz chaotic system. Self-time-delay chaos synchronization of Lorenz chaotic system is realized. Afterwards, based on Lyapunov stability theory self-time-delay chaos synchronization is investigated. Nonlinear feedback controller is given out, the advantage and disadvantage are discussed.(3)Nonlinear observer is used to investigate the problem of parameter identification of two different types of time-delay chaotic system. Closed-loop error system is globally exponential stable or approximately stable by selecting nonlinear gain function in observer, and parameter observer is designed；Identification of parameter c in M-G hyperchaotic system is investigated and a new method of identifying parameter c in M-G system is given. Then we modulates available signal into parameter c of this system in the transmitter and demodulates the signal in the receiver using the proposed parameter identification method, thus secure communication is realized. Then based on the consideration of speed of identification and capability of resisting disturbance,error system of identification converges in setting time through the design of controller. Thus a new setting time identification method is derived.(4)Synchronization and general synchronization of a class of two order chaotic systems with unknown function are investigated. Through the expansion of state variable of drive system and construction of response system, synchronization and general synchronization are realized.Then the control problem of Chen'chaos is discussed. Feedback controler is designed to stabilize the system to any given constant. Furthermore, thracking problem of this system is investigated and general synchronization of Chen'chaos is realized.