Based Adaptive Method Of Chaos Control And Synchronization Study

The control and synchronization of chaotic systems have been the research hotspots of nonlinear science for recent years.The subject of control and synchronization of chaotic systems have received a large amount of attentions due to its particularity,complexity and outlook for application.Based on fundamental characteristic of chaotic signals,which are similar to stochastic signal,extremely sensitive dependence upon initial conditions and not being predicted for long time,and so on,we study the control and synchronization of chaotic systems by adaptive method.The work of this thesis is presented as follow:1. It is very common for nonlinear systems to produce diverge and chaos when the parameters are varied.But this phenomenon is not expected to actual system.This paper discussed an adaptive control method in m-dimesion and two-parameter dynamic system based on linear and nonlinear parameteric disturbance.We can control the system to unstable fixed points when the system is under chaotic circumvent or period attraction points by chosing fit control parameters.2. Chaotic system is very sensitive to initial condition and system parameters.It is a challenge problem to realize synchronization of two chaotic systems with different parameters and initial values. Based on the Lyapunov stability theory, an adaptive synchronization scheme was put forward. Control function and parameter adaptive law can be chosen suitably such that the global stability of synchronization systems was ensured even if there exist parameters errors between driving system and response system. This controller is easy constructed.3. This paper presents an adaptive approach to the control and synchronization of chaotic nonlinear dynamic systems based on a unified frame for both the control and synchronization under some assumptions.Based on the nonlinear state feedback approach,we designed an adaptive controller .The controller not only can adaptively estimate the control parameter,but also has some robustness against parameter variations and external disturbances.Assuming the boundedness of chaotic attractors and limit cycles,the approach,which is both global and not reliant on complete knowledge of the systems involved,is rigorously proved by means of Lyapunov theory.This approach can be used in all systems which satisfy the assumptions.4. In recent years, chaos synchronization and it's application in secure communication have been the research hotspots.But many current method is discussed based on the parameters of active system is known and the passive system can be constituted.Because in actual system,parameters are always varied and system is always been interferenced by environment,so it is necessary to research chaos adaptive synchronization to uncertain system. This paper address the drive-driven synchronization problem of a class of chaotic systems with unknown parameters.An adaptive observer-based driven systems is constructed to realize asymptotical synchronization and estimate the unknown parameters via a scalar transmitted signal.Lyapunov approach guaranteed the right of the scheme.Moreover,the proposed scheme is applied to secure communication system.The information signal is masked by the output of the chaotic transmitter.The transmitted signal is a sum of the information and the output of the chaotic transmitter.The transmitted signal is injected into the transmitter and,simultaneously,transmitted to the receiver.By the proposed adaptive observer design technique,a chaotic receiver is then derived to recover the information signal.