An Adaptive Variable Structure Observers Method For Chaotic Syschronization And Control

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,complexitr and outlook for application.The merit of adaptive control is not need construct accurate mathematic equation of the system but all state variable of the system can be adjusted flexibly,so it does not need the upperbounds of the uncertaintyes in advance. Sliding mode variable structure control is a species of control strategy of nonlinearity,it's adventage is more robust with respect to noise and parameter mismatch.This paper integrate adaptive control and sliding mode variable structure control,propose a adaptive sliding mode variable structure observer method for a class of chaotic systems with uncertainties in which all state variable are not measured. The approach not noly achieve synchronization and control of a class of chaotic systems with single variable tremsmission ,but also through appropriate coordinate conversion to achieve synchronization and control of a class of chaotic systems with multivariable transmitsion.The main work of this paper is presented as follows:1. The limit of nonlinear systems which satisfied Lipschitz condition is considered in this paper. It summarizes the study trends of nonlinear observers, compares the various design methods of nonlinear observers.2. Based on single variable transmission. Chaotic systems and observer are regarded as objective and response. A method based on adaptive sliding mode variable structure observer is present for synchronization and control of a class of chaotic systems with uncertainties. The approach is not only more robust with respect to noise and parameter mismatch in the error dynamics, but also does not need the upperbounds of the uncertainties in advance and the inertial filter. Theoretical analysis and simulation results proved the effectiveness of the method.3. Using a method of adaptive sliding mode variable structure observer for synchronization and control of a class of chaotic systems with multivariable transmission ,it through appropriate coordinate conversion to design a control law and a adaptation mechanism to achieve synchronization and control of a class of chaotic systems with multivariable transmitsion . The approach is not only more robust with respect to noise and parameter mismatch in the error dynamics, but also does not need the upperbounds of the uncertainties in advance . Theoretical analysis and simulation results illustrate the validity.