Nonlinear Observer-based Chaotic Synchronization Control Study

Study on chaotic synchronization control , the controllers of (hyper) chaotic synchronization systems are designed based on nonlinear state observers design theory under different constraints in this thesis. 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 studies the existence problem of observers based on Lyapunov stability theory, and summarizes the study trends of nonlinear observers, compares the various design methods of nonlinear observers.2. The scheme of the synchronization for a class of chaotic systems which contains a scalar nonlinear part by an observers is simple and effective in this paper. It designs subtly the output of chaotic systems applied Hurwitz theorem, recombines pole-assignment theory, realizes synchronization for a class of chaotic systems based on the observers design of chaotic systems.3. We present the design methods of nonlinear observer in accordance with nonlinear term satisfying Lipschitz condition and dissatisfying Lipschitz condition based on single variable transmission. Chaotic systems and observer are regarded as objective and response. By means of the design scheme of observer can realize the synchronization control of a class of chaotic systems.4. By the state feedback exact linearization method and observer theory, a control approach is presented for a class of chaotic systems in which state variables cannot be all measured. The approach projects feedback control law by state feedback exact linearization method, finds feedback control law based on observers using estimated state instead of unknown state in feedback control law of chaotic systems. The method can realize stabilization control and track of chaotic systems, and simulation results illustrate the validity.