Research On Synchronization And Control Of Chaos Based On Backstepping Theory

To construct general scalar (hyper) chaotic signal synchronization systems, the controllers of (hyper) chaotic signal synchronization systems are designed based on backstepping design theory under different constraints in this thesis. The main work of this thesis is presented as follows:1. First a backstepping design of the controller is proposed for a class of nonlinear systems with known parameters in the strict-feedback form, then an adaptive backstepping design of the controller is proposed for such systems with unknown parameters. Using the controller proposed, the closed-loop error systems can asymptotically stabilize.2. A general scalar chaotic signal synchronization system is developed by taking the system in the strict-feedback form as the response system in which the parameters and the weights of the artificial control terms are both variant. A feedback controller and associated parameter adaptive laws are constructed via adaptive backstepping approach with tuning functions under an assumption that the parameters and the structure of the system which provides a scalar chaotic signal are known. Using the controller and the parameter adaptive laws proposed, the output of the general system asymptotically synchronizes with any scalar chaotic signal. Both theory analysis and simulation results illustrate the validity of the general scalar chaotic signal synchronization system and its controller.3. Based on the nonlinear control system theory and backstepping approach, a systematic procedure is developed for the design of a nonlinear feedback controller to control the output signal of a smooth (hyper) chaotic system to asymptotically synchronize with any scalar (hyper) chaotic signal of any unknown (hyper) chaotic system under an assumption of the (hyper) chaotic signal with r-order continuous derivatives. The result, which is global, is rigorously proved by means of Lyapunov theory. Simulation results also illustrate the validity of the controller.4. Based on extended state observer and the design of a controller via backstepping, a general scalar chaotic signal synchronization system is developed First the driversystem which provides a chaotic reference signal is looked upon a standard or standard-like system, then a nonlinear response system in the strict-feedback form is constructed. The states and the structure of the driver system are estimated by an extended state observer. The controller is designed via backstepping approach to control the output of the general response system to asymptotically synchronize with any scalar chaotic signal under some assumptions of the scalar chaotic reference signal without r-order continuous derivatives and the driver system with unknown parameters and unknown structure. Both theory analysis and simulation results illustrate the validity of the general scalar chaotic signal synchronization system.