Control And Synchronization Of Uncertain Chaotic Systems

The relative problems of chaos control and chaos synchronization are studied in this thesis using the methods of theoretical derivation and numerical simulation. The main achievements contained in the research are as follows:Synchronization control for a class of master-slave chaotic systems with parameter uncertainties, external noise disturbances and sector nonlinear input is analyzed. It designs a class of sliding mode controllers testifying theoretically that the effectiveness of the controller is beyond the impact from the parameter uncertainties and external noise disturbances of the system under control and thus it is of strong robust nature. The effectiveness of this controller is proved by numerical simulations for the master-slave Duffing-Holmes systems.Controller for uncertain Lorenz system with multiple inputs containing sector nonlinearities and deadzones is designed, its effectiveness is demonstrated theoretically. By this controller, the controlled Lorenz system can asymptotically drive the system orbits to arbitrarily objective trajectories, even .with, parameter uncertainties, sector nonlinearities and deadzones in the inputs, and the external noise. Thus it has strong robustness, and the effectiveness is proved by numerical simulations.A method of synchronization control for a class of uncertain master-slave chaotic systems with sector nonlinear inputs containing deadzones is proposed, and a sliding mode controller is designed. It theoretically demonstrates that, by this controller, the controlled master-slave chaotic systems can be synchronized quickly and effectively, even with uncertainties, sector nonlinearities and deadzones in the inputs, thus have strong robustness. Through the numerical simulations of the synchronization of Chen system with itself and with another Lu system, it demonstrates the effectiveness of this controller.Synchronization for a class of different chaotic systems is researched, and the synchronization of the slave system and the different master system with uncertain parameters is achieved. By the designed adaptive controller, the controlled Lii system can quickly synchronize to the Rossler system with uncertain parameters, and the controlled Lorenz system and Lu system can quickly and respectively synchronize to the Chen system with uncertain parameters.