The Research On Adaptive Sliding Mode Control Of A Class Of Nonlinear Chaotic System

Chaos is a special complex behavior in dynamic discipline,which can not be predicted for a long time and is sensitive to the initial value.Chaos control and synchronization have become the focus of research because of the application of chaos in secure communication,digital communication,biological system and so on.The research on chaos control and synchronization has made great progress.However,how to make full use of chaos can bring benefits to our life is still a subject worthy of study.In this paper,through the theoretical proof and numerical simulation,the following contents have been studied.For a class of third-order chaotic systems,its stability was studied considering the unavoidable disturbance of the system.Under the condition of that we ensure the system has a unique solution,then we assume that a function of the system or an added function is used to represent the unknowns of the system.Based on Lyapunov stability theory,the method of an adaptive sliding-mode control is proposed in order to realize the stability of the system.The effective controller was designed under the condition,and it is proved that the state vector of the system tends to zero asymptotically in the presence of unknown disturbances by using this controller.Finally,using the example to simulate,and the trajectory of each state of the system verifies the validity of the designed controller.The synchronization problem of a kind of drive response chaotic system was studied.The response system in this kind of system has the same structure as the drive system except that it has unknown parameters and is influenced by external disturbance.Aiming at this kind of system,the dynamic error system between the drive system and the response system is given,and the problem of synchronization is transformed into the problem of realizing the stability of the dynamic error system.The condition that the state vector of the dynamic error system can be asymptotically stable was obtained,Two kinds of design methods of adaptive sliding mode control are proposed and two adaptive controllers were designed.According to the validity of the control law,the theory is proved and the simulation results show that the control law is valid.Finally,the characteristics of the proposed two methods are described.