Adaptive Control Of Nonlinear Systems And Chaotic Synchronization Control

The practical systems are almost nonlinear, therefore, the study of adaptive control of nonlinear with uncertain parameters are of great significance both in theory and in practical application. Adaptive control is considered as one of the most effective approaches when solving the control problem of uncertain dynamics with unkonwn constant parameters, because adaptive control can adjust control gains or system parameters online to adapt to the affection factors of environmental changes or disturbance, ect. Hence, asymptotic convergence of tracking error is obtained when time approaches to infinite. However, for estimation of parameters, only boundedness can be guaranteed. It is always hoped that estimation of parameter can converge to its true value, this target can be realized by constructing strong Lyapunov functions (positive definite, radially unbounded and its derivative is negative definite) of systems. During the last two decades, chaos control and synchronization has become one of the hot topics in nonlinear science field, and exhibits wide-scope potential application in various disciplines such as secure communication, information engineering and life science and so on. Adaptive control approach has been widely used to dealing with control and synchronization of chaotic systems with uncertain parameters.Based on Lyapunov stability theory,this dissertation considers the parameters convergence properties of strict-feedback nonlinear systems and synchronization of (hyper)chaotic systems from an adaptive control viewpoint. The main contributions included in the dissertation are summarized as follows.Firstly, a strict-feedback nonlinear systems is developed. The design of both the control and the update laws are based on Backstepping techniques and tuning function schemes. Under an appropriate persistency of excitation condition, it is shown that all the closed-loop signals are globally uniformly bounded and both convergence of the tracking error and parameter estimation error to zero asymptotically, by constructing an explicit, global, strong Lyapunov function. The feasibility and effectiveness of the proposed method is illustrated with a simulation example.Secondly, based on Lyapunov stability theory, control laws and parameter update laws are designed for two different hyperchaotic systems with fully uncertain parameters, the states of the drive system and the response system are ultimately asymptotically hybrid projective synchronization. Simulation results are presented to show the feasibility and effectiveness of the proposed methodAt last, a learning control approach is applied to the function projective synchronization of different chaotic systems with unknown periodically time-varying parameters. According to Lyapunov-Krasovskii functional stability theory, a differential-difference mixed-type parametric learning laws and an adaptive learning control laws are constructed to make the states of two different chaotic systems asymptotically synchronized. The approach is successfully applied to the functional projective synchronization between Lorenz system and Chen system. Numerical simulations results are presented to verify the effectiveness of the proposed approach.