Unmodeled Dynamics Of Nonlinear Systems, Adaptive Control Theory

In this paper, robust adaptive control problems for two classes of nonlinear systems with unmodeled dynamics are investigated. The main results can be listed as follows:In Chapter 1, we summarize the development of adaptive control theory, and point out the two problems to be solved in this paper.In Chapter 2, for a class of nonlinear systems with dynamic uncertainties, robust adaptive stabilization problem is considered. Firstly, by introducing an observer, an augmented system is obtained. Based on the system, we construct reasonably an exp-ISpS Lyapunov function for the unmodeled dynamics, then we obtain an available dynamic signal to dominate the dynamic disturbances. Then an adaptive backstepping controller design scheme is given, nonlinear damping terms are used to conteract the uncertain nonlinear functions. Finally, it is proved that all the signals in the adaptive control system are globally uniformly ultimately bounded. Furthermore, the output can be steered to the origin with any prescribed accuracy. A simulation example further demonstrates the efficiency of the control scheme.Chapter 3 considers the robust adaptive control problem for a class of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions, where the unmodeled dynamics include zero dynamics and output unmodeled dynamics. By using the backstepping technique together with changing supply function method, an adaptive output feedback controller is designed. According to stochastic small-gain theorem, it is shown that all the solutions of the closed-loop system are uniformly bounded in probability, and the output can be regulated to a small neighborhood of the origin in probability. A simulation example demonstrated the control scheme.In Chapter 4, we give the conclusions of this paper and a prospect of thefuture research work .