Adaptive Robust Control For State-Delayed And Uncertain Nonlinear Systems

The control problem of nonlinear systems has been the hot and difficult topic in the present control theory investigation. As we known that nonlinear systems exit in the world extensively, so it is important to investigate adaptive robust control of nonlinear systems. Based on the existing literature, some work has been done in this paper on adaptive robust control of nonlinear systems.We first consider the design problem of robust sliding-model controller for a class of more extensive nonlinear time-delay systems. And a robust exponential approach law sliding mode control method is proposed for the system based on partial differential transformation, that can weakens the control input chattering effectively. Based on sliding control technique and Lyapunov stability method, the system can overcomes the influence of uncertainty, and the system state can be droved into a sliding-mode plane in finite time, and the system stability is also guaranteed.Then, we focus on investigating the problem that too many approximators are used in the controller design of unknown nonlinear systems. Only one fuzzy logic system is employed as approximator to compensate all the unknown items, and at the same time, adaptive technology is adopted on line to identify the unknown parameter. The problem of explosion of complexity in backstepping design procedure is overcome by using the dynamic surface control method. It is proved by constructing appropriate Lyapunov function that all the signals of the closed-loop system are semi-globally ultimate uniformly bounded.Finally, the problem of robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems has been investigated. Considering''explosion of complexity''in backstepping design procedure, a novel adaptive fuzzy dynamic surface model is proposed to approximate uncertain nonlinear functions by using only one fuzzy logic system. We prove the approximation capability of this model and apply it to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. It is proved by constructing appropriate Lyapunov functions that all signals of closed-loop systems are semi-globally ultimate uniform bounded. And this novel method is further investigated by comparing with the adaptive SMC (sliding mode control) method.