Adaptive Fuzzy Control For A Class Of Uncertain Nonlinear System

In practice, it is very difficult to get the precise mathematical model from the traditional modelingmethod. Fuzzy systems with a collection of fuzzy if-then rules are capable of approximating any nonlinearuncertain continuous function on a compact set with arbitrary accuracy. Because of not requiring precisemathematical models,fuzzy control has been successfully applied to many control problems. Adaptivefuzzy control for nonlinear systems has been received more and more attention in recent years. Adaptivefuzzy control is a research field which is composed of the theory of fuzzy control and adaptive control. Thesystem of adaptive fuzzy control can not only improve system performance by modifying itself rules but alsohas quick convergence speed and robust. But, in adaptive fuzzy control researches, the direct and indirectadaptive fuzzy control approaches are usually used in many schemes which just utilize the information ofplant or the fuzzy control rules. The knowledge of experts or human experience can not be used sufficientlyin these control schemes and most methods are designed under the assumption that approximation errorssatisfy squared integral conditions. However, in practice, the approximation error is difficult to satisfysquared integral conditions.In this paper, a comprehensive adaptive fuzzy control strategy is presented for a class of uncertainnonlinear SISO systems with disturbances. The information of plant and the fuzzy control rules is utilizedadequately for the design of this control strategy . The comprehensive controller is composed of three parts:tracking control part, continuous supervisor part and adaptive compensator part.The tracking control part isused to obtain desired output tracking performance; the continuous supervisor part is to guarantee the boundof system states, and the adaptive compensator part is to simultaneously compensate both the approximationerror of fuzzy logic system and the effect of the external disturbances. In stability analysis, the term ofminimum approximation error to be squared integral is not needed. By Lyapunov method, the closed-loopcontrol system is proved to be globally stable, with tracking error converging to zero. Simulations resultsshow that better tracking performance is obtained by using this method compared with the direct or indirectadaptive fuzzy control approaches.