Robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors

This paper describes the design of the robust adaptive fuzzy controller for uncertain single-input single-output nonlinear dynamical systems with unknown nonlinearitics. These unknown nonlinearities are approximated by the fuzzy system with a set of fuzzy IF-THEN rules whose parameters are adjusted on-line according to some adaptive laws for the purpose of controlling the output of the nonlinear system to track a given trajectory. The Lyapunov synthesis approach is used to develop a state-feedback adaptive control algorithm based on the adaptive fuzzy model. The key assumption is that the reconstruction errors satisfy certain bounding conditions. The control law consists of two terms. One is the certainty equivalent control and the other is the bounding control. A bounding parameter adaptive law is used to obtain this bounding control. The overall control system guarantees that the tracking error converges in the small neighborhood of zero and that all signals involved are uniformly bounded. It is also shown that, in the special case, the tracking error exponentially converges to zero even though the approximation errors exist. (C) 2002 Elsevier Science B.V. All rights reserved.