Direct adaptive fuzzy controller with small number of fuzzy rules for nanaffine nonlinear system

A direct adaptive state-feedback controller for highly nonlinear systems is proposed. This paper considers uncertain or ill-defined nonaffine nonlinear systems and employ a static fuzzy logic system (FLS) with flexible structure, i.e., on-line variation of the number of fuzzy rules. The FLS approximates and adaptively cancels an unknown plant nonlinearity. A control law and adaptive laws for unknown fuzzy parameters and bounding constant are established so that the whole closed-loop system is stable in the sense of Lyapunov. The tracking error is guaranteed to be uniformly asymptotically stable rather than uniformly ultimately bounded with the aid of an additional robustifying control term. No a priori knowledge of an upper bound on a lumped uncertainty is required.