Adaptive Fuzzy Control With Guaranteed Convergence of Optimal Approximation Error

Abstract

With no a priori knowledge of plant boundary functions, a novel direct adaptive fuzzy controller (AFC) for a class of single-input single-output (SISO) uncertain affine nonlinear systems is developed in this paper. Based on the theory of fuzzy logic systems (FLSs) with variable universes of discourse (UDs), sufficient conditions that guarantee that the optimal fuzzy approximation error (FAE) is locally convergent are given. By the use of the output tracking error and its derivatives as input variables and by the selection of suitable adjusting parameters, a variable UD FLS with an optimal FAE local convergence is constructed, and its parameter adaptive law is derived by virtue of the Lyapunov stability theorem. Under the assumption that the optimal FAE is bounded, it is proved that the closed-loop system is asymptotically stable in the sense that all variables are uniformly ultimately bounded and that the tracking errors converge to zero. The proposed approach eliminates the influence of the FAE on the tracking errors by means of the inherent mechanism of the variable UD FLS. Thus, it has the potential to achieve high control performance without additional compensation under only a few fuzzy rules. Simulation studies demonstrate the superiority of the proposed AFC in terms of the settling time, tracking accuracy, smoothness of the control input, and robustness against external disturbances and parameter variations.