A novel adaptive fuzzy variable structure control for a class of nonlinear uncertain systems via backstepping

Abstract

This paper presents a new design of adaptive fuzzy variable structure control to solve the traditional problem of model reference adaptive control (MRAC) for a class of single-input, single-output minimum-phase uncertain nonlinear systems via backstepping. Instead of taking the tedious coordinate transformation and yielding a “hard” high-gain controller, we introduce smooth B-spline-type membership functions into the controller so as to compensate for the uncertainties much “softer”, i.e., in a much smoother and locally weighted manner. To be rigorous, it is shown that the stability of the closed-loop system can be assured and the tracking error can globally approach to an arbitrary preset dead-zone range. In order to demonstrate the effectiveness of the developed novel controller, an example is extensively simulated to provide quite satisfactory performance.