Observer Based Adaptive Fuzzy Controller with Modulated Membership Functions for Nonlinear System

Abstract

An observer based adaptive fuzzy controller for nonlinear system is proposed. Parameters in the proposed adaptive fuzzy controller are tuned on-line by the genetic algorithm (GA). For on-line tuning, a parsimonious parameterization scheme for fuzzy controller called orthogonal modulated membership functions (mmf)35 is utilized. A simplified GA called micro GA that greatly improves the learning efficiency is applied. The valid range of mmf parameters will be proved in this paper. With the valid range of mmf parameters, the search by MGA for the optimal parameterization of the adaptive fuzzy controller is more focused resulting in fast convergence to the optimal solutions. A Lyapunov theorem based supervisory control is added to the fuzzy controller assuring that close loop stability is always maintained for the adaptive fuzzy controller during the learning process.