Parallel Distributed Fuzzy Sliding Mode Control for Nonlinear Mismatched Uncertain Systems

Abstract

A new design approach of a parallel distributed fuzzy sliding mode controller for nonlinear systems with mismatched time varying uncertainties is presented in this paper. The nonlinear system is approximated by the Takagi-Sugeno fuzzy linear model. The approximation error between the nonlinear system and the fuzzy linear model is considered as one part of the uncertainty in the uncertain nonlinear system. The time varying uncertainties are assumed to have the format which enables the design of the coefficient matrix of the sliding function to satisfy a sliding coefficient matching condition. With the sliding coefficient matching condition satisfied, a parallel distributed fuzzy sliding mode controller (PDFSC) is designed. The stability and the sliding mode of the fuzzy sliding control system are guaranteed. Also, the nonlinear system is shown to be invariant on the sliding surface. Moreover, the chattering around the sliding surface in the sliding mode control can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed fuzzy sliding mode controller.

Control and synchronization of chaotic systems using a novel indirect model reference fuzzy controller

“…In some of these approaches, the fuzzy system is used as a powerful general function approximator, and different classical methods are used to estimate the parameters of the fuzzy control system. For example, Tao and Taur (2007) proposed a fuzzy sliding mode controller, and Chen et al (2009) investigated a fuzzy identification-based backstepping controller. The model reference adaptive control system is an adaptive servo system, in which the desired performance is expressed in terms of a reference model (Astrom 2008).…”