Abstract

A new robust adaptive multiple models based fuzzy control scheme for a class of unknown nonlinear systems is proposed in this paper. The nonlinear system is expressed by using the Takagi–Sugeno (T–S) method, and some identification adaptive T–S models along with their corresponding controllers, are used in order to control efficiently the unknown system. The modeling error that is produced due to the use of the T–S plant model can cause instability problems if it is not taken into account in the adaptation rules. In this paper, in order to solve this problem, we design a control scheme that is based on updating rules that utilize the σ-modification method. Every T–S controller is updated indirectly by using the robust updating rules and the final control signal is determined by using a performance index and a switching rule. By using the Lyapunov stability theory it is shown that σ-modification based rules can ensure the robustness of the system and define a bound for the steady state identification error. The main objectives of the robust controller are: (i) to ensure that the real plant system will remain stable despite the existence of modeling errors and (ii) to ensure that the real plant will track with a high accuracy the state trajectory of a given reference model. The effectiveness of the proposed method is demonstrated by computer simulations on a well known benchmark problem.

Introduction

Robustness issues are very crucial in control systems design, especially in cases when fuzzy or neural networks (NNs) theory tools are used to mathematically express an unknown nonlinear plant [1] along with adaptive control techniques which are used to control the plant. The necessity for using fuzzy or NNs theory in system modeling is imperative when the system’s nonlinearities impose difficulties to the controller design procedure. One of the most popular fuzzy models is the T–S formulation [2]. The main advantage of this method is that it uses linear submodels which are fuzzy blended and finally produce the nonlinear fuzzy model. These linear models are easily controlled by using linear control techniques and finally another fuzzy blending of the subcontrollers produces the final nonlinear controller of the system. Another characteristic of T–S representation is the “universal function approximation” property which offers the possibility to approximate any nonlinear function to any degree of accuracy [3].