Universal fuzzy models and universal fuzzy controllers based on generalized T-S fuzzy models

This paper investigates the universal fuzzy models problem and universal fuzzy controllers problem for discrete-time general nonlinear systems based on a class of generalized T-S fuzzy models. The generalized T-S fuzzy models, which are shown to be universal function approximators, are also proved to be universal fuzzy models for non-affine nonlinear systems under some sufficient conditions. The results of static and dynamic universal fuzzy controllers for two classes of nonlinear systems are then given, respectively, and constructive procedures to obtain the universal fuzzy controllers are also provided.

I. Introduction

Takagi and Sugeno (T-S) type fuzzy models [1] have been widely studied in recent decades and proved to be one of the most successful approaches to control design of complex nonlinear systems [2]–[8]. A T-S fuzzy model describes a nonlinear system by a set of fuzzy IF-THEN rules in the form of local linear or affine models which are smoothly connected by fuzzy membership functions. And this relatively simple and uniform structure demonstrates great advantages in stability analysis and controller design of fuzzy control systems in view of powerful conventional control theory. Due to the great efforts of researchers, a large volume of works on theoretical results of stability analysis and controller synthesis of T-S fuzzy systems have been reported in fuzzy control literature [1]–[8].