Universal Fuzzy Models and Universal Fuzzy Controllers for Stochastic Nonaffine Nonlinear Systems

This paper investigates the universal fuzzy model and universal fuzzy controller problems for stochastic nonaffine nonlinear systems. The underlying mechanism of stochastic fuzzy logic is first discussed, and a stochastic generalized fuzzy model with new stochastic fuzzy rule base is then given. Based on their function approximation capability, these kinds of stochastic generalized fuzzy models are shown to be universal fuzzy models for stochastic nonaffine nonlinear systems under some sufficient conditions. An approach to stabilization controller design for stochastic nonaffine nonlinear systems is then developed through their stochastic generalized Takagi-Sugeno (T-S) fuzzy approximation models. Then, the results of universal fuzzy controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy controllers, are also provided, respectively. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach.

I. Introduction

The takagi–sugeno (T–S)-type dynamic fuzzy model [1] has been recognized as one of the most successful tools to handle complex nonlinear systems. T–S fuzzy models enjoy great advantages in stability analysis and controller design for nonlinear systems because of their relatively simple and fixed structure, and universal function approximation capability. Significant efforts have been devoted to study the analysis and synthesis problems of T–S fuzzy control systems [1]–[9]. See the survey paper [3] and the references therein for details.