Fuzzy Systems Approach to Approximation and Stabilization of Conventional Affine Nonlinear Systems

This paper investigates the stabilization of conventional nonlinear systems by fuzzy control approach. Firstly, it is shown that the class of nonlinear systems whose stabilization problem can be solved by the fuzzy control approach available today based on T-S fuzzy control models is affine nonlinear systems as this is the only class of nonlinear systems which can be approximated to any degree of accuracy by T-S fuzzy control models; secondly, it shows that the stabilization problem of an affine nonlinear system can be solved as a robust stabilization problem of its T-S fuzzy approximator with approximation error bound as the system uncertainty bound; thirdly, for an affine nonlinear system, an approximation scheme is proposed to construct its T-S approximator and the corresponding approximation error bound is obtained; finally, it discusses briefly how to solve the stabilization problem of an affine nonlinear system by solving its corresponding robust stabilization problem based on its T-S fuzzy approximator and approximation error bound by Lyapunov's method.

I. Introduction

Fuzzy control approach is usually viewed as a control methodology for model-unknown systems. For a given model-unknown nonlinear control system, such an approach usually divides into two phases: The first phase is using a T-S fuzzy system as the model of the given system and identifying the parameters of the fuzzy system by learning from data; After such a fuzzy model of the given model-unknown system is identified, the second phase is stability analysis and control design based on Lyapunov method. Most recent progresses in fuzzy system identification and control are based on such an approach.