Modeling of Takagi-Sugeno Fuzzy Control Design for Nonlinear Systems

Pu-Sheng Tsai ； Ter-Feng Wu ； Nien-Tsu Hu ； Jen-Yang Chen

《電腦學刊》 28卷2期 (2017/04) Pp. 207-216

https://doi.org/10.3966/199115592017042802016

摘要

In this paper, we first develop a procedure for constructing Takagi-Sugeno fuzzy systems from input-output pairs to identify nonlinear dynamic systems. The fuzzy system can approximate any nonlinear continuous function to any arbitrary accuracy that is substantiated by the Stone Weierstrass theorem. A learning-based algorithm is proposed in this paper for the identification of T-S models. Our modeling algorithm contains four blocks: fuzzy C-Mean partition block, LS coarse tuning, fine turning by gradient descent, and emulation block. The ultimate target is to design a fuzzy modeling to meet the requirements of both simplicity and accuracy for the input-output behavior. In the second part, we propose a discrete time fuzzy system that is composed of a dynamic fuzzy model and a fuzzy state feedback controller. This requires that for all the local linear models, a common positive-definite matrix P can be found to satisfy the Lyapunov stability criterion, although this is an extremely difficult problem for all systems. Thus in this paper, Fuzzy controller design is divided into two procedures. In the first step, we express the fuzzy model by a family of local state space models, and the controller is designed by state feedback control law for each local linear state space model. In the second step, we establish a global stability condition to guarantee the stability of the global closed loop system in order to circumvent the problem of determining the common P.

關鍵字

fuzzy modeling ； linear matrix inequality ； Lyapunov stability criterion ； maximum gradient descent ； parameter identification