Estimation-based control law for appproximating Takagi-Sugeno-based controller

Abstract

This paper aims to manage the problem of matrix inversion in advanced Takagi-Sugeno-based controllers such as most of the non-Parallel Distributed Compensation. These controllers are difficult to use in embedded computers that have limited performances due to technologic resources. The originality of the proposed method is to use an observer written under the descriptor form for approximating the fuzzy matrix inversion. Thanks to such an observer, the advanced controller can be approximated in both steady and transient phases. Consequently, an Estimation-based Control Law for Approximating Takagi-Sugeno-based (ECLATS) controller is developed using Lyapunov stability analysis and Linear Matrix Inequalities formulation. This ECLATS controller can provide similar performances than the advanced fuzzy ones, but without any matrix inversion. Numerical examples prove the efficiency of the estimation by comparison.