Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems

TLDR

This paper presents a systematic procedure for fuzzy control system design that includes fuzzy model construction, rule reduction, and robust compensation for nonlinear systems. The method constructs a generalized Takagi‑Sugeno fuzzy model with a decomposed A_i and B_i structure, successively reduces IF‑THEN rules while converting reduction errors into model uncertainties, and then designs a decay‑rate controller that guarantees robust stability. Two illustrative examples confirm the effectiveness of the systematic procedure.

Abstract

This paper presents a systematic procedure of fuzzy control system design that consists of fuzzy model construction, rule reduction, and robust compensation for nonlinear systems. The model construction part replaces the nonlinear dynamics of a system with a generalized form of Takagi-Sugeno fuzzy systems, which is newly developed by us. The generalized form has a decomposed structure for each element of A/sub i/ and B/sub i/ matrices in consequent parts. The key feature of this structure is that it is suitable for constructing IF-THEN rules and reducing the number of IF-THEN rules. The rule reduction part provides a successive procedure to reduce the number of IF-THEN rules. Furthermore, we convert the reduction error between reduced fuzzy models and a system to model uncertainties of reduced fuzzy models. The robust compensation part achieves the decay rate controller design guaranteeing robust stability for the model uncertainties. Finally, two examples demonstrate the utility of the systematic procedure developed.