Reduced-Complexity Affine Representation for Takagi-Sugeno Fuzzy Systems

Abstract

This paper presents a systematic approach to reduce the complexity of sector nonlinearity TS fuzzy models using existing linear dependencies between local linear submodels. The proposed approach results in a decrease of the fuzzy model rules from 2P to p + 1 rules while maintaining equivalence to the TS fuzzy model. An LMI formulation is presented to obtain conditions for stability analysis and stabilizing controllers design with some examples to offer a comparison between the two models. The main purpose of reduced-complexity models is to keep the design and the structure of the nonlinear control and observer schemes as simple as possible for real-time implementation, especially when dealing with highly nonlinear systems with a very large number of premise variables. Two real-world robotics examples are provided to highlight the interests and the curent limitations of the proposed approach.