Reduced-Complexity Affine Representation for Takagi-Sugeno Fuzzy Systems

Amine Dehak (1) , Tran Anh-Tu Nguyen (1) , Antoine Dequidt (1) , Laurent Vermeiren (1) , Michel Dambrine (1)

1 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201

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.

Domaines: Automatique / Robotique

Amine Dehak, Tran Anh-Tu Nguyen, Antoine Dequidt, Laurent Vermeiren, Michel Dambrine. Reduced-Complexity Affine Representation for Takagi-Sugeno Fuzzy Systems. 21st IFAC (International Federation of Automatic Control) IFAC World Congress, Jul 2020, Berlin, Germany. pp.8031-8036, ⟨10.1016/j.ifacol.2020.12.2235⟩. ⟨hal-03405660⟩