Reducing the number of vertices in some Takagi-Sugeno models: example in the mechanical field

Thierry-Marie Guerra (1) , Miguel Bernal , Mathias Blandeau (1)

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

This paper is concerned with the building of application-oriented model-based Takagi-Sugeno models that arise from sector nonlinearity methodology. Despite its exactness, this modeling technique produces a polytopic embedding with a number of vertices of 2 raised to the number of nonlinearities which, if high, represents a rapid growth in the number of linear matrix inequalities (needed to solve even the simplest control and observation schemes). A solution for model reduction is proposed based on the similarity of Taylor approximations amongst nonlinearities, with a measurable bound on the approximation, which - as proven with a suitable application example - brings the methodology closer to real-time demands.

Mots clés: Model-based control; Model reduction; Convex optimization; Takagi-Sugeno models; Linear Matrix Inequalities; mechanical systems

Domaines: Automatique / Robotique

Thierry-Marie Guerra, Miguel Bernal, Mathias Blandeau. Reducing the number of vertices in some Takagi-Sugeno models: example in the mechanical field. 3rd IFAC Conference on Embedded Systems, Computational Intelligence and Telematics in Control CESCIT 2018, Jun 2018, Faro, Portugal. pp.133-138, ⟨10.1016/j.ifacol.2018.06.250⟩. ⟨hal-03411309⟩