Premium
Revisiting the TP Model Transformation: Interpolation and Rule Reduction
Author(s) -
Silva Campos Víctor Costa,
Tôrres Leonardo Antônio Borges,
Palhares Reinaldo Martinez
Publication year - 2015
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.866
Subject(s) - mathematics , transformation (genetics) , mathematical optimization , model transformation , interpolation (computer graphics) , representation (politics) , reduction (mathematics) , fuzzy logic , fuzzy rule , tensor product , fuzzy control system , computer science , artificial intelligence , discrete mathematics , pure mathematics , motion (physics) , biochemistry , chemistry , geometry , consistency (knowledge bases) , politics , political science , law , gene
The tensor‐product ( TP ) model transformation is a numerical technique that finds a convex representation, akin to a Takagi‐Sugeno ( TS ) fuzzy model, from a given linear parameter varying ( LPV ) model of a system. It samples the LPV model over a limited domain, which allows the use of the higher order singular value decomposition ( HOSVD ) and convex transformations that leads to the TS representation of the LPV model. In this paper, we discuss different strategies that could be used on the sampling step of the TP model transformation (which in turn lead to different membership function properties of a TS fuzzy model). Additionally, this paper discusses how the other steps could be used to reduce the number of rules of a given TS fuzzy model. In cases where nonzero singular values were discarded in the rule reduction, we also show how to obtain an uncertain model that covers the original.