Revisiting the TP model transformation : interpolation and rule reduction.

Abstract

The tensor-product (TP) model transformation is a numerical technique that finds a convex representation, akin to aTakagi-Sugeno (TS) fuzzy model, from a given linear parameter varying (LPV) model of a system. It samples the LPV modelover a limited domain, which allows the use of the higher order singular value decomposition (HOSVD) and convex transfor-mations that leads to the TS representation of the LPV model. In this paper, we discuss different strategies that could be usedon the sampling step of the TP model transformation (which in turn lead to different membership function properties of a TSfuzzy model). Additionally, this paper discusses how the other steps could be used to reduce the number of rules of a given TSfuzzy model. In cases where nonzero singular values were discarded in the rule reduction, we also show how to obtain anuncertain model that covers the original.