ABSTRACT
This chapter presents the reasons and advantages of the approximation and complexity trade-off readily supported by the tensor product (TP) model transformation through the extraction of nonexact representation of quasi-linear parameter-varying (qLPV) models. Specifically, Sections 5.1 and 5.2 show mathematically that the set of functions possibly approximated to arbitrary degrees of accuracy by TP models with a bounded number of components lies nowhere dense in the set of continuous functions. This property hence necessitates a trade-off between the accuracy and complexity of the TP form for a certain class of modeling and control problems. The present content is based mostly on the works of [TBP02], [BKPH04], [TBP07], [BPK+07], [BYVKP03], [BYVK+02]. Again, readers who are less interested in the mathematical details of the theory may skip the first two sections and move to the examples given in Section 5.3.
