Comments on 'Identification of non-linear parametrically varying models using separable least squares’ by F. Previdi and M. Lovera: black-box or open box?

This note compares and contrasts the non-linear parameter varying (NLPV) and state-dependent parameter (SDP) model classes. It shows that, while they have similarities, the two-stage SDP modelling procedure, involving non-parametric identification, followed by parametric estimation, is quite different from the single stage NLPV procedure. In particular, the SDP procedure allows for the identification of the model structure and the nature of the non-linearities, prior to the estimation of the parameters that characterize this identified model structure. In contrast to NLPV modelling, therefore, SDP estimation opens up the ‘black box’ and reveals the inner nature of the non-linear system.