State-space LPV model identification using kernelized machine learning

This paper presents a nonparametric method for identification of MIMO linear parameter-varying (LPV) models in state-space form. The states are first estimated up to a similarity transformation via a nonlinear canonical correlation analysis (CCA) operating in a reproducing kernel Hilbert space (RKHS). This enables to reconstruct a minimal-dimensional inference between past and future input, output and scheduling variables, making it possible to estimate a state sequence consistent with the data. Once the states are estimated, a least-squares support vector machine (LS-SVM)-based identification scheme is formulated, allowing to capture the dependency structure of the matrices of the estimated state-space model on the scheduling variables without requiring an explicit declaration of these often unknown dependencies; instead, it only requires the selection of nonlinear kernel functions and the tuning of the associated hyper-parameters.