An RKHS Approach to Controlling Smoothness in Nonparametric LPV-IO Identification

Abstract

Although kernel methods have been successfully applied to many different problems in system identification, choosing an optimal kernel structure can be challenging - particularly in higher-order problems. However by noting that structural information, such as linearity, separability and smoothness, is contained in the functional derivatives, it can be seen that the kernel selection problem can be reduced to a simpler regularisation problem over specified derivatives. In this vein, here a novel approach to the control of smoothness in nonparametric LPV identification is proposed. By constraining the derivatives of the scheduling dependencies through a regularisation term, the model smoothness can be linearly controlled through the regularisation hyper parameter, without needing to optimise over the kernel function. A simulation example is presented to show how different structural hypotheses can be tested at minimal extra cost to the user, with the proposed approaches validated against a method from the literature.