Shrinking complexity of scheduling dependencies in LS-SVM based LPV system identification

Abstract

In the past years, Linear Parameter-Varying (LPV) identification has rapidly evolved from parametric identification methods to nonparametric methods allowing the relaxation of restrictive assumptions. For example, Least-Square Support Vector Machines (LS-SVMs) offer an attractive way of estimating LPV models directly from data without requiring from the user to specify the functional dependencies of the model coefficients on the scheduling variable. These methods have also been recently extended in order to automatically determine the model order directly from data by the help of regularization. Nonetheless, despite all these recent improvements, LPV identification methods still require some strong a priori such as i) the dependencies are static or dynamic, ii) it is known which variables are considered to be the scheduling or iii) all coefficient functions of the underlaying system depend on all scheduling variables. This prevents the complexity of the scheduling dependency of the model to be shrunk gradually and independently until an optimal bias-variance trade off is found. In this paper, a novel reformulation of the LPV LS-SVM approach is proposed which, besides of the non-parametric estimation of the coefficient functions, achieves data-driven coefficient complexity selection via convex optimization. The properties of the introduced approach are illustrated by a simulation study.