A Bayesian approach for model identification of LPV systems with uncertain scheduling variables

Abstract

This paper presents a Gaussian Process (GP) based Bayesian method that takes into account the effect of additive noise on the scheduling variables for identification of linear parameter-varying (LPV) models in input-output form. The proposed method approximates the noise-free coefficient functions by a local linear expansion on the observed scheduling variables. Therefore, additive noise on the scheduling variables is reconstructed as a corrective term added to the output noise that is proportional to the squared gradient obtained from the posterior of the Gaussian Process. An iterative procedure is given so that the obtained solution converges to the best estimation of the coefficient functions according to the given measure of fitness. Moreover, the expectation and covariance functions estimated by GP are modified for the noisy scheduling variable case to include the noise contribution on the estimated expectation and covariance functions. The model training procedure identifies noise level in the measurements including outputs and scheduling variables by estimating the noise variances, as well as other defined hyperparameters. Finally, the performance of the proposed method is compared to the standard GP approach through a numerical example.