LPV model identification with an unknown scheduling variable in the presence of missing observations – a robust global approach

Abstract

This study focuses on identifying the linear parameter varying (LPV) system with an unknown scheduling variable in the presence of missing measurements and the system output data contaminated with outliers. The parameter interpolated LPV autoregressive exogenous (ARX) model with an unknown scheduling variable is considered and the scheduling variable dynamic is described by a non-linear state-space model. The outliers treatment and unknown scheduling variable estimation with missing observations are both taken into consideration. The robust LPV model is established based on the Student's t -distribution in order to handle the outliers and the particle smoother is adopted to estimate the true scheduling variable from incomplete data set. The formulations of the proposed algorithm are finally derived in the expectation-maximisation algorithm scheme and the formulas to estimate the unknown parameters of LPV ARX model and scheduling variable dynamic model are derived simultaneously. A numerical example and a chemical process are used to present the efficacy of the proposed approach.