Generalized expectation–maximization approach to LPV process identification with randomly missing output data

• The parameter varying property of the system and the missing output data problem are handled simultaneously.
• The prior distributions of the multi-mode LPV FIR model parameters are constructed.
• The algorithm to estimate parameters of the prior distributions and LPV model simultaneously from process data is derived.
• The algorithm to estimate the multi-mode LPV OE model is derived.
• The proposed algorithm is verified through a pilot-scale experiment.

This paper considers parameter estimation for linear parameter varying (LPV) systems with randomly missing output data. The multi-model LPV model is adopted and the identification problem is formulated under the scheme of the generalized expectation–maximization (GEM) algorithm. In order to deal with the missing output data, the local models are firstly taken to have the finite impulse response (FIR) model structure. To alleviate potential overparameterization problem, a prior on FIR model coefficients is imposed and the GEM algorithm is modified to derive the maximum a posterior (MAP) estimates of the multi-mode LPV FIR model parameters. Since the FIR model is not suitable for general control applications, a multi-mode LPV output error (OE) model is then identified by applying the GEM algorithm to the same identification data set with parameters initialized based on the estimated FIR models. One simulation example and two experiments are presented to demonstrate the efficiency of the proposed method.