A Bayesian approach for estimation of linear-regression LPV models

In this paper, a Bayesian framework for identification of linear parameter-varying (LPV) models with finite impulse response (FIR) dynamic structure is introduced, in which the dependency structure of LPV system on the scheduling variables is identified based on a Gaussian Process (GP) formulation. Using this approach, a GP is employed to describe the distribution of the coefficient functions, that are dependent on the scheduling variables, in LPV linear-regression models. First, a prior distribution over the nonlinear functions representing the unknown coefficient dependencies of the model to be estimated is defined; then, a posterior distribution of these functions is obtained given measured data. The mean value of the posterior distribution is used to provide a model estimate. The approach is formulated with both static and dynamic dependency of the coefficient functions on the scheduling variables. The properties and performance of the proposed method are evaluated using illustrative examples.