LPV Model Order Selection from Noise-corrupted Output and Scheduling Signal Measurements

摘要

In parametric identification of Linear Parameter-Varying (LPV) systems, it is important to achieve a low variance of the model estimate by limiting the number of parameters to be identified. This is the well known “model order selection” problem, which consists of selecting the number of input and output delays and the basis functions characterizing the dependence of the LPV model parameters on the scheduling signal. Ignoring the effect of noise on the observations of the scheduling signals may lead to a bias in the final estimate and, as a consequence, also to an incorrect selection of the model order. In this paper, we introduce a “bias-corrected cost function” for the identification of LPV systems from noise-corrupted observations of the output and scheduling variable. The introduced cost function provides a bias-free parameter estimation along with model order selection. The proposed identification approach has two main advantages: (i) the problem of model order selection can be handled by adding a LASSO-like penalty term to the bias-corrected cost function; (ii) it provides a bias-free cost as a criterion to tune some hyper-parameters influencing the final parameter estimate.