Online Identification of Switched Arx-Laguerre Model Using Sliding Window Technique

The switched ARX-Laguerre model is a very important reduced complexity representation of a class of linear hybrid systems modeled by a switched Auto Regressive eXogenous model (SARX). This model is obtained by expanding the coefficients of every ARX sub-model on two independent Laguerre bases. Then, the SARX-Laguerre model is characterized by several Laguerre poles whose optimal values guarantee a significant parametric reduction. To identify the parameters of the SARXLaguerre model, we propose in this article an analytical method to optimize the poles and a recursive method to identify the Fourier coefficients. To create an online parametric identification algorithm of the SARX-Laguerre model we propose to realize the identification procedure on a sliding window. To evaluate the performance of the proposed online parametric identification algorithm of the SARX-Laguerre model, we use a numerical example.