Sliding window to identification of the ARX-Laguerre multimodel

In this paper, we illustrate the principle of development of multimodel approach based on the ARX-Laguerre model with its recursive vector representation. We propose an analytical solution to optimize the Laguerre poles which depend on Fourier coefficients defining the ARX-Laguerre multimodel, and that are identified using the RLS method. The identification procedures of the Laguerre poles and Fourier coefficients are combined and carried out on a sliding window to provide an online identification algorithm of the ARX-Laguerre multimodel. Therefore, we confirm by an example of numerical simulation the online identification performance. These simulations also validate the performance of the optimization method of the Laguerre poles.