System modeling based on ARX-Laguerre bases

In this work a new black-box linear ARX-Laguerre model has been introduced to overcome the handicap of the over parametrization problem in the ARX model. This is obtained by proposing the expansion of the ARX model parameters associated with the input and the output on two independent Laguerre orthonormal bases. This new linear representation is characterized by filtering the input and the output as well of the system represented by the ARX model. The new ARX-Laguerre model is used to reduce the complexity parametric of two nonlinear model: the multimodel ARX and the NARX model. These decomposition given two new reduced complexity nonlinear model entitled respectively the multimodel ARX-Laguerre and the NARX-Laguerre. The parsimony of the expansion is strongly linked to the choice of the poles defining both Laguerre bases.