New methods of Laguerre pole optimization for the ARX model expansion on Laguerre bases

The ARX-Laguerre model is a very important reduced complexity representation of linear system. However a significant reduction of this model is subject to an optimal choice of both Laguerre poles. Therefore we propose in this paper two new methods to estimate, from input/output measurements, the optimal values of Laguerre poles of the ARX-Laguerre model. The first method is based on the Newton-Raphson's iterative technique where we prove that the gradient and the Hessian can be expressed analytically. The second method is based on Genetic Algorithms. Both proposed algorithms are tested on a numerical example and on a heating benchmark.