Optimal expansions of multivariable ARX processes on Laguerre bases via the Newton-Raphson method

In this article, an optimal linear MIMO system approximation by using discrete-time MIMO autoregressive with exogenous input (ARX) model is proposed. Each polynomial function of the MIMO ARX model associated with the inputs and with the outputs is expanded on independent Laguerre orthonormal basis. The resulting model is entitled MIMO ARX-Laguerre model. The optimal approximation of which is ensured once the poles characterizing each Laguerre orthonormal basis are set to their optimal values. In this paper, a new method to estimate, from input/output measurements, the optimal Laguerre poles of the MIMO ARX-Laguerre model is proposed. The method consists in applying the Newton-Raphson's iterative technique in which the gradient and the Hessian are expressed analytically. The proposed algorithm is tested on a numerical example and on a benchmark system. Simulation results show the effectiveness of the proposed optimal modeling method. Copyright (c) 2015 John Wiley & Sons, Ltd.