Pole optimization of NARX-Laguerre model using Gradient method

The NARX-Laguerre model serves as a significantly simplified representation of nonlinear systems, achieved by expressing the coefficients of the NARX model through five independent Laguerre bases. This particular model is defined by five Laguerre poles, the optimal values of which ensure a noteworthy reduction in parameters. In this paper, we suggest an approach to estimate the NARX-Laguerre poles based on input/output measurements, employing the gradient method. The algorithm proposed for optimizing these poles is tested through a numerical example.