Optimal Laguerre series expansion of discrete volterra models

This paper is concerned with the selection of optimal Laguerre bases for the orthonormal series expansion of discrete-time Volterra models. The aim is to minimize the number of functions needed to provide a given approximation accuracy, thus simplifying the modeling and control problems associated with these models. This issue was addressed by Fu and Dumont [8] focusing on linear systems, which are equivalent to a first-order Volterra model. The present work is a generalization of the work mentioned above focusing on second-order models. The main result is an analytic strict global solution for the optimal expansion of the second-order Volterra kernel. An example is provided to illustrate some theoretical aspects of the mathematical results presented in the paper.