Polynomial and rational approximation with the APRICOT Library of the SMAC toolbox

The APRICOT Library of the new SMAC Toolbox for Matlab implements a set of optimization tools to convert numerical data into simple yet accurate polynomial or rational expressions. Approximants are obtained, for which the number of terms in the numerator and denominator is as low as possible. The motivations for generating sparse expressions are twofold. First, it is a natural way to prevent data overfitting and to ensure a smooth behavior between the points used for approximation. Then, it allows simple Linear Fractional Representations to be obtained, which are tractable for analysis and design purposes. This paper surveys the main existing approximation techniques, which are all implemented in the APRICOT Library. It also applies them to model the drag coefficient of a generic fighter aircraft benchmark.