Creating Sparse Rational Approximations for Linear Fractional Representations using Genetic Programming

The objective of this paper is to stress that the size of a Linear Fractional Representation (LFR) significantly depends on the way tabulated or irrational data are approximated during the modeling process. It is notably shown that rational approximants can result in much smaller LFR than polynomial ones. In this context, a new method is introduced to generate sparse rational models, which avoid data overfitting and lead to simple yet accurate LFR, thanks to a symbolic regression technique. Genetic Programming is implemented to select sparse monomials and coupled with a nonlinear iterative procedure to estimate the coefficients of the surrogate model. Furthermore, a μ-analysis based proof is given to check the nonsingularity of the resulting rational functions. The proposed method is evaluated on an aeronautical example and successfully compared to more classical approaches.