Creating Sparse Rational Approximations for Linear Fractional Representations Using Genetic Programming

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  author =       "Georges Hardier and Clement Roos and Cedric Seren",
  title =        "Creating Sparse Rational Approximations for Linear
                 Fractional Representations Using Genetic Programming",
  booktitle =    "3rd IFAC International Conference on Intelligent
                 Control and Automation Science, ICONS 2013",
  year =         "2013",
  editor =       "Pedro M. Ferreira",
  pages =        "393--398",
  address =      "Sichuan, Chengdu, China",
  month =        sep # " 2-4",
  publisher =    "International Federation of Automatic Control",
  keywords =     "genetic algorithms, genetic programming",
  bibdate =      "2014-11-28",
  bibsource =    "DBLP,
  isbn13 =       "978-3-902823-45-8",
  URL =          "",
  DOI =          "doi:10.3182/20130902-3-CN-3020.00065",
  abstract =     "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 modelling
                 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
                 mu-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

Genetic Programming entries for Georges Hardier Clement Roos Cedric Seren