An Algorithm for Converting Nonlinear Differential Equations to Integral Equations with an Application to Parameter Estimation from Noisy Data

  • François Boulier
  • Anja Korporal
  • François Lemaire
  • Wilfrid Perruquetti
  • Adrien Poteaux
  • Rosane Ushirobira
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8660)


This paper provides a contribution to the parameter estimation methods for nonlinear dynamical systems. In such problems, a major issue is the presence of noise in measurements. In particular, most methods based on numerical estimates of derivations are very noise sensitive. An improvement consists in using integral equations, acting as noise filtering, rather than differential equations. Our contribution is a pair of algorithms for converting fractions of differential polynomials to integral equations. These algorithms rely on an improved version of a recent differential algebra algorithm. Their usefulness is illustrated by an application to the problem of estimating the parameters of a nonlinear dynamical system, from noisy data.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • François Boulier
    • 1
  • Anja Korporal
    • 2
  • François Lemaire
    • 1
  • Wilfrid Perruquetti
    • 2
    • 3
  • Adrien Poteaux
    • 1
  • Rosane Ushirobira
    • 2
  1. 1.Computer Algebra GroupUniversité Lille 1, LIFL, UMR CNRS 8022France
  2. 2.Inria, Non-A teamFrance
  3. 3.École Centrale de Lille, LAGIS, UMR CNRS 8219France

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