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Theses

Identifiabilité de systèmes d'équations aux dérivées partielles semi-discrétisées et applications à l'identifiabilité paramétrique de modèles en pharmacocinétique et en pollution.

Abstract : Before estimating the parameters appearing in a linear or non-linear, controlled or uncontrolled, dynamical system, it is necessary to study the unicity of the parameters compared to the experimental data. This study is still called identifiability. Several methods were developed these last years, in particular the input-output method based on the use of differential algebra. The results obtained from it make it possible to set up numerical methods to obtain a first estimate of the parameters, this without any knowledge a priori of their value. This first estimate can then be used as starting point of iterative algorithms specialized in the study of the ill-posed problems: the regularization of Tikhonov.
In this thesis, two nonlinear models in pharmacokinetic were first of all studied. Then, we were interested in a model of pollution described by a parabolic partial derivative equation. The source term to be identified was modelled by the product of the function flow with the Dirac mass, of support the position of the polluting source. The goal of the work was to provide a first estimate of the polluting source. After having obtained the identifiability of the continuous problem, the identifiability of an approximated model was obtained by using the
step of input-output method. The approximated model was obtained by approaching the Dirac mass by a Gaussian function and by discretizing the system in space then. The results of identifiability were obtained whatever the number of points of discretization in space. From this study, we deduced numerical algorithms giving a first estimate of the polluting source.
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https://tel.archives-ouvertes.fr/tel-00011838
Contributor : Nathalie Verdière <>
Submitted on : Tuesday, March 28, 2006 - 5:00:33 PM
Last modification on : Wednesday, September 5, 2018 - 3:15:59 PM
Long-term archiving on: : Monday, September 20, 2010 - 1:59:13 PM

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Nathalie Verdière. Identifiabilité de systèmes d'équations aux dérivées partielles semi-discrétisées et applications à l'identifiabilité paramétrique de modèles en pharmacocinétique et en pollution.. Mathématiques [math]. Université de Technologie de Compiègne, 2005. Français. ⟨tel-00011838v2⟩

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