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Stabilisation Globale de Systèmes Dynamiques Positifs Mal Connus. Applications en Biologie

Ludovic Mailleret 1
1 COMORE - Modeling and control of renewable resources
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Works presented in this thesis focus on problems related to the control of positive systems of nonlinear ordinary di erential equations. Biological models, that aim at describing the evolution of positive quantities, do belong to this class of systems. These models often include some parts, related to the phenomenon s biology, which have unknown analytical expressions but are known in a qualitative manner. In this thesis, we propose to use these qualitative properties together with a control law, based on the measurement of the uncertain part, in order to globally stabilize any trajectory towards a single equilibrium. A brief state of the art on positive systems begins the thesis. We introduce then a control law, able to ensure the global stabilization of the considered class of systems. The introduction of an adaptive part enhance our approach, so that the control law is able to deal with some parameter uncertainties. We apply these results to some biological models: fishery magement model, bioreactors exploiting microorganisms... One of our main applications concerns cascade bioreactions occuring in bioreactors. Some experimental tests of our approach on an anaerobic digester, an e cient but multi-stable waste water treatment plant, validate our approach.
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Submitted on : Wednesday, August 18, 2004 - 1:32:27 PM
Last modification on : Tuesday, December 8, 2020 - 3:41:14 AM
Long-term archiving on: : Friday, April 2, 2010 - 8:19:27 PM

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  • HAL Id : tel-00006700, version 1

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Ludovic Mailleret. Stabilisation Globale de Systèmes Dynamiques Positifs Mal Connus. Applications en Biologie. Ecologie, Environnement. Université Nice Sophia Antipolis, 2004. Français. ⟨tel-00006700⟩

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