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Theses

Control of the chemostat: Some Results

Gonzalo Robledo 1
1 COMORE - Modeling and control of renewable resources
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This thesis deals with the control of some ecological systems in the chemostat (an experimental device used for microorganism growth in idealized conditions). We start with a brief description of the competition and trophic chain model in the chemostat and we recall some basic concepts of control theory adapted to the models stated above. This frame makes possible to show some applications and to point out the mathematical complexity of the problem.

The first part consider the robust control of a simple chemostat characterized by deterministic imprecisions in the model and the output and moreover with delays in the output. We build a family of feedback control laws which stabilizes the variables in a polytope determined by the bounds of imprecisions. Moreover, we stabilize the output around a reference value in the case presence of delays but absence of imprecisions.

The second part considers the feedback control of a competition model between two species making possible the coexistence of them. We generalize a result given by P. De Leenheer and H. Smith in two ways: we consider more general uptake functions and we take into account the mortality of species.

The third part considers the open-loop control for a trophic chain in the chemostat. We give a method for reduction of dimension which makes possible to characterize the attainable set of the system and to obtain a result related with the partial controllability of the chain.
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Submitted on : Friday, May 19, 2006 - 3:35:24 PM
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  • HAL Id : tel-00069800, version 1

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Gonzalo Robledo. Control of the chemostat: Some Results. Mathematics [math]. Université Nice Sophia Antipolis, 2006. English. ⟨tel-00069800⟩

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