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Minimal time problem for a fed-batch bioreactor with a non admissible singular arc

Térence Bayen 1, 2, 3 Francis Mairet 4 Marc Mazade 2
1 MODEMIC - Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme
CRISAM - Inria Sophia Antipolis - Méditerranée , MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
4 BIOCORE - Biological control of artificial ecosystems
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique
Abstract : In this paper, we consider an optimal control problem for a system describing a fed-batch bioreactor with one species and one substrate. Our aim is to find an optimal feedback control in order to steer the system to a given target in minimal time. The growth function is of Haldane type implying the existence of a singular arc. Unlike many studies on the minimal time problem governed by an affine system w.r.t. the control with one input, we assume that the singular arc is non-necessary controllable. This brings interesting issues in terms of optimal synthesis. Thanks to the Pontryagin Maximum Principle, we provide the optimal synthesis of the problem, It turns out that singular extremal trajectories are no longer optimal on a subset of the singular arc.
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Térence Bayen, Francis Mairet, Marc Mazade. Minimal time problem for a fed-batch bioreactor with a non admissible singular arc. European Control Conference (ECC), Université de Strasbourg (Unistra). Strasbourg, FRA. IEEE Control Systems Society., Jun 2014, Strasbourg, France. pp.165-170, ⟨10.1109/ECC.2014.6862444⟩. ⟨hal-01095694⟩

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