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Analysis of an optimal control problem connected to bioprocesses involving a saturated singular arc

Térence Bayen 1, 2, 3 Marc Mazade 2 Francis Mairet 4
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
INRA - Institut National de la Recherche Agronomique, CRISAM - Inria Sophia Antipolis - Méditerranée , LOV - Laboratoire d'océanographie de Villefranche
Abstract : This paper is devoted to the study of an optimal control problem under the presence of a saturation point on the singular locus. We consider the minimal time problem for a system describing a fed-batch reactor with one species and one substrate. Our aim is to find an optimal feedback control that steers the system to a given target in minimal time. The growth function is of Haldane type implying the existence of a singular arc. Unlike other studies on the minimal time problem governed by affine systems w.r.t. the control, we assume that the singular arc is non-necessary controllable everywhere. This brings interesting issues in terms of optimal synthesis. Thanks Pontryagin's Principle and numerical simulations, we provide an optimal synthesis of the problem.
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Térence Bayen, Marc Mazade, Francis Mairet. Analysis of an optimal control problem connected to bioprocesses involving a saturated singular arc. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2015, 20 (1), pp.39-58. ⟨10.3934/dcdsb.2015.20.39⟩. ⟨hal-00879385v2⟩

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