An Optimal Control Strategy Separating Two Species of Microalgae in Photobioreactors

Walid Djema 1, 2 Laetitia Giraldi 3, 2 Olivier Bernard 1, 2
1 BIOCORE - Biological control of artificial ecosystems
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique, LOV - Laboratoire d'océanographie de Villefranche
3 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We investigate a minimal-time control problem in a chemostat continuous photo-bioreactor model that describes the dynamics of two distinct microalgae populations. More precisely, our objective in this paper is to optimize the time of selection-or separation-between two species of microalgae. We focus in this work on Droop's model which takes into account an internal quota storage for each microalgae species. Using Pontryagin's principle, we develop a dilution-based control strategy that steers the model trajectories to a suitable target in minimal time. Our study reveals that singular arcs play a key role in the optimization problem. A numerical optimal-synthesis, based on direct optimal control tools, is performed throughout the paper, thereby confirming the optimality of the provided feedback-control law, which is of type bang-singular.
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Walid Djema, Laetitia Giraldi, Olivier Bernard. An Optimal Control Strategy Separating Two Species of Microalgae in Photobioreactors. DYCOPS 2019 - 12th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems, Apr 2019, Florianopolis, Brazil. ⟨hal-01891910v2⟩

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