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An Optimal Control Strategy Separating Two Species of Microalgae in Photobioreactors

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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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Dates and versions

hal-01891910 , version 1 (10-10-2018)
hal-01891910 , version 2 (24-01-2019)

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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. ⟨10.1016/j.ifacol.2019.06.178⟩. ⟨hal-01891910v2⟩
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