An Optimal Control Strategy Separating Two Species of Microalgae in Photobioreactors

Walid Djema (1, 2) , Laetitia Giraldi (2) , Olivier Bernard (1)

1 BIOCORE - Biological control of artificial ecosystems
2 McTAO - Mathematics for Control, Transport and Applications

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.

Mots clés: microalgae; chemostat; Optimization; feedback control; nonlinear; Droop's model

Domaines: Automatique; Optimisation et contrôle [math.OC]

Walid Djema, Laetitia Giraldi, Olivier Bernard. An Optimal Control Strategy Separating Two Species of Microalgae in Photobioreactors. DYCOPS 2019 - 12th Dynamics and Control of Process Systems, including Biosystems, Apr 2019, Florianopolis, Brazil. ⟨hal-01891910v1⟩