An Optimal Control Strategy Separating Two Species of Microalgae in Photobioreactors

Abstract

We investigate a minimal-time control problem in a chemostat continuous photobioreactor model that describes the dynamics of two distinct microalgae populations. More precisely, our objective 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.