Optimal control separating two microalgae species competing in a chemostat

Walid Djema (1) , Olivier Bernard (1, 2) , Térence Bayen (3)

1 BIOCORE - Biological control of artificial ecosystems
2 LOV - Laboratoire d'océanographie de Villefranche
3 LMA - EA2151 Laboratoire de Mathématiques d'Avignon

In this work, we study the question of selecting in minimal-time a microalgae species of interest using the Droop model to describe the dynamics of two distinct populations competing for a limiting nutrient. This amounts to consider an optimal control problem governed by a five-dimensional affine control system in which the control is the dilution rate. Throughout this paper, the optimal control strategies allowing the strain of interest to dominate the population in minimal-time is discussed. These results are illustrated using a numerical direct optimization method (implemented in Bocop).

Keywords: Optimal control; Pontryagin Maximum Principle; Singular arc; Droop's model; Chemostat system

Domains: Mathematics [math]; Optimization and Control [math.OC]

Walid Djema, Olivier Bernard, Térence Bayen. Optimal control separating two microalgae species competing in a chemostat. CDC 2020 - 59th IEEE Conference on Decision and Control, Dec 2020, Jeju Island / Virtual, South Korea. ⟨10.1109/CDC42340.2020.9304115⟩. ⟨hal-02939495⟩