Optimal periodic control of the chemostat with Contois growth function

Térence Bayen (1) , Alain Rapaport (2) , Fatima Zahra Tani (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

In this work, we examine the benefit of having periodic dilution rate in the chemostat model in terms of averaged conversion rate. We compare the effect of bringing a same substrate quantity by a periodic rate with a constant rate. We show that for the classical chemostat model with a Contois growth function, the performance of the averaged conversion rate can be improved under certain conditions. Using Pontryagin's Principle, we characterize the extremals of the problem which minimizes the averaged substrate concentration among periodic trajectories of a given period.

Mots clés: Optimal Periodic Control; Over-yielding; Pontryagin Maximum Principle; Chemostat Model

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

Térence Bayen, Alain Rapaport, Fatima Zahra Tani. Optimal periodic control of the chemostat with Contois growth function. IFAC International Conference on Mathematical Modelling - MATHMOD 2018, Feb 2018, Vienna, Austria. pp.730-734, ⟨10.1016/j.ifacol.2018.03.124⟩. ⟨hal-01716606⟩