Improvement of performances of continuous biological water treatment with periodic solutions

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

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

We study periodic solutions of the chemostat model under an integral constraint, either on the flow rate (Pb. 1) or on the substrate concentration (Pb. 2). We give conditions on the growth kinetics for which it is possible to improve the averaged water quality (Pb. 1) or the total quantity of treated water (Pb. 2) over a given time period, compared to steady-state. When this is possible, we characterize optimal periodic solutions and show a duality between the two optimization problems. The results are illustrated on four types of growth kinetics, given by Monod, Haldane, Hill and Contois functions.

Keywords: Chemostat model; periodic control; integral constraint; convexity; optimal control; duality

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

Térence Bayen, Alain Rapaport, Fatima Zahra Tani. Improvement of performances of continuous biological water treatment with periodic solutions. 2019. ⟨hal-02281538v2⟩