Optimal control of microbial production in the chemostat

Type Article
Date 2022
Language English
Author(s) Bayen Terence1, Cazenave-Lacroutz Henri1, Coville Jérôme2, Mairet FrancisORCID3
Affiliation(s) 1 : Avignon Université, Laboratoire de Mathématiques d'Avignon (EA 2151) F-84018 France
2 : UR 546 Biostatistique et Processus Spatiaux, INRAE, Domaine St Paul Site Agroparc, F-84000 Avignon, France
3 : Ifremer, Physiology and Biotechnology of Algae laboratory, rue de l'Ile d'Yeu, 44311 Nantes, France
Source Ifac Papersonline (2405-8963) (Elsevier BV), 2022 , Vol. 55 , N. 16 , P. 208-213
DOI 10.1016/j.ifacol.2022.09.025
Keyword(s) Optimal control, Pontryagin maximum principle, singular arcs, chemostat system, dynamical system, global stability

In this work, we study the problem of maximizing microbial production within a continuous stirred-tank reactor with n ≥ 1 species and one substrate. The interaction between species is described by the chemostat system including a mutation factor. The optimization problem falls into an optimal control problem of Lagrange type in which the control parameter is the dilution rate of the reactor. Thanks to the Pontryagin Maximum Principle, we obtain necessary conditions on optimal controls that involve a singular arc. These computations are highlighted thanks to numerical simulations via a direct method. We also study the related optimization problem at steady-state which provides an insight into optimal solutions of the optimal control problem in terms of turnpike phenomenon.


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