Stabilization of the chemostat system with mutations and application to microbial production

T Bayen (1) , J Coville (2) , F Mairet (3)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 BioSP - Biostatistique et Processus Spatiaux
3 PHYTOX - Unité Physiologie et Toxines des Microalgues Toxiques et Nuisibles

In this paper, we consider the chemostat system with n ≥ 1 species, one limiting substrate, and mutations between species. Our objective is to globally stabilize the corresponding dynamical system around a desired equilibrium point. Doing so, we introduce auxostat feedback controls which are controllers allowing the regulation of the substrate concentration. We prove that such feedback controls globally stabilize the resulting closed-loop system near the desired equilibrium point. This result is obtained by combining the theory of asymptotically autonomous systems and an explicit computation of solutions to the limit system. The performance of such controllers is illustrated on an optimal control problem of Lagrange type which consists in maximizing the production of species over a given time period w.r.t. the dilution rate chosen as control variable.

Mots clés: Dynamical system; chemostat system; global stabilization; feedback control; optimal control; Pontryagin maximum principle

Domaines: Optimisation et contrôle [math.OC]; Systèmes dynamiques [math.DS]

T Bayen, J Coville, F Mairet. Stabilization of the chemostat system with mutations and application to microbial production. 2022. ⟨hal-03767646⟩