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

In this article, we consider the chemostat system with 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...

Full description

Saved in:
Bibliographic Details
Published in:Optimal control applications & methods 2023-11, Vol.44 (6), p.3342-3360
Main Authors: Bayen, Térence, Coville, Jérôme, Mairet, Francis
Format: Article
Language:English
Subjects:
Bioreactors
Control systems
Controllers
Dilution
Dynamical systems
Feedback
Mathematics
Microorganisms
Mutation
Optimal control
Optimization
Substrates
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this article, we consider the chemostat system with 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.
ISSN:0143-2087
1099-1514
DOI:10.1002/oca.3041