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arXiv · 2602.21999

Target controllability for a minimum time problem in a trait-structured chemostat model

Claudia Alvarez-Latuz·Terence Bayen·Jerome Coville
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Abstract

In this paper, we consider a minimum time control problem governed by a trait-structured chemostat model including mutation and one limiting substrate. Our first main result proves the well-posedness of the control-to-state mapping. We subsequently analyze the class of auxostat-type controls, feedback laws designed to regulate substrate concentration, and prove that the corresponding solutions converge to a stationary state of the system. These convergence results are used to show the reachability of a target set corresponding to the selection of a population with a low weighted averaged half-saturation constant. Finally, we show the existence of an optimal control for the minimum time problem associated with reaching the target set. These theoretical findings are completed by numerical simulations.

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Claudia Alvarez-Latuz, Terence Bayen, Jerome Coville. 2026-02-25. Target controllability for a minimum time problem in a trait-structured chemostat model. https://arxiv.org/abs/2602.21999

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