Target controllability for a minimum time problem in a trait-structured chemostat model
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arXiv
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| Format: | Preprint |
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2026
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| author | Alvarez-Latuz, Claudia Bayen, Terence Coville, Jerome |
| author_facet | Alvarez-Latuz, Claudia Bayen, Terence Coville, Jerome |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21999 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Target controllability for a minimum time problem in a trait-structured chemostat model Alvarez-Latuz, Claudia Bayen, Terence Coville, Jerome Optimization and Control Analysis of PDEs Dynamical Systems 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. |
| title | Target controllability for a minimum time problem in a trait-structured chemostat model |
| topic | Optimization and Control Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2602.21999 |