# Minimal time control of the two tanks gradostat model under a cascade Input constraint

1 MODEMIC - Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme
CRISAM - Inria Sophia Antipolis - Méditerranée , MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
Abstract : We study the minimum time control problem of a series of two interconnected chemostats under the input constraint $u_{2}\leq u_{1}$, where $u_{i}$ are the respective dilution rates in the tanks. This constraint brings controllability issues in the study of the optimal strategies. We overcome this difficulty by splitting the state domain into two subdomains, one with no lack of controllability of the target, and its complement where any optimal trajectory satisfies $u_{1}=u_{2}$. We explicitly compute the complete optimal synthesis that depends on the position of the target with respect to a semipermeable curve that passes through a steady-state singular point.
Type de document :
Article dans une revue
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (4), pp.2568-2594. 〈10.1137/130950379〉
Liste complète des métadonnées

https://hal.inria.fr/hal-01086153
Contributeur : Alain Rapaport <>
Soumis le : samedi 22 novembre 2014 - 17:38:08
Dernière modification le : mercredi 7 novembre 2018 - 23:10:06

### Citation

Terence Bayen, Alain Rapaport, Matthieu Sebbah. Minimal time control of the two tanks gradostat model under a cascade Input constraint. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (4), pp.2568-2594. 〈10.1137/130950379〉. 〈hal-01086153〉

### Métriques

Consultations de la notice