Minimal time control of the two tanks gradostat model under cascade inputs constraint

Terence Bayen (1, 2, 3) , Alain Rapaport (2, 1) , Matthieu Sebbah (4)

1 MODEMIC - Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
3 I3M - Institut de Mathématiques et de Modélisation de Montpellier
4 Inria Chile

We study the minimum time control problem of a series of two interconnected chemostats under the input constraint u(2) <= 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 encounter this difficulty by splitting the state domain into two sub-domains, one with no lack of controllability of the target, and its complementary is such that any optimal control fulfills u(1) = u(2). We explicit the complete optimal synthesis that depends on the position of the target with respect to a semi-permeable curve that passes through a steady-state singular point.

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique

Terence Bayen, Alain Rapaport, Matthieu Sebbah. Minimal time control of the two tanks gradostat model under cascade inputs constraint. European Control Conference ECC2014, Université de Strasbourg (Unistra). France, FRA. IEEE Control Systems Society., Jun 2014, Strasbourg, France. pp.1256 - 1261, ⟨10.1109/ECC.2014.6862148⟩. ⟨hal-01086152⟩