Analysis of a state constraint optimal control problem related to the modelling of coastal lagoons

Térence Bayen (1) , Loïc Dagnas (2) , Hector Ramirez Cabrera (3) , Alain Rapaport (4) , Antoine Rousseau (1, 5) , Matthieu Sebbah (6)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Inria Chile
3 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]
4 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
5 LEMON - Littoral, Environment: MOdels and Numerics
6 Departamento de Matematica [Valparaiso]

In this work, we study a non-autonomous optimal control problem under state constraints. The system under consideration describes the salt and volume concentration of a costal lagoon occasionally connected to the sea. The dynamics is non-autonomous in the sense that it takes into account two seasons (dry and hot). Our aim is to maximize the volume of the pumped water w.r.t. water consumption over one year, while fulfilling ecological constraint. We first characterize the set of initial conditions for which there exists a control function such that the corresponding trajectory satisfies the ecological constraint over one year. This allows us to explicit for any initial condition an optimal control policy maximizing the pumped water over one year.

Domaines: Modélisation et simulation; Sciences de l'environnement; Optimisation et contrôle [math.OC]

Térence Bayen, Loïc Dagnas, Hector Ramirez Cabrera, Alain Rapaport, Antoine Rousseau, et al.. Analysis of a state constraint optimal control problem related to the modelling of coastal lagoons. 2017. ⟨hal-01468979⟩