Analysis and optimization of a simple crop irrigation model

Nesrine Kalboussi (1, 2) , Sébastien Roux (2) , Kenza Boumaza (2) , Carole Sinfort (1) , Alain Rapaport (2)

1 UMR ITAP - Information – Technologies – Analyse Environnementale – Procédés Agricoles
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

We propose a new simplified crop irrigation model and study the optimal control which consists in maximizing the biomass production at harvesting time, under a constraint on the total amount of water used. Under water scarcity, we show that the optimal strategy could have a singular arc and therefore can be better than a simple bang-bang control as commonly used. The gain is illustrated on numerical simulations. This result is a promising rst step towards the application of control theory to the problem of optimal irrigation scheduling.

Mots clés: crop irrigation; water management; optimal control; state constraint

Domaines: Optimisation et contrôle [math.OC]; Agronomie

Nesrine Kalboussi, Sébastien Roux, Kenza Boumaza, Carole Sinfort, Alain Rapaport. Analysis and optimization of a simple crop irrigation model. 2019. ⟨hal-01991296v1⟩