Optimal control of a crop irrigation model under water scarcity

We consider a simple crop irrigation model and study the optimal control which consists of maximizing the biomass production at harvesting time. A specificity this work is to impose quota on water used for irrigation, in context limited resources. The written as 2d non-autonomous dynamical system with state constraint, non-smooth right member given by threshold-based soil stress functions. show that when below threshold giving largest possible production, the strategy irrigating once. then solution can have one or several singular arcs, therefore be better than bang-bang controls, commonly used. gains over the best controls are illustrated numerical simulations. These new feedback we obtain are promising first step towards concrete application theory problem irrigation scheduling under scarcity.