Analysis and optimization of a simple crop irrigation model

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.