About optimal crop irrigation planing under water scarcity
Résumé
We study theoretically on a simple crop model the problem of optimizing the crop biomass at harvesting date, choosing the temporal distribution of water under the constraint of a total water volume available for the season.
We show with the tools of the optimal control theory that the optimal solution may present a singular arc, under a lower water availability, which leads to a bang-singular-bang solution.
This differs from the usual irrigation policies under water scarcity, which are bang-bang.