Common structures of optimal solutions for a crop irrigation problem under various constraints and criteria *

We consider a simplified crop irrigation model written as a non-autonomous, non-smooth controlled system. Different operating contexts and objectives lead to the study of optimal control problems with various state constraints, criterion and targets. We look for feedback solutions and we derive the optimality necessary conditions for the unified formulation. We show that there are only two parametrized time-varying feedback strategies consisting of the best and the worst practices, independent of the chosen objective, and suitable for numerical analysis.