Optimal structures of crop irrigation strategies with state constraints

We investigate an optimal control problem of crop irrigation with non-autonomous and non-smooth dynamics. Depending on contexts and objectives, several formulations associated to different constraints and criteria can be derived. Our work aims at providing optimal feedback solutions for these problems by deriving and analyzing the optimality necessary conditions. To this end, we assemble the different problems into a common formulation, and we carry out a dedicated way of handling state constraints. We show that all optimal irrigation strategies belong to a family of simple parameterized time-varying feedback controls, independently of the context and objective, and suitable for computational purposes.