Optimal Control of Irrigation with Field Capacity Modes: Characterizing the Minimal Water Consumption Solution

In this work, we address the daily irrigation problem of minimizing water consumption. This problem has the particularity that the dynamics is described via field capacity modes which can model the fact that the soil has different dynamics when it is saturated or not. An analysis is carried out to ensure that the normal Maximum Principle for nonsoomoth problems can be applied to this problem, and, it is observed that the numerical solution fulfills the necessary conditions of optimality.