  In this paper we introduce an optimal control approach to Richards' equation
in an irrigation framework, aimed at minimizing water consumption while
maximizing root water uptake. We first describe the physics of the nonlinear
model under consideration, and then develop the first-order necessary
optimality conditions of the associated boundary control problem. We show that
our model provides a promising framework to support optimized irrigation
strategies, thus facing water scarcity in irrigation. The characterization of
the optimal control in terms of a suitable relation with the adjoint state of
the optimality conditions is then used to develop numerical simulations on
different hydrological settings, that supports the analytical findings of the
paper.
