Irrigation planning: an optimal control approach

Abstract

We aim to plan the water usage in the irrigation of a given farmland keeping, at same time, the field cultivation in a good state of preservation. This problem is modeled and tackled as an optimal control problem: minimize the water flow (control) so that the extent water amount in the soil (trajectory) fulfills the cultivation water requirements. To estimate rainfall, we consider two models: one based on the average monthly rainfall of the last 10 years in Lisbon area and another which considers the best linear combination of average monthly rainfall from the last 10 years and the amount of rainfall in the previous month. We study the behavior of the solutions under different weather scenarios and we compare the solutions obtained using our model of rainfall with solutions obtained having a prior knowledge of the rainfall.