Optimal control of a multi-field irrigation problem: validation of a numerical solution by the optimality conditions

In this paper, we address the problem of minimizing the total water consumption over the period of a year used to supply different fields with different types of crops.We start by recalling a previous study, where the authors developed an optimal control model for this problem by minimizing the water flowing into a reservoir and where the water from the precipitation can be collected. The numerical solution obtained using such model is analyzed.The main result in this paper is the theoretical validation of the numerical solution via a verifications that such solution satisfies the necessary conditions of optimality in the form of a Maximum Principle. This way, we are giving further evidence of the optimality of the numerical solution found.This work was partially supported by NORTE Regional Operational Program through Project NORTE–45–2015–02 STRIDE – Smart Cyberphysical, Mathematical, Computational and Power Engineering Research for Disruptive Innovation in Production, Mobility, Health, and Ocean Systems and Technologies, as well as projects POCI–01- 0145-FEDER-006933 -SYSTEC–Research Center for Systems and Technologies - Institute of Systems and Robotics, Universidade do Porto, UID/MAT/00013/2013 - CMAT - Centro de Matematica da Universidade do Minho, and ´ PTDC/EEI-AUT/2933/2014, POCI-01-0145-FEDER-016858 TOCCATTA, funded by FEDER funds through COMPETE2020 - Programa Operacional Competitividade e Internacionalizac¸ao (POCI) and by national funds through ˜ FCT - Fundac¸ao para a Ci ˜ encia e a Tecnologia.