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

Abstract

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.