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Mathematical Problems in Engineering
Volume 2016, Article ID 5076879, 10 pages
Research Article

Optimal Control Applied to an Irrigation Planning Problem

1CMAT and Departamento de Matemática e Aplicações, Universidade do Minho, Campus de Azurém, 4800-058 Guimarães, Portugal
2SYSTEC-ISR, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-464 Porto, Portugal
3Centro de Física, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal

Received 31 December 2015; Revised 22 March 2016; Accepted 26 April 2016

Academic Editor: Jean-Christophe Ponsart

Copyright © 2016 Sofia O. Lopes et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a mathematical model to study the water usage for the irrigation of given farmland to guarantee that the field crop is kept in a good state of preservation. This problem is formulated as an optimal control problem. The lack of analytic solution leads us to turn to numerical methods to solve the problem numerically. We then apply necessary conditions of optimality to validate the numerical solution. To deal with the high degree of unpredictability of water inflow due to weather, we further propose a replan strategy and we implement it.