A parametric optimal control problem applied to daily irrigation

We conduct sensitivity analysis of an optimal control problem applied to agricultural irrigation. The aim is to minimize the square of the amount of irrigation water while ensuring the health grow of the crop. A crucial parameter of our model is the percentage of water loss due to deep percolation,...

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Published inMathematical modelling of natural phenomena Vol. 20; p. 2
Main Authors Lemos-Paião, Ana P., Lopes, Sofia O., de Pinho, M. D. R.
Format Journal Article
LanguageEnglish
Published 2025
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ISSN0973-5348
1760-6101
DOI10.1051/mmnp/2024020

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Abstract We conduct sensitivity analysis of an optimal control problem applied to agricultural irrigation. The aim is to minimize the square of the amount of irrigation water while ensuring the health grow of the crop. A crucial parameter of our model is the percentage of water loss due to deep percolation, β , a parameter hard to estimate and subject to perturbations. Thus, our problem is a parametric state constrained optimal control problem with a L 2 cost. Our goal is to study how perturbations of β affect the optimal solutions of our problem using sensitivity analysis of our problem using sensitivity analysis. To solve numerically our optimal control problem we use the direct method, transcribing the problem into a non-linear programming problem. We show how sensitivity analysis applied to the non-linear programming problem provides information on the variation of optimal solutions of the original problem in terms of β . Valid approximations of optimal solution and cost, provided by sensitivity analysis, are computed for values of β within of a certain neighbourhood. Remarkably, we show that for all β in such neighbourhood, the irrigation period is kept constant. Only the flow rate of irrigation water changes.
AbstractList We conduct sensitivity analysis of an optimal control problem applied to agricultural irrigation. The aim is to minimize the square of the amount of irrigation water while ensuring the health grow of the crop. A crucial parameter of our model is the percentage of water loss due to deep percolation, β , a parameter hard to estimate and subject to perturbations. Thus, our problem is a parametric state constrained optimal control problem with a L 2 cost. Our goal is to study how perturbations of β affect the optimal solutions of our problem using sensitivity analysis of our problem using sensitivity analysis. To solve numerically our optimal control problem we use the direct method, transcribing the problem into a non-linear programming problem. We show how sensitivity analysis applied to the non-linear programming problem provides information on the variation of optimal solutions of the original problem in terms of β . Valid approximations of optimal solution and cost, provided by sensitivity analysis, are computed for values of β within of a certain neighbourhood. Remarkably, we show that for all β in such neighbourhood, the irrigation period is kept constant. Only the flow rate of irrigation water changes.
Author Lopes, Sofia O.
de Pinho, M. D. R.
Lemos-Paião, Ana P.
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