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 L2 cost. Our goal is to study how perturbations of β aect the optimal solutions 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 ow rate of irrigation water changes.

Ana P. Lemos-Paião

Sofia O. Lopes

Maria d. R. de Pinho

Mathematical Modelling of Natural Phenomena

THE MATHEMATICAL MODELING OF NATURAL PHENOMENA (MMNP) 是一本国际研究期刊，主要发表生物学、医学、化学、物理学等领域数学建模的顶级原创和评论论文、短通讯和论文集。该杂志的范围是专门研究具有足够先进模型的数学建模，主要研究ODE系统驻点的存在性和稳定性的工作没有考虑。该期刊的范围还包括应用数学和数学分析，以将其应用于现实世界的问题。该杂志基本上是在代表活跃研究领域的热点问题的基础上运作的。每个专题问题都有自己的编辑委员会。邀请作者为已发布的问题提交论文或提出新问题。该期刊发表数学建模整个领域的研究文章和评论，并将继续提供有关这个不断扩大的主题的最新趋势和发展的信息.

Mathematical Modelling of Natural Phenomena (MMNP) is an international research journal that primarily publishes top original research papers, reviews, short communications, and proceedings in the fields of biology, medicine, chemistry, and physics related to mathematical modeling. The journal focuses on advanced mathematical modeling research, particularly concerning the existence and stability of equilibrium points in ordinary differential equation (ODE) systems. Its scope also includes applied mathematics and mathematical analysis, aiming to apply these theories to real-world problems. The journal operates based on hot topics in active research areas, with each special issue having its own editorial board. We invite authors to submit papers for published issues or propose new topics. The journal is committed to publishing research articles and reviews in the field of mathematical modeling and continues to provide the latest trends and developments in this expanding subject.

《Mathematical Modelling of Natural Phenomena》（MMNP）是一本国际研究期刊，主要发表生物学、医学、化学、物理学等领域的数学建模顶级原创论文、评论、短通讯和论文集。该期刊专注于具有先进模型的数学建模研究，尤其关注常微分方程（ODE）系统的驻点存在性和稳定性等问题。期刊的范围还包括应用数学和数学分析，旨在将这些理论应用于现实世界的问题。该期刊主要围绕活跃研究领域的热点问题进行运作，每个专题都有专门的编辑委员会。我们邀请作者为已发布的专题提交论文或提出新问题。期刊致力于发表数学建模领域的研究文章和评论，并持续提供关于这一不断扩展主题的最新趋势和发展信息。

Category	Quartile
数学	4
数学, 数学与计算生物学	4
数学, 应用数学	4
数学, 数学跨学科应用	4

A parametric optimal control problem applied to daily irrigation

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Category	Quartile
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS	1