Optimal control of a crop irrigation model under water scarcity

Boumaza, Kenza; Kalboussi, Nesrine; Rapaport, Alain; Roux, Sébastiên; Sinfort, Carole

doi:10.1002/oca.2749

Cited by 9 publications

(10 citation statements)

References 26 publications

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“…As it is well known once we have the guarantee that λ = 0, we can normalize all the multipliers and proceed to work with λ = 1. For simplicity, this is the approach that we take next 2 .…”

Section: Consider the Unmaximized Hamiltonianmentioning

confidence: 99%

“…They illustrate their findings with numerical simulations. A different irrigation model is proposed in [2] to study, via optimal control problem, the maximization of the biomass production at harvesting time, when a quota on the water used for irrigation is imposed. An interesting feature of this work is the introduction of a non-autonomous dynamical system with a state constraint and a non-smooth right member which is given by threshold-based soil and crop water stress functions.…”

Section: Introductionmentioning

confidence: 99%

“…Alternatively, it is an easy task to see that (OCP) satisfies assumptions H1-H6, as well as the constraint qualification (CQ), in[13] 2. It is worth mentioning here that numerical methods may compute values for λ that are not necessarily equal to one and, consequently, the numerical multipliers may not be normalized.…”

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confidence: 99%

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Analytical Study for Different Extremal State Solutions of an Irrigation Optimal Control Problem with Field Capacity Modes

Lemos-Paião

Lopes

Pinho

2022

Int. J. Appl. Comput. Math

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In this paper we study the problem of daily irrigation of an agricultural crop using optimal control. The dynamics is a model based on field capacity modes, where the state, x, represents the water in the soil and the control variable, u, is the flow rate of water from irrigation. The variation of water in the soil depends on the field capacity of the soil, $$x_{FC}$$ x FC , weather conditions, losses due to deep percolation and irrigation. Our goal is to minimize the amount of water used for irrigation while keeping the crop in a good state of preservation. To enforce such requirement, the state constraint $$x(t) \ge x_{\min }$$ x ( t ) ≥ x min is coupled with the dynamics, where $$x_{\min }$$ x min is the hydrological need of the crop. Consequently, the problem under study is a state constrained optimal control problem. Under some mild assumptions, we consider several basic profiles for the optimal trajectories. Appealing to the Maximum Principle (MP), we characterize analytically the solution and its multipliers for each case. We then illustrate the analytical results running some computational simulations, where the analytical information is used to partially validate the computed solutions. The need to study irrigation strategies is of foremost importance nowadays since 80% of the fresh water used on our planet is used in agriculture.

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Section: Consider the Unmaximized Hamiltonianmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analytical Study for Different Extremal State Solutions of an Irrigation Optimal Control Problem with Field Capacity Modes

Lemos-Paião

Lopes

Pinho

2022

Int. J. Appl. Comput. Math

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“…These approaches are based on relatively complex models with many variables and parameters, which provide quite precise descriptions of the state of the soil-crop-climate system, but are also quite heavy to conduct intensive optimization over a tactic time horizon [23,24]. Other approaches are based on much simpler models (i.e., reduced models) that do not intend to give a precise description of the internal functioning of the soil-crop system, but rather focus on flux balance, and can therefore predict soil composition, water consumption, and biomass production at the field scale only [28][29][30][31][32]. This kind of models is thus better suited to apply optimization tools, because of their relatively small size.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, Kalboussi et al [30,31] proposed a generic crop model named "TOYCROP" which is the basic version of the more advanced model "OPTIRRIG model". TOYCROP was developed to determine optimal irrigation and nitrogen management via treated wastewater [31,32].…”

Section: Introductionmentioning

confidence: 99%

Model-Based Approach for Treated Wastewater Reuse Strategies Focusing on Water and Its Nitrogen Content “A Case Study for Olive Growing Farms in Peri-Urban Areas of Sousse, Tunisia”

Kefi

Kalboussi

Rapaport

et al. 2023

Water

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One of Tunisia’s main challenges is to conserve and protect water resources for current and future generations. Using non-conventional water in agriculture, such as treated wastewater, can be a sustainable water-saving solution. Therefore, the objectives of this study are (i) to analyze the value chain of treated wastewater for olive growing farms production and (ii) to apply mathematical modeling to maximize the olive production in optimizing irrigation distribution and nitrogen amendment in olive growing farms. The work is carried out in a peri-urban irrigated perimeter of Msaken, Sousse, which is mainly occupied by olive trees and irrigated by treated wastewater. A SWOT analysis is also applied to identify the strengths and weaknesses of reuse in this study area. Moreover, mathematical models are used to determine the optimal schedule for fertigation with treated wastewater. In this process, data on rainfall, soil, water quality and olive production were collected from local farmers, local decision makers, field and laboratory experiments. SWOT results determine farmers’ perceptions of reusing treated wastewater for irrigation. The viability analysis, in terms of soil humidity and nitrogen, shows that the nitrogen stress is not a limiting factor for olive biomass production, but water stress is. This analysis provides numerical values for the maximum irrigation rate and total amount of irrigation water to ensure maximum olive production. It was found that the maximum irrigation could be 5.77 m3/day/ha and the total annual water requirement is 1240 m3/ha. Modeling appears to be an important tool to help local decision makers and to support and encourage local farmers to reuse treated wastewater under safe conditions and without environmental risks.

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