Optimal Control for an Irrigation Planning Problem: Characterisation of Solution and Validation of the Numerical Results

Lopes, Sofia O.; Fontes, Fernando A. C. C.; Pereira, Rui M. S.; Pinho, Maria do Rosário de; Ribeiro, Carolina Paula Baptista

doi:10.1007/978-3-319-10380-8_16

Cited by 6 publications

(4 citation statements)

References 7 publications

(7 reference statements)

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“…Optimal control theory emerged as a field of research in the 1950s in response to problems concerning the aerospace exploitation [3] of the solar system. Nowadays, optimal control is a recognized tool, known for its efficacy, which is applied to different areas, such as robotics [4], biological systems [5], health problems [6], economy problems [7], oil extraction problems [8], and agriculture problems [9], among many others. The goal of optimal control theory is to find a control law for a given system such that a certain optimality criterion is achieved.…”

Section: Introductionmentioning

confidence: 99%

“…In optimal control problems (OCP), it is possible to define decision variables subject to restrictions in the form of differential equations, where these decisions variables are not necessarily smooth (non-differentiable functions). In an OPC, it is also possible to use different tools to solve the problem, to characterize it, to study the sensitivity of its variables, to study the stability of the problem and to apply predictive control to replan the problem [9][10][11]. The nature of the problems addressed in this paper is fit for optimal control theory.…”

Section: Introductionmentioning

confidence: 99%

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Optimized Planning of Different Crops in a Field Using Optimal Control in Portugal

et al. 2018

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Climate change is a proven fact. In the report of 2007 from IPCC, one can read that global warming is an issue to be dealt with urgently. In many parts of the world, the estimated rise of temperature (in a very near future) is significant. One of the most affected regions is the Iberian Peninsula, where the increasing need for water will very soon be a problem. Therefore, it is necessary that decision makers are able to decide on all issues related to water management. In this paper, we show a couple of mathematical models that can aid the decision making in the management of an agricultural field at a given location. Having a field, in which different crops can be produced, the solution of the first model indicates the area that should be used for each crop so that the profit is as large as possible, while the water spent is the smallest possible guaranteeing the water requirements of each crop. Using known data for these crops in Portugal, including costs of labour, machines, energy and water, as well as the estimated value of the products obtained, the first mathematical model developed, via optimal control theory, obtains the best management solution. It allows creating different scenarios, thus it can be a valuable tool to help the farmer/decision maker decide the crop and its area to be cultivated. A second mathematical model was developed. It improves the first one, in the sense that it allows considering that water from the rainfall can be collected in a reservoir with a given capacity. The contribution of the collected water from the rainfall in the profit obtained for some different scenarios is also shown.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimized Planning of Different Crops in a Field Using Optimal Control in Portugal

et al. 2018

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“…Although preliminary results on this subjects are presented in [5][6][7][8][9], here we improve them and discuss them in detail. Additionally, here we propose the implementation of the replan methodology.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Applied to an Irrigation Planning Problem

Lopes

Fontes

Pereira

et al. 2016

Mathematical Problems in Engineering

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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.

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“…In [6], the authors present the "Initial Planning Problem" for rainfall: this includes an extra term taking into account the rainfall in the previous time period (this rainfall model was statistically proven to be significant) where a comparison between this new model and the solution knowing the rainfall a priori was shown. A characterization of the solution using the necessary conditions of optimality was made in [8], and thereby the numerical results were validated. Most of these results and further details are collected in [11].…”

Section: Introductionmentioning

confidence: 99%

Optimal Control for an Irrigation Problem with Several Fields and Common Reservoir

Lopes

Fontes²

2016

Lecture Notes in Electrical Engineering

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Abstract. In a previous study, the authors developed the planning of the water used in the irrigation systems of a given farmland in order to ensure that the field cultivation is in a good state of preservation. In this paper, we introduce a model to minimize the water flowing into a reservoir that supplies different fields with different types of crops. This model is described as an optimal control problem where the water flow from a tap and the water used in the fields are the controls. The trajectories are described as the humidity in the soil and the amount of water in the reservoir.

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Optimal Control for an Irrigation Planning Problem: Characterisation of Solution and Validation of the Numerical Results

Cited by 6 publications

References 7 publications

Optimized Planning of Different Crops in a Field Using Optimal Control in Portugal

Optimized Planning of Different Crops in a Field Using Optimal Control in Portugal

Optimal Control Applied to an Irrigation Planning Problem

Optimal Control for an Irrigation Problem with Several Fields and Common Reservoir

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