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

Autor: Ana P. Lemos-Paião, Sofia O. Lopes, M. d. R. de Pinho
Přispěvatelé: Universidade do Minho
Rok vydání: 2022
Předmět:
Zdroj: International Journal of Applied and Computational Mathematics. 8
ISSN: 2199-5796
2349-5103
DOI: 10.1007/s40819-022-01266-9
Popis: 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, xFC, 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)≥xmin is coupled with the dynamics, where xmin 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.
This work was supported by the FEDER/COMPETE/NORTE2020/POCI/FCT funds, under project To CHAIR - POCI-01-0145-FEDER-028247, with the collaboration of the Portuguese Foundation for Science and Technology in the framework of the Strategic Funding, through CFIS and SYSTEC, under grants UID/FIS/04650/2019 and UID/EEA/00147/2019-SYSTEC. The authors are grateful to the Direção Regional de Agricultura e Pescas do Norte – Portugal for the access to weather data, as well as to the Reviewers of this paper for their valuable comments and suggestions that helped them improving the final version of this paper.
Databáze: OpenAIRE
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