Abstract
In this paper we introduce an optimal control approach to Richards’ equation in an irrigation framework, aimed at minimizing water consumption while maximizing root water uptake. We first describe the physics of the nonlinear model under consideration, and then develop the first-order necessary optimality conditions of the associated boundary control problem. We show that our model provides a promising framework to support optimized irrigation strategies, thus facing water scarcity in irrigation. The characterization of the optimal control in terms of a suitable relation with the adjoint state of the optimality conditions is then used to develop numerical simulations on different hydrological settings, that support the analytical findings of the paper.
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Acknowledgements
MB acknowledges the partial support of RIUBSAL project funded by Regione Puglia under the call “P.S.R. Puglia 2014/2020 - Misura 16 - Cooperazione - Sottomisura 16.2 “Sostegno a progetti pilota e allo sviluppo di nuovi prodotti, pratiche, processi e tecnologie”: in particular he thanks Mr. Giuseppe Leone and Mrs. Gina Dell’Olio for supporting the project activities; FVD has been supported by REFIN Project, grant number 812E4967, funded by Regione Puglia: both authors acknowledge the partial support of GNCS-INdAM. RG acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number RGPIN-2021-02632.
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Fabio V. Difonzo and Roberto Guglielmi are contributed equally to this work.
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Berardi, M., Difonzo, F.V. & Guglielmi, R. A preliminary model for optimal control of moisture content in unsaturated soils. Comput Geosci 27, 1133–1144 (2023). https://doi.org/10.1007/s10596-023-10250-1
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DOI: https://doi.org/10.1007/s10596-023-10250-1