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Title: A unique value function for an optimal control problem of irrigation water intake from a reservoir harvesting flash floods
Authors: Unami, Koichi  kyouindb  KAKEN_id  orcid https://orcid.org/0000-0001-6910-1094 (unconfirmed)
Mohawesh, Osama
Author's alias: 宇波, 耕一
Keywords: Optimal control problem
Value function
Hamilton–Jacobi–Bellman equation
Viscosity solution
Irrigation scheme
Reservoir operation
Issue Date: Nov-2018
Publisher: Springer Nature
Journal title: Stochastic Environmental Research and Risk Assessment
Volume: 32
Issue: 11
Start page: 3169
End page: 3182
Abstract: Operation of reservoirs is a fundamental issue in water resource management. We herein investigate well-posedness of an optimal control problem for irrigation water intake from a reservoir in an irrigation scheme, the water dynamics of which is modeled with stochastic differential equations. A prototype irrigation scheme is being developed in an arid region to harvest flash floods as a source of water. The Hamilton–Jacobi–Bellman (HJB) equation governing the value function is analyzed in the framework of viscosity solutions. The uniqueness of the value function, which is a viscosity solution to the HJB equation, is demonstrated with a mathematical proof of a comparison theorem. It is also shown that there exists such a viscosity solution. Then, an approximate value function is obtained as a numerical solution to the HJB equation. The optimal control strategy derived from the approximate value function is summarized in terms of rule curves to be presented to the operator of the irrigation scheme.
Description: 砂漠の洪水を灌漑用水に変える --ヨルダンの乾燥地で数理的最適戦略によるプロトタイプを運用--. 京都大学プレスリリース. 2018-03-08.
Rights: © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
URI: http://hdl.handle.net/2433/229528
DOI(Published Version): 10.1007/s00477-018-1527-z
Related Link: http://www.kyoto-u.ac.jp/ja/research/research_results/2017/180305_3.html
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