ОПТИМАЛЬНЕ КЕРУВАННЯ ІНТЕНСИВНІСТЮ ТОЧКОВИХ ДЖЕРЕЛ ВОДИ В НЕНАСИЧЕНОМУ ПОРИСТОМУ СЕРЕДОВИЩІ
Moisture transport through unsaturated porous medium with inserted point sources, described by Richards-Klute equation is a very complicated for calculations and unstable process. It can be explained by the fact that the physical process, described by this equation, is characterized by a large amoun...
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| Дата: | 2025 |
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| Автори: | , , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine
2025
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| Теми: | |
| Онлайн доступ: | https://jais.net.ua/index.php/files/article/view/665 |
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| Назва журналу: | Problems of Control and Informatics |
Репозитарії
Problems of Control and Informatics| Резюме: | Moisture transport through unsaturated porous medium with inserted point sources, described by Richards-Klute equation is a very complicated for calculations and unstable process. It can be explained by the fact that the physical process, described by this equation, is characterized by a large amount of diverse parameters. To reduce the difficulty an approach, based on Kirchhoff transformation, is offered, allowing to reduce the quasilinear parabolic initial-boundary problem to a linear and dimensionless problem. In this paper a two-dimensional quasilinear problem of optimal control using point sources for a rectangular unsaturated porous medium with known initial conditions, fixed humidity at the bottom bound and the given target humidity, is being considered. In this setting this problem is studied and solved for the first time. To solve the linear dimensionless optimal control problem on non-stationary moisture transport in an unsaturated porous medium, received using Kirchhoff transformation, a variation algorithm identifying the optimal source power is used, which allows modelling the process with realistic assumptions. In the paper, correctness of linearized dimensionless problem on moisture transport is proved. In particular, theorems on existence and uniqueness of the generalized solution are proven as well as existence and uniqueness of optimal control of the source power. In the paper, modelling of moisture transport from an inserted source in a dry ground area is made. Results for numerical experiments demonstrating high accuracy of the method are given. The proposed method allows to solve actual problem of optimal parameter choice for a drip irrigation system, and to improve its effectiveness.
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