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Time optimal control problem with integral constraint for the heat transfer process
Sh. A. Alimova, G. I. Ibragimovbc a Department of Mathematics,
National University of Uzbekistan,
100174 Tashkent, Uzbekistan
b Institute of Mathematics,
Uzbekistan Academy of Science,
Student town,
100174 Tashkent, Uzbekistan
c Tashkent State University of Economics,
49 Islom Karimov St,
100066, Tashkent, Uzbekistan
Аннотация:
In the present paper a mathematical model of thermocontrol processes is studied. Several convectors are installed on the disjoint subsets $\Gamma_k$ of the wall $\partial\Omega$ of a volume $\Omega$ and each convector produces a hot or cold flow with magnitude equal to $\mu_k(t)$, which are control functions, and on the surface $\partial\Omega\setminus\Gamma$, $\Gamma=\bigcup\Gamma_k$, a heat exchange occurs by the Newton law. The control functions $\mu_k(t)$ are subjected to an integral constraint. The problem is to find control functions to transfer the state of the process to a given state. A necessary and sufficient condition is found for solvability of this problem. An equation for the optimal transfer time is found, and an optimal control function is constructed explicitly.
Ключевые слова и фразы:
heat transfer process, control function, integral constraint, optimal control, optimal time.
Поступила в редакцию: 24.11.2022
Образец цитирования:
Sh. A. Alimov, G. I. Ibragimov, “Time optimal control problem with integral constraint for the heat transfer process”, Eurasian Math. J., 15:1 (2024), 8–22
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj488 https://www.mathnet.ru/rus/emj/v15/i1/p8
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