Abstract:
The optimal control of moving sources governed by a parabolic equation and a system of ordinary differential equations with initial and boundary conditions is considered. For this problem, an existence and uniqueness theorem is proved, sufficient conditions for the Fréchet differentiability of the cost functional are established, an expression for its gradient is derived, and necessary optimality conditions in the form of pointwise and integral maximum principles are obtained.
Key words:
moving sources, integral identity, maximum principle, Hamilton–Pontryagin function, necessary optimality conditions, control problem for a parabolic equation.
Citation:
R. A. Teymurov, “On a class of optimal control problems with distributed and lumped parameters”, Zh. Vychisl. Mat. Mat. Fiz., 56:3 (2016), 409–420; Comput. Math. Math. Phys., 56:3 (2016), 396–406
\Bibitem{Tey16}
\by R.~A.~Teymurov
\paper On a class of optimal control problems with distributed and lumped parameters
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2016
\vol 56
\issue 3
\pages 409--420
\mathnet{http://mi.mathnet.ru/zvmmf10366}
\crossref{https://doi.org/10.7868/S0044466916030182}
\elib{https://elibrary.ru/item.asp?id=25678770}
\transl
\jour Comput. Math. Math. Phys.
\yr 2016
\vol 56
\issue 3
\pages 396--406
\crossref{https://doi.org/10.1134/S0965542516030167}
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Linking options:
https://www.mathnet.ru/eng/zvmmf10366
https://www.mathnet.ru/eng/zvmmf/v56/i3/p409
This publication is cited in the following 2 articles:
M. J. Mardanov, R. A. Teymurov, “Necessary optimality conditions in an optimal control problem for a parabolic equation with nonlocal integral conditions”, Dokl. Math., 95:1 (2017), 99–102
M. D. Mardanov, R.A. TEIMUROV, “NEOBKhODIMYE USLOVIYa OPTIMALNOSTI V ODNOI ZADAChE OPTIMALNOGO UPRAVLENIYa DLYa PARABOLIChESKOGO URAVNENIYa S NELOKALNYMI INTEGRALNYMI USLOVIYaMI, “Doklady Akademii nauk””, Doklady Akademii nauk, 2017, no. 2, 135
Citation in format AMSBIB
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