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Ural Math. J., 2019, Volume 5, Issue 1, Pages 13–23 (Mi umj70)  

On the —hernous’ko time-optimal problem for the equation of heat conductivity in a rod

Abdulla A. Azamov, Jasurbek A. Bakhramov, Odiljon S. Akhmedov

Institute of Mathematics, National University of Uzbekistan named after Mirzo Ulugbek, Durmon yuli st., 29 Tashkent, 100125, Uzbekistan

Abstract: The time-optimal problem for the controllable equation of heat conductivity in a rod is considered. By means of the Fourier expansion, the problem reduced to a countable system of one-dimensional control systems with a combined constraint joining control parameters in one relation. In order to improve the time of a suboptimal control constructed by F.L. Chernous’ko, a method of grouping coupled terms of the Fourier expansion of a control function is applied, and a synthesis of the improved suboptimal control is obtained in an explicit form.

Keywords: heat equation, time-optimal problem, Pontryagin maximum principle, suboptimal control, synthesis of control.

Funding Agency Grant Number
Ministry of Innovative Development of the Republic of Uzbekistan OT-Φ4-84
This work was supported by a grant from the Ministry of Innovative Development of the Republic of Uzbekistan (Project No. OT-Φ4-84).


DOI: https://doi.org/10.15826/umj.2019.1.002

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Citation: Abdulla A. Azamov, Jasurbek A. Bakhramov, Odiljon S. Akhmedov, “On the —hernous’ko time-optimal problem for the equation of heat conductivity in a rod”, Ural Math. J., 5:1 (2019), 13–23

Citation in format AMSBIB
\Bibitem{AzaBakAkh19}
\by Abdulla~A.~Azamov, Jasurbek~A.~Bakhramov, Odiljon~S.~Akhmedov
\paper On the —hernous’ko time-optimal problem for the equation of heat conductivity in a rod
\jour Ural Math. J.
\yr 2019
\vol 5
\issue 1
\pages 13--23
\mathnet{http://mi.mathnet.ru/umj70}
\crossref{https://doi.org/10.15826/umj.2019.1.002}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=MR3995651}
\zmath{https://zbmath.org/?q=an:1448.49027}
\elib{https://elibrary.ru/item.asp?id=38948042}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85071755789}


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