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

On the Ñhernous’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 Ñhernous’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 Ñhernous’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}