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Matematicheskie Zametki, 2020, Volume 107, Issue 4, Pages 483–497
DOI: https://doi.org/10.4213/mzm12530 (Mi mzm12530) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Gamkrelidze Convexification and Bogolyubov's Theorem

E. R. Avakovab, G. G. Magaril-Il'yaevbcd

a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
b Lomonosov Moscow State University
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
d Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz
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DOI: https://doi.org/10.4213/mzm12530
Abstract: The interconnection between an optimal control problem and its convexification in the sense of Gamkrelidze and Bogolyubov is studied. Bogolyubov's classical result for the simplest problem of variational calculus is obtained as a corollary.
Keywords: optimal control problem, second conjugate function, convexification.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00649-а
This work was supported by the Russian Foundation for Basic Research under grant 17-01-00649-a.
Received: 02.08.2019
Revised: 19.09.2019
English version:
Mathematical Notes, 2020, Volume 107, Issue 4, Pages 539–551
DOI: https://doi.org/10.1134/S0001434620030219
Bibliographic databases:
Document Type: Article
UDC: 517.977.52
Language: Russian
Citation: E. R. Avakov, G. G. Magaril-Il'yaev, “Gamkrelidze Convexification and Bogolyubov's Theorem”, Mat. Zametki, 107:4 (2020), 483–497; Math. Notes, 107:4 (2020), 539–551
Citation in format AMSBIB
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\paper Gamkrelidze Convexification and Bogolyubov's Theorem
\jour Mat. Zametki
\yr 2020
\vol 107
\issue 4
\pages 483--497
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\crossref{https://doi.org/10.4213/mzm12530}
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\transl
\jour Math. Notes
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\vol 107
\issue 4
\pages 539--551
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  • https://www.mathnet.ru/eng/mzm12530
  • https://doi.org/10.4213/mzm12530
  • https://www.mathnet.ru/eng/mzm/v107/i4/p483
    • This publication is cited in the following 1 articles:
    1. E. R. Avakov, G. G. Magaril-Il'yaev, “Implicit Function. Controllability and Perturbation of Optimal Control Problems”, Math. Notes, 109:4 (2021), 503–516  mathnet  crossref  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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