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Mat. Zametki, 2020, Volume 107, Issue 4, Pages 483–497 (Mi mz12530)  

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

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.

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm12530

Full text: PDF file (496 kB)
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English version:
Mathematical Notes, 2020, 107:4, 539–551

Bibliographic databases:

UDC: 517.977.52
Received: 02.08.2019
Revised: 19.09.2019

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}
\elib{https://elibrary.ru/item.asp?id=43274321}
\transl
\jour Math. Notes
\yr 2020
\vol 107
\issue 4
\pages 539--551
\crossref{https://doi.org/10.1134/S0001434620030219}
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  • http://mi.mathnet.ru/eng/mz12530
  • https://doi.org/10.4213/mzm12530
  • http://mi.mathnet.ru/eng/mz/v107/i4/p483

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following 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
  • Математические заметки Mathematical Notes
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