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Gamkrelidze Convexification and Bogolyubov’s Theorem

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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.

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References

  1. N. N. Bogolubov, “Sur quelques méthodes nouvelles dans le calculus des variations,” Ann. Math. Pura Appl. 7(1), 249–271 (1929).

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  3. R. V. Gamkrelidze, “On sliding optimal states,” Dokl. AN SSSR 143(6), 1243–1245 (1962).

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  5. R. V. Gamkrelidze, Foundations of Optimal Control (Izd. Tbilisk. Univ., Tbilisi, 1977) [in Russian].

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  6. E. R. Avakov and G. G. Magaril-Il’yaev, “Local infimum and a family of maximum principles in optimal control,” Mat. Sb. (in press).

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Funding

This work was supported by the Russian Foundation for Basic Research under grant 17-01-00649-a.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, 117997, Russia

    E. R. Avakov

  2. Lomonosov Moscow State University, Moscow, 119991, Russia

    E. R. Avakov & G. G. Magaril-Il’yaev

  3. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, 101447, Russia

    G. G. Magaril-Il’yaev

  4. Southern Mathematical Institute of Vladikavkaz Scientific Center of Russian Academy of Sciences, Vladikavkaz, 362027, Russia

    G. G. Magaril-Il’yaev

Authors
  1. E. R. Avakov
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  2. G. G. Magaril-Il’yaev
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Corresponding authors

Correspondence to E. R. Avakov or G. G. Magaril-Il’yaev.

Additional information

Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 4, pp. 483–497.

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Avakov, E.R., Magaril-Il’yaev, G.G. Gamkrelidze Convexification and Bogolyubov’s Theorem. Math Notes 107, 539–551 (2020). https://doi.org/10.1134/S0001434620030219

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  • DOI: https://doi.org/10.1134/S0001434620030219

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