Geodesic
Gamkrelidze Convexification and Bogolyubov's Theorem
Matematičeskie zametki, Tome 107 (2020) no. 4, pp. 483-497 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : convexification. 
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E. R. Avakov; G. G. Magaril-Il'yaev. Gamkrelidze Convexification and Bogolyubov's Theorem. Matematičeskie zametki, Tome 107 (2020) no. 4, pp. 483-497. http://geodesic.mathdoc.fr/item/MZM_2020_107_4_a0/

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

[2] A. D. Ioffe, V. M. Tikhomirov, Teoriya ekstremalnykh zadach, Nelineinyi analiz i ego prilozheniya, Nauka, M., 1974 | MR | Zbl

[3] R. V. Gamkrelidze, “O skolzyaschikh optimalnykh rezhimakh”, Dokl. AN SSSR, 143:6 (1962), 1243–1245 | MR | Zbl

[4] V. M. Alekseev, V. M. Tikhomirov, S. V. Fomin, Optimalnoe upravlenie, Nauka, M., 1979 | MR | Zbl

[5] R. V. Gamkrelidze, Osnovy optimalnogo upravleniya, Izd-vo Tbilisskogo un-ta, Tbilisi, 1977

[6] E. R. Avakov, G. G. Magaril-Ilyaev, “Lokalnyi infimum i semeistvo printsipov maksimuma v optimalnom upravlenii”, Matem. sb. (to appear)