Geodesic
Gamkrelidze Convexification and Bogolyubov's Theorem
Matematičeskie zametki, Tome 107 (2020) no. 4, pp. 483-497.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2020_107_4_a0,
     author = {E. R. Avakov and G. G. Magaril-Il'yaev},
     title = {Gamkrelidze {Convexification} and {Bogolyubov's} {Theorem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {483--497},
     publisher = {mathdoc},
     volume = {107},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_4_a0/}
}
TY  - JOUR
AU  - E. R. Avakov
AU  - G. G. Magaril-Il'yaev
TI  - Gamkrelidze Convexification and Bogolyubov's Theorem
JO  - Matematičeskie zametki
PY  - 2020
SP  - 483
EP  - 497
VL  - 107
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2020_107_4_a0/
LA  - ru
ID  - MZM_2020_107_4_a0
ER  - 
%0 Journal Article
%A E. R. Avakov
%A G. G. Magaril-Il'yaev
%T Gamkrelidze Convexification and Bogolyubov's Theorem
%J Matematičeskie zametki
%D 2020
%P 483-497
%V 107
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2020_107_4_a0/
%G ru
%F MZM_2020_107_4_a0
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)