Geodesic
On the system of Jacobi equations in a~time-optimal problem
Izvestiya. Mathematics , Tome 21 (1983) no. 2, pp. 375-397.

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

A perturbation method is used to obtain second-order conditions in a nonautonomous time-optimal problem with vectorgram of full dimension. These conditions are formulated in the language of focal points in the classical variational calculus. Bibliography: 16 titles. 
@article{IM2_1983_21_2_a8,
     author = {N. T. Tynyanskii and A. V. Arutyunov},
     title = {On the system of {Jacobi} equations in a~time-optimal problem},
     journal = {Izvestiya. Mathematics },
     pages = {375--397},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1983_21_2_a8/}
}
TY  - JOUR
AU  - N. T. Tynyanskii
AU  - A. V. Arutyunov
TI  - On the system of Jacobi equations in a~time-optimal problem
JO  - Izvestiya. Mathematics 
PY  - 1983
SP  - 375
EP  - 397
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1983_21_2_a8/
LA  - en
ID  - IM2_1983_21_2_a8
ER  - 
%0 Journal Article
%A N. T. Tynyanskii
%A A. V. Arutyunov
%T On the system of Jacobi equations in a~time-optimal problem
%J Izvestiya. Mathematics 
%D 1983
%P 375-397
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1983_21_2_a8/
%G en
%F IM2_1983_21_2_a8
N. T. Tynyanskii; A. V. Arutyunov. On the system of Jacobi equations in a~time-optimal problem. Izvestiya. Mathematics , Tome 21 (1983) no. 2, pp. 375-397. http://geodesic.mathdoc.fr/item/IM2_1983_21_2_a8/

[1] Pontryagin L. S. i dr., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1969

[2] Gamkrelidze R. V., Osnovy optimalnogo upravleniya, Tbilisi, 1977 | MR

[3] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977 | MR

[4] Breakwell I. V., Ho Yu-Chi., “On congugate point condition for the control problem”, Int. J. Enging. Sci., 2:6 (1965), 565–579 | DOI | MR | Zbl

[5] Boltyanskii V. G., Matematicheskie metody optimalnogo upravleniya, Nauka, M., 1969 | MR

[6] Pontryagin L. S., “K teorii differentsialnykh igr”, Uspekhi matem. nauk, 21:4 (1966), 219–275 | MR

[7] Arutyunov A. V., Gladkost funktsii znachenii optimalnogo vremeni v zadachakh bystrodeistviya, Kandidatskaya dissertatsiya, 1981

[8] Bliss G. A., Lektsii po variatsionnomu ischisleniyu, IL, M., 1950

[9] Clarke F. H., “On the inverse function theorem”, Pacific J. Math., 64:1 (1976), 97–102 | MR | Zbl

[10] Skripnik V. P., “Ob odnoi kraevoi zadache i nekotorykh voprosakh koleblemosti reshenii”, Matem. sbornik, 55:4 (1961), 449–474 | MR

[11] Krotov V. F., Gurman V. I., Metody i zadachi optimalnogo upravleniya, Nauka, M., 1973 | MR | Zbl

[12] Zhidkov Yu. N., Neobkhodimye usloviya optimalnosti v dvukhurovnevykh ierarkhicheskikh dinamicheskikh sistemakh s vektornymi kriteriyami, VTs AN SSSR, M., 1981, s. 17–22 | MR

[13] Levitin E. S., Milyutin A. A., Osmolovskii N. P., “Usloviya vysshikh poryadkov lokalnogo minimuma v zadachakh s ogranicheniyami”, Uspekhi matem. nauk, 33:6 (1978), 85–148 | MR

[14] Osmolovskii N. P., “Usloviya vtorogo poryadka slabogo lokalnogo minimuma v zadache optimalnogo upravleniya (neobkhodimost i dostatochnost)”, Dokl. AN SSSR, 225:2 (1975), 259–262 | MR | Zbl

[15] Arutyunov A. V., Tynyanskii N. T., “Usloviya pervogo i vtorogo poryadka v zadache optimalnogo bystrodeistviya”, Uspekhi matem. nauk, 36:6 (1981), 199–200 | MR | Zbl

[16] Ioffe A. D., Tikhomirov V. M., Teoriya ekstremalnykh zadach, Nauka, M., 1974 | MR | Zbl