Geodesic
Necessary optimality conditions for the one class stochastic optimal control problems
Trudy Instituta matematiki, Tome 26 (2018) no. 1, pp. 79-87.

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

The optimal control problem in stochastic systems with distributed parameters of Goursat-Darboux type is considered. A stochastic analogue of the Pontryagin maximum principle is obtained and singular controls are investigated. 
@article{TIMB_2018_26_1_a10,
     author = {K. B. Mansimov and R. O. Mastaliyev},
     title = {Necessary optimality conditions for the one class stochastic optimal control problems},
     journal = {Trudy Instituta matematiki},
     pages = {79--87},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2018_26_1_a10/}
}
TY  - JOUR
AU  - K. B. Mansimov
AU  - R. O. Mastaliyev
TI  - Necessary optimality conditions for the one class stochastic optimal control problems
JO  - Trudy Instituta matematiki
PY  - 2018
SP  - 79
EP  - 87
VL  - 26
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMB_2018_26_1_a10/
LA  - ru
ID  - TIMB_2018_26_1_a10
ER  - 
%0 Journal Article
%A K. B. Mansimov
%A R. O. Mastaliyev
%T Necessary optimality conditions for the one class stochastic optimal control problems
%J Trudy Instituta matematiki
%D 2018
%P 79-87
%V 26
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMB_2018_26_1_a10/
%G ru
%F TIMB_2018_26_1_a10
K. B. Mansimov; R. O. Mastaliyev. Necessary optimality conditions for the one class stochastic optimal control problems. Trudy Instituta matematiki, Tome 26 (2018) no. 1, pp. 79-87. http://geodesic.mathdoc.fr/item/TIMB_2018_26_1_a10/

[1] Egorov A. I., “Ob optimalnom upravlenii protsessami v nekotorykh sistemakh raspredelennymi parametrami”, Avtomatika i telemekhanika, 25:5 (1964), 613–623 | Zbl

[2] Egorov A. I., “Optimalnye protsessy v sistemakh s raspredelennymi parametrami i nekotorye zadachi teorii invariantnosti”, Izv. AN SSSR. Ser. matem., 29:6 (1965), 1205–1260 | Zbl

[3] Akhiev S. S., K teorii neobkhodimykh uslovii optimalnosti pervogo i vtorogo poryadka, Azerb. gos. un-t, Baku, 1974, 43 pp.

[4] Aschepkov L. T., Vasilev O. V., “Ob optimalnosti osobykh upravlenii v sistemakh Gursa-Darbu”, Zhurn. vychisl. mat. i mat. fiziki, 15:5 (1975), 1157–1167 | MR | Zbl

[5] Aschepkov L. T., Vasilev O. V., Kovalenok I. L., “Usilennoe uslovie optimalnosti osobykh upravlenii v sisteme Gursa-Darbu”, Differents. uravneniya, 1980, no. 6, 1054–1059 | MR | Zbl

[6] Srochko V. A., “Usloviya optimalnosti dlya odnogo klassa sistem s raspredelennymi parametrami”, Sib. mat. zhurn., 1984, no. 2, 56–65

[7] Melikov T. K., Issledovanie osobykh protsessov v nekotorykh optimalnykh sistemakh, avtoref. dis. kand. fiz.-mat. nauk, Baku, 1976, 17 pp.

[8] Mansimov K. B., Neobkhodimye usloviya optimalnosti osobykh protsessov v zadachakh optimalnogo upravleniya, avtoref. dis. d-ra fiz.-mat. nauk, Baku, 1994, 43 pp.

[9] Mansimov K. B., Mardanov M. Dzh., Kachestvennaya teoriya optimalnogo upravleniya sistemami Gursa-Darbu, “Elm”, Baku, 2010, 360 pp.

[10] Tikhonov A. N., Samarskii A.A., Uravneniya matematicheskoi fiziki, Nauka, M., 1977, 736 pp. | MR

[11] Rachinskii V. V., Vvedenie v obschuyu teoriyu dinamiki sorbtsii i khromatografii, Nauka, M., 1964, 136 pp.

[12] Ermolev Yu. M., Gulenko V. P., Tsarenko T. I., Konechno-raznostnyi metod v zadachakh optimalnogo upravleniya, “Naukova dumka”, Kiev, 1978, 164 pp. | MR

[13] Shaikhet L. E., “Ob optimalnom upravlenii odnim klassom stokhasticheskikh differentsialnykh uravnenii v chastnykh proizvodnykh”, Matem. zametki, 31:6 (1982), 933–936 | MR | Zbl

[14] Shaikhet L. E., “O neobkhodimom uslovii optimalnosti upravleniya stokhasticheskimi differentsialnymi uravneniyami giperbolicheskogo tipa”, Teoriya sluchainykh protsessov, 12 (1984), 96–101

[15] Shaikhet L. E., “Optimalnoe upravlenie nekotorymi giperbolicheskimi i integralnymi uravneniyami”, Teoriya sluchainykh protsessov, 15 (1987), 110–116 | Zbl

[16] Plotnikov V. I., Sumin V. I., “Problema ustoichivosti nelineinykh sistem Gursa–Darbu”, Differents. uravneniya, 8:5 (1972), 845–856 | MR | Zbl

[17] Srochko V. A., Variatsionnyi printsip maksimuma i metody linearizatsii v zadachakh optimalnogo upravleniya, Izd-vo IGU, Irkutsk, 1989, 160 pp. | MR

[18] Vasilev O. V. , Srochko V. A., Terletskii V. A., Metody optimizatsii, v. 2, Optimalnoe upravleniya, Nauka, Novosibirsk, 1990, 151 pp. | MR

[19] Gabasov R., Kirillova F. M., Osobye optimalnye upravleniya, URSS, M., 2011, 256 pp.

[20] Alekseev V. M., Tikhomirov V. M., Fomin S. V., Optimalnoe upravlenie, Nauka, M., 1979, 429 pp. | MR

[21] Kolodii N. A., Stokhasticheskie uravneniya Volterra na ploskosti, avtoref. dis. kand. fiz.-mat. nauk, Volgograd, 2009, 21 pp. | Zbl

[22] Akhmedov K. T., Akhiev S. S., “Ob integralnom predstavlenii reshenii nekotorykh sistem differentsialnykh uravnenii”, Izv. AN Azerb. SSR. Ser. fiz.-tekhn. i matem. nauk, 1973, no. 2, 116–120 | Zbl

[23] Mansimov K. B., “K teorii neobkhodimykh uslovii optimalnosti v odnoi zadache s raspredelennymi parametrami”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 41:10 (2001), 1505–1520 | MR

[24] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1983, 392 pp. | MR