Geodesic
On an optimal control problem for a linear system with variable structure
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 1, pp. 63-70 
R. O. Mastaliyev. On an optimal control problem for a linear system with variable structure. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 1, pp. 63-70. http://geodesic.mathdoc.fr/item/VMJ_2016_18_1_a7/
@article{VMJ_2016_18_1_a7,
     author = {R. O. Mastaliyev},
     title = {On an optimal control problem for a~linear system with variable structure},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {63--70},
     year = {2016},
     volume = {18},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2016_18_1_a7/}
}
TY  - JOUR
AU  - R. O. Mastaliyev
TI  - On an optimal control problem for a linear system with variable structure
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2016
SP  - 63
EP  - 70
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMJ_2016_18_1_a7/
LA  - ru
ID  - VMJ_2016_18_1_a7
ER  - 
%0 Journal Article
%A R. O. Mastaliyev
%T On an optimal control problem for a linear system with variable structure
%J Vladikavkazskij matematičeskij žurnal
%D 2016
%P 63-70
%V 18
%N 1
%U http://geodesic.mathdoc.fr/item/VMJ_2016_18_1_a7/
%G ru
%F VMJ_2016_18_1_a7

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

The necessary and sufficient condition for optimality in the form of the Pontryagin maximum principle in optimal control problem with variable linear structure, described by linear difference and integral-differential equations of Volterra type, is obtained. Under some additional assumptions sufficient optimality conditions are also derived.

[1] Ostrovskii G. M., Volin Yu. M., Modelirovanie slozhnykh khimiko-tekhnologicheskikh skhem, Khimiya, M., 1975, 311 pp.

[2] Agafonova I. A., Gulin L. L., Rasina I. V., Matematicheskoe modelirovanie i optimizatsiya protsessa metilirovaniya dinatrievoi soli sulfaminoantiprina, Dep. v VINITI AN SSSR No 3457, M., 1978, 19 pp.

[3] Beletskii V. V., “Dinamika dvunogoi khodby”, Izv. AN SSSR. Mekhanika tverdogo tela, no. 3, 3–14

[4] Gurman V. I., Orlov A. G., “Dostatochnye usloviya optimalnosti slozhnykh protsessov”, Avtomatika i telemekhanika, 1978, no. 4, 127–134 | Zbl

[5] Gurman V. I., Orlov A. G., Slozhnye protsessy dvunogoi khodby, Preprint No 95, IPM im. M. V. Keldysha, 1979, 39 pp.

[6] Arsenashvili A. I., Tadumadze T. A., “Neobkhodimye usloviya optimalnosti dlya upravlyaemykh sistem s peremennoi strukturoi i nepreryvnymi usloviyami preemstvennosti”, Tr. IPM im. I. N. Vekua Tbilisskogo gos. un-ta, 27, Tbilisi, 1998, 35–48

[7] Ismailov R. R., Mansimov K. B., “Ob usloviyakh optimalnosti v odnoi stupenchatoi zadache upravleniya”, Zhurn. vych. matatematiki i mat. fiziki, 46:10 (2006), 1758–1770 | MR

[8] Abdullaev A. A., Mansimov K. B., Neobkhodimye usloviya optimalnosti v protsessakh, opisyvaemykh sistemoi integralnykh uravnenii tipa Volterra, Izd-vo Elm, Baku, 2013, 224 pp.

[9] Gurman V. I., “K teorii optimalnykh diskretnykh protsessov”, Avtomatika i telemekhanika, 1973, no. 6, 53–58 | Zbl

[10] Mansimov K. B., Diskretnye sistemy, Izd.-vo BGU, Baku, 2002, 114 pp.

[11] Mastaliev R. O., “Ob odnoi stupenchatoi zadache optimalnogo upravleniya diskretnymi sistemami”, Vestn. Bakinskogo un-ta. Ser. fiz.-mat. nauk, 2010, no. 1, 33–39

[12] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1969, 384 pp.

[13] Gabasov R., Kirillova F. M., Optimizatsiya lineinykh sistem, Izd-vo BGU, Minsk, 1973, 185 pp.

[14] Gabasov R., Kirillova F. M., Printsip maksimuma v teorii optimalnogo upravleniya, Nauka i tekhnika, Minsk, 1974, 274 pp. | MR

[15] Kolmanovskii V. B., “Ob asimptoticheskikh svoistvakh reshenii nekotorykh nelineinykh sistem Volterra”, Avtomatika i telemekhanika, 2000, no. 4, 42–50 | MR | Zbl

[16] Kolmanovskii V. B., “Ob asimptoticheskoi ekvivalentnosti reshenii nekotorykh raznostnykh uravnenii”, Avtomatika i telemekhanika, 2001, no. 4, 47–56 | MR | Zbl

[17] Vasileva A. B., Tikhonov A. N., Integralnye uravneniya, Izd-vo MGU, M., 1989, 550 pp.

[18] Tsalyuk Z. B., “Integralnye uravneniya Volterra”, Itogi nauki i tekhniki. Ser. Mat. analiz, 15, 1977, 131–198 | MR | Zbl