Geodesic
On extension of conflict control problems on infinite horizon
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2011), pp. 105-112 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The extension of a conflict control problem with infinite horizon is constructed. This extension is the projective limit of restricted games. Relations between “sensitivity to target set” and the existence of the optimal control are studied. Special attention is paid to the pursuit-evasion game with “joint control/relaxed control”.
Keywords: an extension for infinity horizon game, existence of maximin, sensitivity of value. 
@article{VUU_2011_1_a10,
     author = {D. V. Khlopin},
     title = {On extension of conflict control problems on infinite horizon},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {105--112},
     year = {2011},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2011_1_a10/}
}
TY  - JOUR
AU  - D. V. Khlopin
TI  - On extension of conflict control problems on infinite horizon
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2011
SP  - 105
EP  - 112
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VUU_2011_1_a10/
LA  - ru
ID  - VUU_2011_1_a10
ER  - 
%0 Journal Article
%A D. V. Khlopin
%T On extension of conflict control problems on infinite horizon
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2011
%P 105-112
%N 1
%U http://geodesic.mathdoc.fr/item/VUU_2011_1_a10/
%G ru
%F VUU_2011_1_a10
D. V. Khlopin. On extension of conflict control problems on infinite horizon. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2011), pp. 105-112. http://geodesic.mathdoc.fr/item/VUU_2011_1_a10/

[1] Yang L., Lektsii po variatsionnomu upravleniyu i teorii optimalnogo upravleniya, Mir, M., 1974, 488 pp. | MR

[2] Gamkrelidze R. V., Osnovy optimalnogo upravleniya, Izd-vo Tbilis. un-ta, Tbilisi, 1977, 254 pp. | MR

[3] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977, 623 pp. | MR

[4] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 456 pp. | MR | Zbl

[5] Krasovskii N. N., “Differentsialnaya igra ukloneniya. 1”, Izv. AN SSSR. Tekhn. kibernetika, 1973, no. 2, 3–18 | MR

[6] Krasovskii N. N., Igrovye zadachi o vstreche dvizhenii, Nauka, M., 1970, 420 pp. | MR | Zbl

[7] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi: zadacha o minimume garantirovannogo rezultata, Nauka, M., 1985, 516 pp. | MR

[8] Chentsov A. G., Konechno-additivnye mery i relaksatsii ekstremalnykh zadach, UIF “Nauka”, Ekaterinburg, 1993, 232 pp.

[9] Chentsov A. G., Asymptotic attainability, Kluwer Academic Publishers, Dordrecht, 1997 | MR | Zbl

[10] Chentsov A. G., Khlopin D. V., “Nekotorye konstruktsii rasshireniya igrovykh zadach s informatsionnoi diskriminatsiei”, Problemy upravleniya i informatiki, 2000, no. 5, 5–17 | MR

[11] Engelking R., Obschaya topologiya, Mir, M., 1986, 751 pp. | MR

[12] Filippov V. V., Fedorchuk V. V., Obschaya topologiya. Osnovnye konstruktsii, Fizmatlit, M., 2006, 336 pp.

[13] Yu. G. Borisovich, B. D. Gelman, A. D. Myshkis, V. V. Obukhovskii, Vvedenie v teoriyu mnogoznachnykh otobrazhenii i differentsialnykh vklyuchenii, Kom. Kniga, M., 2005, 216 pp. | MR

[14] Tolstonogov A. A., Differentsialnye vklyucheniya v banakhovom prostranstve, Nauka, M., 1986, 296 pp. | MR | Zbl

[15] Chentsov A. G., “Ob odnoi igrovoi zadache upravleniya na minimaks”, Izv. AN SSSR. Tekhn. kibernetika, 1975, no. 1, 39–46 | MR | Zbl

[16] Chentsov A. G., Metod programmnykh iteratsii dlya differentsialnoi igry sblizheniya-ukloneniya, Dep. v VINITI 04.06.79, No 1933-79, AN SSSR. UNTs. IMM, Sverdlovsk, 1979, 103 pp.