About presentation of maximin in the game problem with constraints of asymptotic character
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2010), pp. 104-119 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The abstract game problem of control and its relaxations connected with a weakening of constraints on the choice of programmed strategies are considered. In this case, the series of maximin problems is realized; for this series, the sets of admissible strategies of participants form directed systems. It is established that realized maximins are convergent. The representation of the corresponding generalized limit is established.
Mots-clés : maximin
Keywords: attraction set, constraints of asymptotic character.
@article{VUU_2010_3_a11,
     author = {A. G. Chentsov},
     title = {About presentation of maximin in the game problem with constraints of asymptotic character},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {104--119},
     year = {2010},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2010_3_a11/}
}
TY  - JOUR
AU  - A. G. Chentsov
TI  - About presentation of maximin in the game problem with constraints of asymptotic character
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2010
SP  - 104
EP  - 119
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VUU_2010_3_a11/
LA  - ru
ID  - VUU_2010_3_a11
ER  - 
%0 Journal Article
%A A. G. Chentsov
%T About presentation of maximin in the game problem with constraints of asymptotic character
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2010
%P 104-119
%N 3
%U http://geodesic.mathdoc.fr/item/VUU_2010_3_a11/
%G ru
%F VUU_2010_3_a11
A. G. Chentsov. About presentation of maximin in the game problem with constraints of asymptotic character. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2010), pp. 104-119. http://geodesic.mathdoc.fr/item/VUU_2010_3_a11/

[1] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977, 624 pp. | MR

[2] Gamkrelidze R. V., Osnovy optimalnogo upravleniya, Izd-vo Tbilis. un-ta, Tbilisi, 1975, 229 pp. | MR

[3] Ioffe A. D., Tikhomirov V. M., Teoriya ekstremalnykh zadach, Nauka, M., 1974, 479 pp. | MR | Zbl

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

[5] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi. Zadacha o minimume garantirovannogo rezultata, Nauka, M., 1985, 518 pp. | MR

[6] Subbotin A. I., Chentsov A. G., Optimizatsiya garantii v zadachakh upravleniya, Nauka, M., 1981, 287 pp. | MR

[7] Kuratovskii K., Mostovskii A., Teoriya mnozhestv, Mir, M., 1970, 416 pp. | MR

[8] Burbaki N., Obschaya topologiya. Osnovnye struktury, Nauka, M., 1968, 272 pp. | MR

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

[10] Chentsov A. G., “Rasshireniya abstraktnykh zadach o dostizhimosti: nesekventsialnaya versiya”, Trudy Instituta matematiki i mekhaniki UrO RAN, 13, no. 2, Ekaterinburg, 2007, 184–217

[11] Chentsov A. G., Shapar Yu. V., “Konechno-additivnye mery i rasshireniya igrovykh zadach s ogranicheniyami asimptoticheskogo kharaktera”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2010, no. 1, 89–111 | MR

[12] Chentsov A. G., Asymptotic attainability, Kluwer Academic Publishers, Dordrecht, Boston, London, 1997, 322 pp. | MR | Zbl

[13] Chentsov A. G., Morina S. I., Extensions and Relaxations, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002, 408 pp. | MR | Zbl

[14] Chentsov A. G., “Asimptoticheski dostizhimye elementy i ikh obobschennoe predstavlenie”, Trudy Instituta matematiki i mekhaniki UrO RAN, 3, Ekaterinburg, 1995, 211–244 | MR | Zbl

[15] Chentsov A. G., “Universalnaya asimptoticheskaya realizatsiya integralnykh ogranichenii i konstruktsii rasshireniya v klasse konechno-additivnykh mer”, Trudy Instituta matematiki i mekhaniki UrO RAN, 5, Ekaterinburg, 1998, 328–356 | MR | Zbl

[16] Chentsov A. G., Finitely additive measures and relaxations of extremal problems, Plenum Publishing Corporation, New York, London, Moscow, 1996, 244 pp. | MR | Zbl

[17] Chentsov A. G., “Rasshireniya v klasse konechno-additivnykh mer i usloviya asimptoticheskoi nechuvstvitelnosti pri oslablenii chasti ogranichenii”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2009, no. 1, 131–152