On a~generalization of one game control problem in the class of finitely additive measures
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2010), pp. 86-102.

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

We consider a terminal game control problem for a linear system with discontinuous coefficients under impulse controls and constraints. We construct a generalized game control problem in the class of finitely additive measures with the property of the weak absolute continuity with respect to the restriction of the Lebesgue measure to some “sufficient” measurable structure.
Mots-clés : maximin
Keywords: finitely additive measure, directionality, generalized control.
@article{IVM_2010_7_a7,
     author = {A. G. Chentsov and Yu. V. Shapar'},
     title = {On a~generalization of one game control problem in the class of finitely additive measures},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {86--102},
     publisher = {mathdoc},
     number = {7},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_7_a7/}
}
TY  - JOUR
AU  - A. G. Chentsov
AU  - Yu. V. Shapar'
TI  - On a~generalization of one game control problem in the class of finitely additive measures
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2010
SP  - 86
EP  - 102
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2010_7_a7/
LA  - ru
ID  - IVM_2010_7_a7
ER  - 
%0 Journal Article
%A A. G. Chentsov
%A Yu. V. Shapar'
%T On a~generalization of one game control problem in the class of finitely additive measures
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2010
%P 86-102
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2010_7_a7/
%G ru
%F IVM_2010_7_a7
A. G. Chentsov; Yu. V. Shapar'. On a~generalization of one game control problem in the class of finitely additive measures. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2010), pp. 86-102. http://geodesic.mathdoc.fr/item/IVM_2010_7_a7/

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

[2] Krasovskii N. N., Teoriya upravleniya dvizheniem, Nauka, M., 1968 | MR

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

[4] Gamkrelidze R. V., Osnovy optimalnogo upravleniya, Izd-vo Tbilissk. un-ta, Tbilisi, 1977 | MR | Zbl

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

[6] Chentsov A. G., “Universalnaya asimptoticheskaya realizatsiya integralnykh ogranichenii i konstruktsii rasshireniya v klasse konechno-additivnykh mer”, Tr. in-ta matem. i mekh. UrO RAN, 5, Ekaterinburg, 1998, 328–356 | Zbl

[7] Chentsov A. G., Asymptotic attainability, Kluwer Publishers, Dordrecht–Boston–London, 1997 | MR | Zbl

[8] Chentsov A. G., Finitely additive measures and relaxations of extremal problems, Plenum Publishing Corporation, 1996 | MR | Zbl

[9] Kuratovskii K., Mostovskii A., Teoriya mnozhestv, Mir, M., 1970 | MR

[10] Engelking R., Obschaya topologiya, Mir, M., 1986 | MR

[11] Burbaki N., Obschaya topologiya. Osnovnye struktury, Nauka, M., 1968 | MR

[12] Kelli Dzh. L., Obschaya topologiya, Nauka, M., 1981 | MR

[13] Neve Zh., Matematicheskie osnovy teorii veroyatnostei, Mir, M., 1969 | MR | Zbl

[14] Rao K. P. S. B., Rao M. B., Theory of charges. A study of finitely additive measures, Academic Press, London, 1983 | MR

[15] Danford H., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, In. lit., M., 1962

[16] Christensen J. P. R., “Finitely additive measure defined on a sigma-field is automatically conntably additive”, Atti Sem. Fis. Univ. Modena, 49:2 (2001), 509–511 | MR | Zbl

[17] Chentsov A. G., “K voprosu o kompaktifikatsii puchka traektorii odnoi abstraktnoi upravlyaemoi sistemy”, Izv. vuzov. Matematika, 2006, no. 5, 55–66 | MR | Zbl

[18] Chentsov A. G., Morina S. I., Extensions and relaxation, Kluwer Academic Publishers, Dordrecht–Boston–London, 2002 | MR | Zbl

[19] Chentsov A. G., Khlopin D. V., “Nekotorye konstruktsii rasshireniya igrovykh zadach s informatsionnoi diskriminatsiei”, Probl. upr. i inform., 2000, no. 5, 5–17 | MR

[20] Zavalischin D. S, Sesekin A. N., Impulsnye protsessy. Modeli i prilozheniya, Nauka, M., 1991 | MR

[21] Dykhta V. A., Samsonyuk O. N., Optimalnoe impulsnoe upravlenie s prilozheniyami, Fizmatlit, M., 2000 | MR | Zbl

[22] Khalanai A., Veksler D., Kachestvennaya teoriya impulsnykh sistem, Mir, M., 1971 | MR