On a class of control problems with incomplete information
Informatics and Automation, Optimal control, Tome 291 (2015), pp. 76-85.

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

For a class of nonlinear control systems with constrained control, we consider a terminal control problem of reaching a target point in which the initial point of the process and the vector of parameters of the system belong to known sets and there is no information on which point from the set of initial states is true and which parameter of the system from the set of parameters is true. We establish sufficient conditions for the existence of a solution to the problem in the class of guaranteeing program packages of Yu.S. Osipov and A.V. Kryazhimskiy. We also present the results of calculation of a model example.
@article{TRSPY_2015_291_a6,
     author = {N. L. Grigorenko and A. E. Rumyantsev},
     title = {On a class of control problems with incomplete information},
     journal = {Informatics and Automation},
     pages = {76--85},
     publisher = {mathdoc},
     volume = {291},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a6/}
}
TY  - JOUR
AU  - N. L. Grigorenko
AU  - A. E. Rumyantsev
TI  - On a class of control problems with incomplete information
JO  - Informatics and Automation
PY  - 2015
SP  - 76
EP  - 85
VL  - 291
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a6/
LA  - ru
ID  - TRSPY_2015_291_a6
ER  - 
%0 Journal Article
%A N. L. Grigorenko
%A A. E. Rumyantsev
%T On a class of control problems with incomplete information
%J Informatics and Automation
%D 2015
%P 76-85
%V 291
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a6/
%G ru
%F TRSPY_2015_291_a6
N. L. Grigorenko; A. E. Rumyantsev. On a class of control problems with incomplete information. Informatics and Automation, Optimal control, Tome 291 (2015), pp. 76-85. http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a6/

[1] Batenko A.P., Sistemy terminalnogo upravleniya, Radio i svyaz, M., 1984 | MR

[2] Blagodatskikh A.I., Petrov N.N., Konfliktnoe vzaimodeistvie grupp upravlyaemykh ob'ektov, Izd-vo Udm. un-ta, Izhevsk, 2009 | MR

[3] Blagodatskikh V.I., Vvedenie v optimalnoe upravlenie: Lineinaya teoriya, Vyssh. shk., M., 2001

[4] Chernousko F.L., Melikyan A.A., Igrovye zadachi upravleniya i poiska, Nauka, M., 1978 | MR

[5] Chikrii A.A., Konfliktno upravlyaemye protsessy, Nauk. dumka, Kiev, 1992

[6] Demidovich B.P., Lektsii po matematicheskoi teorii ustoichivosti, Nauka, M., 1967 | MR

[7] Filippov A.F., “O nekotorykh voprosakh teorii optimalnogo regulirovaniya”, Vestn. Mosk. un-ta. Matematika, mekhanika, astronomiya, fizika, khimiya, 1959, no. 2, 25–32 | Zbl

[8] Grigorenko N.L., Matematicheskie metody upravleniya neskolkimi dinamicheskimi protsessami, Izd-vo MGU, M., 1990

[9] Gusev M.I., “Vnutrennie approksimatsii mnozhestv dostizhimosti upravlyaemykh sistem s fazovymi ogranicheniyami”, Tr. In-ta matematiki i mekhaniki UrO RAN, 19:4 (2013), 73–88 | MR

[10] Krasovskii N.N., Subbotin A.I., Game-theoretical control problems, Springer, New York, 1988 | MR

[11] Krutko P.D., Obratnye zadachi dinamiki upravlyaemykh sistem: Lineinye modeli, Nauka, M., 1987 | MR

[12] Kryazhimskii A.V., Osipov Yu.S., “Idealizirovannye pakety programm i zadachi pozitsionnogo upravleniya s nepolnoi informatsiei”, Tr. In-ta matematiki i mekhaniki UrO RAN, 15:3 (2009), 139–157

[13] Kryazhimskii A.V., Strelkovskii N.V., “Zadacha garantirovannogo pozitsionnogo navedeniya lineinoi upravlyaemoi sistemy k zadannomu momentu vremeni pri nepolnoi informatsii. Programmnyi kriterii razreshimosti”, Tr. In-ta matematiki i mekhaniki UrO RAN, 20:4 (2014), 168–177 | MR

[14] Kurzhanskii A.B., Upravlenie i nablyudenie v usloviyakh neopredelennosti, Nauka, M., 1977 | MR

[15] Kurzhanskii A.B., Filippova T.F., “Ob opisanii puchka vyzhivayuschikh traektorii upravlyaemoi sistemy”, Dif. uravneniya, 23:8 (1987), 1303–1315 | MR

[16] Li E.B., Markus L., Osnovy teorii optimalnogo upravleniya, Nauka, M., 1972 | MR

[17] Lukoyanov N.Yu., Plaksin A.R., “Ob approksimatsii nelineinykh konfliktno-upravlyaemykh sistem neitralnogo tipa”, Tr. In-ta matematiki i mekhaniki UrO RAN, 20:4 (2014), 204–217 | MR

[18] Maksimov V.I., “Ob odnom algoritme upravleniya lineinoi sistemoi pri izmerenii chasti koordinat fazovogo vektora”, Tr. In-ta matematiki i mekhaniki UrO RAN, 20:4 (2014), 218–230 | MR

[19] Nikolskii M.S., “Ob odnoi zadache osuschestvleniya zadannogo dvizheniya. Gibkie sistemy”, DAN, 350:6 (1996), 739–741 | MR

[20] Osipov Yu.S., “Pakety programm: podkhod k resheniyu zadach pozitsionnogo upravleniya s nepolnoi informatsiei”, UMN, 61:4 (2006), 25–76 | DOI | Zbl

[21] Osipov Yu.S., Kryazhimskii A.V., Maksimov V.I., Metody dinamicheskogo vosstanovleniya vkhodov upravlyaemykh sistem, UrO RAN, Ekaterinburg, 2011

[22] Petrosyan L.A., Garnaev A.Yu., Igry poiska, Izd-vo S.-Peterb. un-ta, SPb., 1992 | MR

[23] Pontryagin L.S., Izbrannye trudy, MAKS Press, M., 2004

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

[25] Subbotina N.N., “Universalnye optimalnye strategii v pozitsionnykh differentsialnykh igrakh”, Dif. uravneniya, 19:11 (1983), 1890–1896 | MR | Zbl

[26] Subbotina N.N., “Nekotorye dostatochnye usloviya suschestvovaniya universalnykh strategii”, Issledovanie zadach minimaksnogo upravleniya, UNTs AN SSSR, Sverdlovsk, 1985, 72–81 | MR

[27] Ushakov V.N., Lavrov N.G., Ushakov A.V., “Konstruirovanie reshenii v zadache o sblizhenii statsionarnoi upravlyaemoi sistemy”, Tr. In-ta matematiki i mekhaniki UrO RAN, 20:4 (2014), 277–286 | MR