The problem of finding a guaranteeing program control for a linear system with incomplete information
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 41-49 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a linear control system with constrained control, the problem of terminal control to a target point is considered. The starting point of the process belongs to a known set, but there is no information on which point of the set is the starting point. Sufficient conditions are given for the existence of a solution of the problem in the class of Yu.S. Osipov and A.V. Kryazhimskii's guaranteeing program packages. Calculation results are presented for a model example.
Keywords: control, incomplete information, linear systems, guaranteeing program packages, program control.
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N. L. Grigorenko; Yu. A. Kondrat'eva; L. N. Luk'yanova. The problem of finding a guaranteeing program control for a linear system with incomplete information. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 41-49. http://geodesic.mathdoc.fr/item/TIMM_2015_21_2_a3/

[1] Osipov Yu.S., “Pakety programm: podkhod k resheniyu zadach pozitsionnogo upravleniya s nepolnoi informatsiei”, Uspekhi mat. nauk, 61:4 (370) (2006), 25–76 | DOI | Zbl

[2] 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

[3] 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

[4] Krasovskii N.N., Subbotin A.I., Game-theoretical control problems, Springer-Verlag, New York, 1987, 517 pp. | MR

[5] Subbotin A.I., Chentsov A.G., Optimzatsiya garantii v zadachakh upravleniya, Nauka, M., 1981, 285 pp. | MR

[6] Osipov Yu.S., Kryazhimskii A.V., Maksimov V.I., Metody dinamicheskogo vosstanovleniya vkhodov upravlyaemykh sistem, Izd-vo UrO RAN, Ekaterinburg, 2011, 291 pp.

[7] Blagodatskikh V.I., Vvedenie v optimalnoe upravlenie, Vysshaya shkola, M., 2001, 239 pp.

[8] Li E.B., Markus L., Osnovy teorii optimalnogo upravleniya, Nauka, M., 1972, 574 pp. | MR

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

[10] Pontryagin L.S., Izbrannye trudy, MAKS Press, M., 2004, 552 pp.

[11] 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

[12] 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

[13] 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

[14] Batenko A.P., Sistemy terminalnogo upravleniya, Radio i svyaz, M., 1984, 161 pp. | MR

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

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

[17] Kurzhanskii A.B.,Filippova T.F., “Ob opisanii puchka vyzhivayuschikh traektorii upravlyaemoi sistemy”, Differents. uravneniya, 23:8 (1987), 1305–1315 | MR

[18] Demidovich B.P., Lektsii po matematicheskoi teorii ustoichivosti, Nauka, M., 1967, 472 pp. | MR

[19] Krutko P.D., Obratnye zadachi dinamiki upravlyaemykh sistem. Lineinye modeli, Nauka, M., 1987, 304 pp. | MR

[20] 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

[21] Blagodatskikh A.I., Petrov N.N., Konfliktnoe vzaimodeistvie grupp upravlyaemykh ob'ektov, Udmurt. un-t, Izhevsk, 2009, 266 pp. | MR

[22] Grigorenko N.L., Matematicheskie metody upravleniya neskolkimi dinamicheskimi protsessami, Izd-vo MGU, M., 1990, 197 pp.

[23] Chikrii A.A., Konfliktno upravlyaemye protsessy, Nauk. dumka, Kiev, 1992, 373 pp.