Geodesic
The invariance of sets in the construction of solutions to a problem of approach at a fixed time
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 1, pp. 264-283 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of approach to a compact target set at a fixed time is studied. The construction of its solutions is investigated.
Keywords: control system, game problem of approach, reachable set, integral funnel, invariance, weak invariance. 
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V. N. Ushakov; A. R. Matviichuk; A. V. Ushakov; G. V. Parshikov. The invariance of sets in the construction of solutions to a problem of approach at a fixed time. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 1, pp. 264-283. http://geodesic.mathdoc.fr/item/TIMM_2013_19_1_a26/

[1] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985, 520 pp. | MR

[2] Krasovskii N. N., Lektsii po teorii upravleniya, v. 4, Osnovnaya igrovaya zadacha navedeniya. Pogloschenie tseli. Ekstremalnaya strategiya, Ural. gos. un-t, Sverdlovsk, 1970, 96 pp.

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

[4] Pontryagin L. S., “O lineinykh differentsialnykh igrakh, I”, Dokl. AN SSSR, 156:4 (1964), 738–741 | Zbl

[5] Kurzhanski A. B., Valyi I., Ellipsoidal calculus for estimation and control, Birkhauser, Boston, 1997 | MR | Zbl

[6] Kurzhanski A. A., Varaiya P., Ellipsoidal toolbox, URL: , 2005 http://code.google.com/p/ellipsoids

[7] Chernousko F. L., Otsenivanie fazovogo sostoyaniya dinamicheskikh sistem: Metod ellipsoidov, Nauka, M., 1988, 319 pp. | MR

[8] Gusev M. I., “Otsenki mnozhestva dostizhimosti mnogomernykh upravlyaemykh sistem s nelineinymi perekrestnymi svyazyami”, Tr. In-ta matematiki i mekhaniki UrO RAN, 15, no. 4, 2009, 82–94

[9] Filippova T. F., “Differentsialnye uravneniya ellipsoidalnykh otsenok mnozhestv dostizhimosti nelineinoi dinamicheskoi upravlyaemoi sistemy”, Tr. In-ta matematiki i mekhaniki UrO RAN, 16, no. 1, 2010, 223–232

[10] Kostousova E. K., “Ob ogranichennosti i neogranichennosti vneshnikh poliedralnykh otsenok mnozhestv dostizhimosti lineinykh differentsialnykh sistem”, Tr. In-ta matematiki i mekhaniki UrO RAN, 15, no. 4, 2009, 134–145

[11] Ushakov V. N., Khripunov A. P., “Postroenie integralnykh voronok differentsialnykh vklyuchenii”, Zhurn. vychisl. matematiki i mat. fiziki, 34:7 (1994), 965–977 | MR | Zbl

[12] Guseinov Kh. G., Moiseev A. N., Ushakov V. N., “Ob approoksimatsii oblastei dostizhimosti upravlyaemykh sistem”, Prikl. matematika i mekhanika, 62:2 (1998), 179–187 | MR

[13] Ushakov V. N., Matviichuk A. R., Ushakov A. V., “Approksimatsiya mnozhestv dostizhimosti i integralnykh voronok”, Vestn. Udmurt. un-ta. Matematika. Mekhanika. Kompyuternye nauki, 2011, no. 4, 23–39

[14] Li E.B., Markus L., Osnovy teorii optimalnogo upravleniya, Nauka, M., 1972, 576 pp. | MR

[15] Nikolskii M. S., “Ob approksimatsii mnozhestva dostizhimosti differentsialnogo vklyucheniya”, Vestn. MGU. Ser. 15. Vychisl. matematika i kibernetika, 1987, no. 4, 31–34 | MR

[16] Bazara M., Shetti K., Nelineinoe programmirovanie. Teoriya i algoritmy, Mir, M., 1982, 583 pp. | MR | Zbl

[17] Brokett R. W., “Asymptotic stability and feedback stabilization”, Differential Geometric Control Theory, eds. R. W. Brokett [et al.], Birkhauser, Boston, 1983, 181–191 | MR

[18] Astolfi A., Rapaport A., “Robust stabilization of the angular velocity of a rapid body”, Systems and control letters, 34 (1998), 257–264 | DOI | MR | Zbl

[19] Nikolskii M. S., “Ob otsenke iznutri mnozhestva dostizhimosti nelineinogo integratora R. Broketta”, Differents. uravneniya, 96:11 (2000), 1501–1505 | MR

[20] Vdovin S. A., Tarasev A. M., Ushakov V. N., “Postroenie mnozhestva dostizhimosti integratora Broketta”, Prikl. matematika i mekhanika, 68:5 (2004), 707–724 | MR | Zbl