Geodesic
Construction of solutions in an approach problem of a stationary control system
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 277-286
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We consider a stationary control system on a finite time interval and study the problem of the approach of the system to a compact target set in the phase space. The scheme of the approximate solution of the approach problem is described briefly. A control problem for a gyroscope is given as an illustrating example.
Keywords: control, stationary control system, approach problem, solvability set, reachable set, integral funnel, gyroscope. 
@article{TIMM_2014_20_4_a23,
     author = {V. N. Ushakov and N. G. Lavrov and A. V. Ushakov},
     title = {Construction of solutions in an approach problem of a~stationary control system},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {277--286},
     year = {2014},
     volume = {20},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a23/}
}
TY  - JOUR
AU  - V. N. Ushakov
AU  - N. G. Lavrov
AU  - A. V. Ushakov
TI  - Construction of solutions in an approach problem of a stationary control system
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2014
SP  - 277
EP  - 286
VL  - 20
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a23/
LA  - ru
ID  - TIMM_2014_20_4_a23
ER  - 
%0 Journal Article
%A V. N. Ushakov
%A N. G. Lavrov
%A A. V. Ushakov
%T Construction of solutions in an approach problem of a stationary control system
%J Trudy Instituta matematiki i mehaniki
%D 2014
%P 277-286
%V 20
%N 4
%U http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a23/
%G ru
%F TIMM_2014_20_4_a23
V. N. Ushakov; N. G. Lavrov; A. V. Ushakov. Construction of solutions in an approach problem of a stationary control system. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 277-286. http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a23/

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

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

[3] Kurzhanskii A. B., “Printsip sravneniya dlya uravnenii tipa Gamiltona–Yakobi v teorii upravleniya”, Tr. In-ta matematiki i mekhaniki UrO RAN, 12, no. 1, 2006, 173–183 | MR | Zbl

[4] Kurzhanski A. B., Valyi I., Ellipsoidal calculus for estimation and control, Birkhauser, Laxenburg–Boston, 1997, 321 pp. | MR | Zbl

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

[6] 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

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

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

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

[10] Ushakov A. V., “Ob odnom variante priblizhennogo postroeniya razreshayuschikh upravlenii v zadache o sblizhenii”, Vestn. Udmurt. un-ta. Matematika. Mekhanika. Kompyuternye nauki, 2012, no. 4, 94–107 | Zbl