Numerical construction of attainability domains for systems with impulse control
Trudy Instituta matematiki i mehaniki, Dynamical systems and control problems, Tome 11 (2005) no. 1, pp. 65-73
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A numerical algorithm is suggested for constructing the attainability set of a nonlinear control system with an impulse integrally bounded control that is included in the system linearly. The algorithm is based on the approximation of admissible controls by linear combinations of Dirac delta-functions and discretization of the space of positions of the system. An estimate of accuracy of the suggested algorithm is obtained. An illustrative example is given.
@article{TIMM_2005_11_1_a6,
     author = {O. I. Vdovina and A. N. Sesekin},
     title = {Numerical construction of attainability domains for systems with impulse control},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {65--73},
     year = {2005},
     volume = {11},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2005_11_1_a6/}
}
TY  - JOUR
AU  - O. I. Vdovina
AU  - A. N. Sesekin
TI  - Numerical construction of attainability domains for systems with impulse control
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2005
SP  - 65
EP  - 73
VL  - 11
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMM_2005_11_1_a6/
LA  - ru
ID  - TIMM_2005_11_1_a6
ER  - 
%0 Journal Article
%A O. I. Vdovina
%A A. N. Sesekin
%T Numerical construction of attainability domains for systems with impulse control
%J Trudy Instituta matematiki i mehaniki
%D 2005
%P 65-73
%V 11
%N 1
%U http://geodesic.mathdoc.fr/item/TIMM_2005_11_1_a6/
%G ru
%F TIMM_2005_11_1_a6
O. I. Vdovina; A. N. Sesekin. Numerical construction of attainability domains for systems with impulse control. Trudy Instituta matematiki i mehaniki, Dynamical systems and control problems, Tome 11 (2005) no. 1, pp. 65-73. http://geodesic.mathdoc.fr/item/TIMM_2005_11_1_a6/

[1] Krasovskii N. N., Teoriya upravleniya dvizheniem, Nauka, M., 1968, 476 pp. | MR

[2] Kurzhanski A. B., Vályi I., “Ellipsoidal techniques for dynamic systems”, Dynamics and Control, 1 (1991), 357–378 | DOI | MR | Zbl

[3] Chernousko F. L., “Ellipsoidalnye otsenki oblasti dostizhimosti upravlyaemoi sistemy”, Prikl. matematika i mekhanika, 45:1 (1981), 11–19 | MR

[4] Konstantinov G. N., Normirovanie vozdeistvii na dinamicheskie sistemy, Izd-vo Irkutskogo un-ta, Irkutsk, 1983, 188 pp.

[5] Guseinov Kh. G., Neznakhin A. A., Ushakov V. N., “Priblizhennoe postroenie mnozhestv dostizhimosti upravlyaemykh sistem s integralnymi ogranicheniyami na upravlenie”, Prikl. matematika i mekhanika, 63:4 (1999), 580–590 | MR

[6] Khalanai A., Veksler D., Kachestvennaya teoriya impulsnykh sistem, Mir, M., 1971, 310 pp. | MR

[7] Sesekin A. N., “Svoistva mnozhestva dostizhimosti dinamicheskoi sistemy s impulsnym upravleniem”, Avtomatika i telemekhanika, 1994, no. 2, 52–59 | MR | Zbl

[8] Sesekin A. N., “O mnozhestvakh razryvnykh reshenii nelineinykh differentsialnykh uravnenii”, Izv. vuzov. Matematika, 1994, no. 6, 83–89 | MR | Zbl

[9] Sesekin A. N., “O svyaznosti mnozhestva razryvnykh reshenii nelineinoi dinamicheskoi sistemy s impulsnym upravleniem”, Izv. vuzov. Matematika, 1996, no. 11, 85–93 | MR | Zbl

[10] Zavalishchin S. T., Sesekin A. N., Dynamic Impulse Systems. Theory and Applications, Kluwer Acad. Publ., Dordrecht etc., 1997, 268 pp. | MR | Zbl

[11] Barbashin E. A., Vvedenie v teoriyu ustoichivosti, Nauka, M., 1967, 224 pp. | Zbl

[12] Miller B. M., “Zadacha nelineinogo impulsnogo upravleniya ob'ektami, opisyvaemymi differentsialnymi uravneniyami s meroi. I, II”, Avtomatika i telemekhanika, 1978, no. 1, 75–85 ; No 3, 34–42 | Zbl