Reachable sets and integral funnels of differential inclusions depending on a parameter
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 499 (2021), pp. 49-53.

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

A parameter-dependent control system is considered in Euclidean space $\mathbb{R}^n$. The dependence, on the parameter, of the reachable sets and integral funnels of the differential inclusion corresponding to the system is investigated. Estimates are obtained that characterize this dependence.
Keywords: control system, differential inclusion, reachable set, integral funnel, Hausdorff distance, approximation.
@article{DANMA_2021_499_a10,
     author = {V. N. Ushakov and A. A. Ershov},
     title = {Reachable sets and integral funnels of differential inclusions depending on a parameter},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {49--53},
     publisher = {mathdoc},
     volume = {499},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_499_a10/}
}
TY  - JOUR
AU  - V. N. Ushakov
AU  - A. A. Ershov
TI  - Reachable sets and integral funnels of differential inclusions depending on a parameter
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2021
SP  - 49
EP  - 53
VL  - 499
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DANMA_2021_499_a10/
LA  - ru
ID  - DANMA_2021_499_a10
ER  - 
%0 Journal Article
%A V. N. Ushakov
%A A. A. Ershov
%T Reachable sets and integral funnels of differential inclusions depending on a parameter
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2021
%P 49-53
%V 499
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DANMA_2021_499_a10/
%G ru
%F DANMA_2021_499_a10
V. N. Ushakov; A. A. Ershov. Reachable sets and integral funnels of differential inclusions depending on a parameter. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 499 (2021), pp. 49-53. http://geodesic.mathdoc.fr/item/DANMA_2021_499_a10/

[1] Kurjanski A., Valyi I., Ellipsoidal Calculus for Estimation and Control. Systems Control: Foundations Applications, Birkhäuser Basel and IIASA, Boston–Basel–B., 1997, 321 pp. | MR

[2] Kurzhanskii A.B., Izbrannye trudy, Izd-vo MGU, M., 2009, 756 pp.

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

[4] Chernousko F.L., Melikyan A.A., Igrovye zadachi upravleniya i poiska, Nauka, M., 1978, 270 pp. | MR

[5] Krasovskii N.N., Subbotin A.I., Pozitsionnye differentsialnye igry, Fizmatlit, M., 1974, 456 pp. | MR

[6] Lempio F., Veliov V.M., “Discrete approximation of differential inclusions”, Bayr. Math. Schriften, 54 (1998), 149–232 | MR | Zbl

[7] Nikolskii M.S., “Ob approksimatsii mnozhestva dostizhimosti differentsialnogo vklyucheniya”, Vest. Moskov. un-ta. Ser. 15. Vychisl. matematika i kibernetika, 1987, no. 4, 31–34

[8] Vdovin S.A., Tarasev A.M., Ushakov V.N., “Postroenie mnozhestva dostizhimosti integratora Brokitta”, Prikl. matematika i mekhanika, 68:5 (2004), 707–794 | DOI | MR

[9] Ananevskii I.M., “Sintez upravleniya lineinymi sistemami s pomoschyu metodov teorii ustoichivosti dvizheniya”, Differents. uravneniya, 39:1 (2003), 3–11 | DOI | MR | Zbl

[10] Gusev M.I., “Otsenki mnozhestv dostizhimosti mnogomernykh upravlyaemykh sistem s nelineinymi perekrestnymi svyazyami”, Tr. IMM UrO RAN, 15, no. 4, 2009, 82–94 | DOI

[11] Filippova T.F., “Postroenie mnogoznachnykh otsenok mnozhestv dostizhimosti nekotorykh nelineinykh dinamicheskikh sistem s impulsnym upravleniem”, Tr. IMM UrO RAN, 15, no. 4, 2009, 262–269 | DOI

[12] Ushakov V.N., Matviichuk A.R., Ushakov A.V., “Approksimatsiya mnozhestv dostizhimosti i integralnykh voronok differentsialnykh vklyuchenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 4, 23–39 | Zbl

[13] Ershov A.A., Ushakov V.N., “O sblizhenii upravlyaemoi sistemy, soderzhaschei neopredelennyi parametr”, Matem. sb., 208:9 (2017), 56–99 | DOI | MR | Zbl

[14] Beznos A.V., Grishin A.A., Lenskii A.V., Okhotsimskii D.E., Formalskii A.M., Upravlenie mayatnikom pri pomoschi makhovika, ed. V.V. Aleksandrov, Izd-vo Mosk. un-ta, M., 2009, 170–195 | MR

[15] Polyak B.T., Khlebnikov M.V., Scherbakov P.S., Upravlenie lineinymi sistemami pri vneshnikh vozmuscheniyakh: Tekhnika lineinykh matrichnykh neravenstv, LENAND, M., 2014, 560 pp.