Control Theory Problems and the Rashevskii–Chow Theorem on a Cartan Group

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Control Theory Problems and the Rashevskii–Chow Theorem on a Cartan Group. / Greshnov, A. V.; Zhukov, R. I.

в: Siberian Mathematical Journal, Том 65, № 5, 09.2024, стр. 1096-1111.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{8d1b0813d7904c1683289fb378b10815,

title = "Control Theory Problems and the Rashevskii–Chow Theorem on a Cartan Group",

abstract = "We consider the problem of controlling the nonlinear 5-dimensional systemsthat are induced by horizontal vector fields and which together with their commutators generate some Cartan algebradepending linearly on two piecewise constant controls.We also study the properties of solutions to the systems on interpretinga solution asa horizontal -broken lineon the canonical Cartan group,where the segmentsof are segments of integral curves of the vector fields of the formwith.As regards,we prove that 4 isthe minimal numbersuch thatevery two pointscan be joined by some with.Thus,we obtain the best version of the Rashevskii–Chow theorem on the Cartan group.We also show thatthe minimal number of segments of a closed horizontal broken line on equals 6.",

keywords = "514.85:517, Carnot group, Cartan group, Rashevskii–Chow theorem, horizontal broken line, horizontal vector fields, vertex",

author = "Greshnov, {A. V.} and Zhukov, {R. I.}",

note = "The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0006).",

year = "2024",

month = sep,

doi = "10.1134/S0037446624050100",

language = "English",

volume = "65",

pages = "1096--1111",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",

number = "5",

}

RIS

TY - JOUR

T1 - Control Theory Problems and the Rashevskii–Chow Theorem on a Cartan Group

AU - Greshnov, A. V.

AU - Zhukov, R. I.

N1 - The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0006).

PY - 2024/9

Y1 - 2024/9

N2 - We consider the problem of controlling the nonlinear 5-dimensional systemsthat are induced by horizontal vector fields and which together with their commutators generate some Cartan algebradepending linearly on two piecewise constant controls.We also study the properties of solutions to the systems on interpretinga solution asa horizontal -broken lineon the canonical Cartan group,where the segmentsof are segments of integral curves of the vector fields of the formwith.As regards,we prove that 4 isthe minimal numbersuch thatevery two pointscan be joined by some with.Thus,we obtain the best version of the Rashevskii–Chow theorem on the Cartan group.We also show thatthe minimal number of segments of a closed horizontal broken line on equals 6.

AB - We consider the problem of controlling the nonlinear 5-dimensional systemsthat are induced by horizontal vector fields and which together with their commutators generate some Cartan algebradepending linearly on two piecewise constant controls.We also study the properties of solutions to the systems on interpretinga solution asa horizontal -broken lineon the canonical Cartan group,where the segmentsof are segments of integral curves of the vector fields of the formwith.As regards,we prove that 4 isthe minimal numbersuch thatevery two pointscan be joined by some with.Thus,we obtain the best version of the Rashevskii–Chow theorem on the Cartan group.We also show thatthe minimal number of segments of a closed horizontal broken line on equals 6.

KW - 514.85:517

KW - Carnot group

KW - Cartan group

KW - Rashevskii–Chow theorem

KW - horizontal broken line

KW - horizontal vector fields

KW - vertex

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85204785285&origin=inward&txGid=09df6f31284adc2d284ad6ab719fd45e

UR - https://elibrary.ru/item.asp?id=69920886

UR - https://www.mendeley.com/catalogue/927a2b6b-096a-3c8f-b911-eb8351490b7b/

U2 - 10.1134/S0037446624050100

DO - 10.1134/S0037446624050100

M3 - Article

VL - 65

SP - 1096

EP - 1111

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 5

ER -

ID: 60797940