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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 4, Pages 748–767
DOI: https://doi.org/10.33048/smzh.2022.63.403 (Mi smj7690) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Abnormal extremals of left-invariant sub-Finsler quasimetrics on four-dimensional Lie groups with three-dimensional generating distributions

V. N. Berestovskii, I. A. Zubareva

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (441 kB) Citations (5)
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DOI: https://doi.org/10.33048/smzh.2022.63.403
Abstract: We find the three-dimensional subspaces of four-dimensional Lie algebras which generate the algebras, as well as abnormal extremals on the connected Lie groups determined by these algebras and endowed with the left-invariant sub-Finsler quasimetrics defined by seminorms on the subspaces. Using the structure constants of Lie algebras and dual seminorms, we establish a criterion for the strict abnormality of the extremals.
Keywords: extremal, left-invariant sub-Finsler quasimetric, Lie algebra, optimal control, polar, Pontryagin maximum principle, (strictly) abnormal extremal, time-optimal control problem.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-281
FWNF-2022-0003
Berestovskii is supported by the Mathematical Center in Akademgorodok under Agreement 075–15–2022–281 on April 5, 2022 with the Ministry of Science and Higher Education of the Russian Federation. Zubareva’s work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0003).
Received: 27.10.2021
Revised: 27.02.2022
Accepted: 15.04.2022
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 4, Pages 620–636
DOI: https://doi.org/10.1134/S0037446622040036
Document Type: Article
UDC: 514.752.8+514.763+514.765+514.764.227
MSC: 35R30
Language: Russian
Citation: V. N. Berestovskii, I. A. Zubareva, “Abnormal extremals of left-invariant sub-Finsler quasimetrics on four-dimensional Lie groups with three-dimensional generating distributions”, Sibirsk. Mat. Zh., 63:4 (2022), 748–767; Siberian Math. J., 63:4 (2022), 620–636
Citation in format AMSBIB
\Bibitem{BerZub22}
\by V.~N.~Berestovskii, I.~A.~Zubareva
\paper Abnormal extremals of left-invariant sub-Finsler quasimetrics on four-dimensional Lie groups with three-dimensional generating distributions
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 4
\pages 748--767
\mathnet{http://mi.mathnet.ru/smj7690}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 4
\pages 620--636
\crossref{https://doi.org/10.1134/S0037446622040036}
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