Abnormal Extremals of Left-Invariant Sub-Finsler Quasimetrics on Four-Dimensional Lie Groups Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2021, Volume: 62, Number: 3, Pages: 383-399 Pages count : 17 DOI: 10.1134/S0037446621030010 | ||||
| Tags | (strictly) abnormal extremal; 514.752.8:514.763:514.765:514.764.227; extremal; left-invariant sub-Finsler quasimetric; Lie algebra; optimal control; polar; Pontryagin maximum principle; time-optimal problem | ||||
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Abstract:
We find the abnormal extremals on four-dimensional connected Lie groups with left-invariant sub-Finsler quasimetric defined bya seminorm on a two-dimensional subspace of the Lie algebra generating the algebra.In terms of the structure constants of a Lie algebra and the Minkowski support functionof the unit ball of the seminorm on the two-dimensional subspace of a Lie algebrawhich defines a quasimetric, we establish a criterion for the strict abnormality of these extremals.
Cite:
Berestovskii V.N.
, Zubareva I.A.
Abnormal Extremals of Left-Invariant Sub-Finsler Quasimetrics on Four-Dimensional Lie Groups
Siberian Mathematical Journal. 2021. V.62. N3. P.383-399. DOI: 10.1134/S0037446621030010 WOS Scopus OpenAlex
Abnormal Extremals of Left-Invariant Sub-Finsler Quasimetrics on Four-Dimensional Lie Groups
Siberian Mathematical Journal. 2021. V.62. N3. P.383-399. DOI: 10.1134/S0037446621030010 WOS Scopus OpenAlex
Identifiers:
| Web of science: | WOS:000655743500001 |
| Scopus: | 2-s2.0-85107200837 |
| OpenAlex: | W3168436489 |