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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
V. N. Berestovskii, I. A. Zubareva Sobolev Institute of Mathematics,
4 Koptuyg Av., Novosibirsk 630090, Russia
Abstract:
We find the abnormal extremals on four-dimensional connected Lie groups with left-invariant sub-Finsler quasimetric defined by a 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 function of the unit ball of the seminorm on the two-dimensional subspace of a Lie algebra which defines a quasimetric, we establish a criterion for the strict abnormality of these extremals.
Keywords:
extremal, left-invariant sub-Finsler quasimetric, Lie algebra, optimal control, polar, Pontryagin maximum principle, (strictly) abnormal extremal, time-optimal problem.
Received: 04.11.2020 Revised: 04.11.2020 Accepted: 24.02.2021
Citation:
V. N. Berestovskii, I. A. Zubareva, “Abnormal extremals of left-invariant sub-Finsler quasimetrics on four-dimensional Lie groups”, Sibirsk. Mat. Zh., 62:3 (2021), 477–497; Siberian Math. J., 62:3 (2021), 383–399
Linking options:
https://www.mathnet.ru/eng/smj7570 https://www.mathnet.ru/eng/smj/v62/i3/p477
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