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

DOI10.1134/S0037446622040036zbMath1501.53039arXiv2111.02988OpenAlexW3208464069WikidataQ115248246 ScholiaQ115248246MaRDI QIDQ2160176

I. A. Zubareva, Valeriĭ Nikolaevich Berestovskiĭ

Publication date: 3 August 2022

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.02988

zbMATH Keywords

optimal controlLie algebratime-optimal control problemPontryagin maximum principlepolarextremal(strictly) abnormal extremalleft-invariant sub-Finsler quasimetric

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Analysis on real and complex Lie groups (22E30) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Sub-Riemannian geometry (53C17)

Related Items (2)

Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups \(SU(2)\times{ \mathbb{R} }\) and \(SO(3)\times{ \mathbb{R} }\) with three-dimensional generating distributions ⋮ Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups \(\operatorname{SU}(1,1)\times \mathbb{R}\) and \(\operatorname{SO}_0(2,1)\times \mathbb{R}\) with three-dimensional generating distributions

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• Pontryagin maximum principle, (co)adjoint representation, and normal geodesics of left-invariant (sub-)Finsler metrics on Lie groups

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