Email this article A Sub-Finsler Problem on the Cartan Group
- Authors: Ardentov A.A.1, Le Donne E.2, Sachkov Y.L.1
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Affiliations:
- Ailamazyan Program Systems Institute of Russian Academy of Sciences
- Department of Mathematics and Statistics
- Issue: Vol 304, No 1 (2019)
- Pages: 42-59
- Section: Article
- URL: https://journals.rcsi.science/0081-5438/article/view/175735
- DOI: https://doi.org/10.1134/S0081543819010048
- ID: 175735
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Abstract
We study a sub-Finsler geometric problem on the free nilpotent group of rank 2 and step 3. Such a group is also called the Cartan group and has a natural structure of Carnot group, which we metrize by considering the l∞ norm on its first layer. We adopt the point of view of time-optimal control theory. We characterize extremal curves via the Pontryagin maximum principle. We describe abnormal and singular arcs and construct the bang-bang flow.
About the authors
A. A. Ardentov
Ailamazyan Program Systems Institute of Russian Academy of Sciences
Author for correspondence.
Email: aaa@pereslavl.ru
Russian Federation, Pereslavl-Zalessky, Yaroslavl Region, 152020
E. Le Donne
Department of Mathematics and Statistics
Author for correspondence.
Email: ledonne@msri.org
Finland, Jyväskylä, FI-40014
Yu. L. Sachkov
Ailamazyan Program Systems Institute of Russian Academy of Sciences
Author for correspondence.
Email: yusachkov@gmail.com
Russian Federation, Pereslavl-Zalessky, Yaroslavl Region, 152020
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