Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems
Abstract
We consider control-linear left-invariant time-optimal problems on step 2 Carnot groups with a strictly convex set of control parameters (in particular, sub-Finsler problems). We describe all Casimirs linear in momenta on the dual of the Lie algebra. In the case of rank 3 Lie groups we describe the symplectic foliation on the dual of the Lie algebra. On this basis we show that extremal controls are either constant or periodic. Some related results for other Carnot groups are presented.
Main Author
Format
Articles
Research article
Published
2020
Series
Subjects
Publication in research information system
Publisher
Pleiades Publishing
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202002252180Use this for linking
Review status
Peer reviewed
ISSN
1560-3547
DOI
https://doi.org/10.1134/S1560354720010050
Language
English
Published in
Regular and Chaotic Dynamics
Citation
- Sachkov, Y. L. (2020). Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems. Regular and Chaotic Dynamics, 25(1), 33-39. https://doi.org/10.1134/S1560354720010050
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Funder(s)
European Commission
Funding program(s)
ERC Starting Grant
ERC Starting Grant
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Education and Culture Executive Agency (EACEA). Neither the European Union nor EACEA can be held responsible for them.
Additional information about funding
Sections 1–3 of this work were supported by the Academy of Finland (grant 277923) and by the European Research Council (ERC Starting Grant 713998 GeoMeG). Sections 4–6 of this work were supported by the Russian Science Foundation under grant 17-11-01387 and performed at the Ailamazyan Program Systems Institute of Russian Academy of Sciences.
Copyright© Pleiades Publishing, Ltd., 2020.