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Regular and Chaotic Dynamics, 2020, Volume 25, Issue 1, Pages 33–39
DOI: https://doi.org/10.1134/S1560354720010050 (Mi rcd1048) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Special issue: In honor of Valery Kozlov for his 70th birthday

Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems

Yuri L. Sachkovab

a Department of Mathematics and Statistics, P.O. Box 35, FI-40014, University of Jyväskylä, Finland
b Program Systems Institute of RAS, Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia
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DOI: https://doi.org/10.1134/S1560354720010050
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.
Keywords: optimal control, sub-Finsler geometry, Lie groups, Pontryagin maximum principle.
Funding agency Grant number
Academy of Finland 277923
European Research Council 713998 GeoMeG
Russian Science Foundation 17-11-01387
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.
Received: 29.11.2019
Accepted: 11.12.2019
Bibliographic databases:
Document Type: Article
MSC: 49J15, 53C17
Language: English
Citation: Yuri L. Sachkov, “Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems”, Regul. Chaotic Dyn., 25:1 (2020), 33–39
Citation in format AMSBIB
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\by Yuri L. Sachkov
\paper Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems
\jour Regul. Chaotic Dyn.
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\vol 25
\issue 1
\pages 33--39
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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