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Sbornik: Mathematics, 2020, Volume 211, Issue 2, Pages 275–290
DOI: https://doi.org/10.1070/SM9236 (Mi sm9236) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Symmetries in left-invariant optimal control problems

A. V. Podobryaev

Ailamazyan Program Systems Institute of Russian Academy of Sciences, Ves'kovo, Pereslavl' district, Yaroslavl' oblast', Russia
English version PDF (544 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM9236
Abstract: Left-invariant optimal control problems on Lie groups are considered. When studying the optimality of extreme trajectories, the crucial role is played by symmetries of the exponential map that are induced by symmetries of the conjugate subsystem of the Hamiltonian system of the Pontryagin maximum principle. A general construction is obtained for these symmetries of the exponential map for connected Lie groups with generic coadjoint orbits of codimension not exceeding one and with a connected stabilizer.
Bibliography: 32 titles.
Keywords: symmetry, geometric control theory, Riemannian geometry, sub-Riemannian geometry.
Funding agency Grant number
Russian Science Foundation 17-11-01387
This research was carried out in the Ailamazyan Program Systems Institute of the Russian Academy of Sciences and was supported by the Russian Science Foundation under grant no. 17-11-01387.
Received: 17.02.2019 and 27.08.2019
Russian version:
Matematicheskii Sbornik, 2020, Volume 211, Number 2, Pages 125–140
DOI: https://doi.org/10.4213/sm9236
Bibliographic databases:
Document Type: Article
UDC: 517.977+514.765
MSC: Primary 49J21; Secondary 22E30, 53C17, 53D20
Language: English
Original paper language: Russian
Citation: A. V. Podobryaev, “Symmetries in left-invariant optimal control problems”, Mat. Sb., 211:2 (2020), 125–140; Sb. Math., 211:2 (2020), 275–290
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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