Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 492, Pages 108–111
DOI: https://doi.org/10.31857/S2686954320030182 (Mi danma84) 		 
This article is cited in 2 scientific papers (total in 2 papers)

CONTROL PROCESSES

Periodic time-optimal controls on two-step free-nilpotent Lie groups

Yu. L. Sachkovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation
b Ailamazyan Program Systems Institute of Russian Academy of Sciences, Pereslavl-Zalessky, Yaroslavl Region, Russian Federation
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DOI: https://doi.org/10.31857/S2686954320030182
Abstract: For two-step free nilpotent Lie algebras, we describe symplectic foliations and Casimir functions. A left-invariant time-optimal problem is considered in which the set of admissible controls is given by a strictly convex compact set in the first layer of the Lie algebra that contains the origin in its interior. We describe integrals for the vertical subsystem of the Hamiltonian system of the Pontryagin maximum principle. The properties of solutions to this system for low ranks of the Poisson bivector are described.
Keywords: symplectic foliations, Casimir functions, time-optimal control problem, Pontryagin maximum principle, periodic controls.
Funding agency Grant number
Mathematical Center in Akademgorodok 075-15-2019-1613
This work was supported by the Mathematical Center in Akademgorodok, contract no. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation.
Presented: R. V. Gamkrelidze
Received: 13.02.2020
Revised: 31.03.2020
Accepted: 31.03.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 3, Pages 262–264
DOI: https://doi.org/10.1134/S1064562420030187
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: Yu. L. Sachkov, “Periodic time-optimal controls on two-step free-nilpotent Lie groups”, Dokl. RAN. Math. Inf. Proc. Upr., 492 (2020), 108–111; Dokl. Math., 101:3 (2020), 262–264
Citation in format AMSBIB
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\paper Periodic time-optimal controls on two-step free-nilpotent Lie groups
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\elib{https://elibrary.ru/item.asp?id=42930045}
\transl
\jour Dokl. Math.
\yr 2020
\vol 101
\issue 3
\pages 262--264
\crossref{https://doi.org/10.1134/S1064562420030187}
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    • This publication is cited in the following 2 articles:
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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