Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Dokl. RAN. Math. Inf. Proc. Upr.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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
Full-text PDF (138 kB) Citations (2)
References:
PDF
HTML
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
\Bibitem{Sac20}
\by Yu.~L.~Sachkov
\paper Periodic time-optimal controls on two-step free-nilpotent Lie groups
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2020
\vol 492
\pages 108--111
\mathnet{http://mi.mathnet.ru/danma84}
\crossref{https://doi.org/10.31857/S2686954320030182}
\zmath{https://zbmath.org/?q=an:7424605}
\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}
Linking options:
  • https://www.mathnet.ru/eng/danma84
  • https://www.mathnet.ru/eng/danma/v492/p108
    • This publication is cited in the following 2 articles:
    1. A. V. Podobryaev, “Casimir Functions of Free Nilpotent Lie Groups of Steps 3 and 4”, J Dyn Control Syst, 27:4 (2021), 625  crossref  mathscinet
    2. A. V. Podobryaev, “Coadjoint orbits of three-step free nilpotent Lie groups and time-optimal control problem”, Dokl. Math., 102:1 (2020), 293–295  mathnet  crossref  crossref  zmath  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
    Statistics & downloads:
    Abstract page:151
    Full-text PDF :44
    References:31
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025