Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya"
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Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya", 1991, Volume 39, Pages 41–117 (Mi intd129)  
This article is cited in 5 scientific papers (total in 5 papers)

Morse theory and Lyusternik–Shnirel'man theory in geometric control theory

S. A. Vakhrameev
Full-text PDF (3671 kB) Citations (5)
Abstract: Questions, related to the application of the ideas of global analysis to optimal control problems, are considered. A theory of Lyusternik–Shnirel'man type is constructed for Hilbert manifolds with singularities, the so-called transversally convex subsets. Conditions for the nondegeneracy of the critical points (the extremal controls) are established in the optimal control problem, related to a smooth control system of constant rank, and a formula for their Morse index is given.
English version:
Journal of Mathematical Sciences, 1994, Volume 71, Issue 3, Pages 2434–2485
DOI: https://doi.org/10.1007/BF02111558
Bibliographic databases:
UDC: 517.974+517.977.1+517.977.5
Language: Russian
Citation: S. A. Vakhrameev, “Morse theory and Lyusternik–Shnirel'man theory in geometric control theory”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 39, VINITI, Moscow, 1991, 41–117; J. Math. Sci., 71:3 (1994), 2434–2485
Citation in format AMSBIB
\Bibitem{Vak91}
\by S.~A.~Vakhrameev
\paper Morse theory and Lyusternik--Shnirel'man theory in geometric control theory
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.
\yr 1991
\vol 39
\pages 41--117
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd129}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1143313}
\zmath{https://zbmath.org/?q=an:0835.58006|0802.58015}
\transl
\jour J. Math. Sci.
\yr 1994
\vol 71
\issue 3
\pages 2434--2485
\crossref{https://doi.org/10.1007/BF02111558}
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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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