Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya", Tome 39 (1991), pp. 41-117
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S. A. Vakhrameev. Morse theory and Lyusternik–Shnirel'man theory in geometric control theory. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya", Tome 39 (1991), pp. 41-117. http://geodesic.mathdoc.fr/item/INTD_1991_39_a1/
@article{INTD_1991_39_a1,
author = {S. A. Vakhrameev},
title = {Morse theory and {Lyusternik{\textendash}Shnirel'man} theory in geometric control theory},
journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
pages = {41--117},
year = {1991},
volume = {39},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/INTD_1991_39_a1/}
}
TY - JOUR
AU - S. A. Vakhrameev
TI - Morse theory and Lyusternik–Shnirel'man theory in geometric control theory
JO - Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya
PY - 1991
SP - 41
EP - 117
VL - 39
UR - http://geodesic.mathdoc.fr/item/INTD_1991_39_a1/
LA - ru
ID - INTD_1991_39_a1
ER -
%0 Journal Article
%A S. A. Vakhrameev
%T Morse theory and Lyusternik–Shnirel'man theory in geometric control theory
%J Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya
%D 1991
%P 41-117
%V 39
%U http://geodesic.mathdoc.fr/item/INTD_1991_39_a1/
%G ru
%F INTD_1991_39_a1
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.
