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Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya", 1991, Volume 39, Pages 41–117
(Mi intd129)
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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
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.
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
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https://www.mathnet.ru/eng/intd129 https://www.mathnet.ru/eng/intd/v39/p41
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Abstract page: | 499 | Full-text PDF : | 347 |
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