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Morse theory and Lyusternik-Shnirelman theory in geometric control theory

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Abstract

Questions, related to the application of the ideas of global analysis to optimal control problems, are considered. A theory of Lyusternik-Shnirelman 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.

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  1. S. A. Vakhrameev
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 39, pp. 41–117, 1991.

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Vakhrameev, S.A. Morse theory and Lyusternik-Shnirelman theory in geometric control theory. J Math Sci 71, 2434–2485 (1994). https://doi.org/10.1007/BF02111558

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