Geodesic
Morse theory and Lyusternik--Shnirel'man theory in geometric control theory
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 39 (1991), pp. 41-117

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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. 
@article{INTD_1991_39_a1,
     author = {S. A. Vakhrameev},
     title = {Morse theory and {Lyusternik--Shnirel'man} theory in geometric control theory},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
     pages = {41--117},
     publisher = {mathdoc},
     volume = {39},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTD_1991_39_a1/}
}
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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, Tome 39 (1991), pp. 41-117. http://geodesic.mathdoc.fr/item/INTD_1991_39_a1/