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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