This article is cited 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.

UDC: 517.974+517.977.1+517.977.5

 English version: Journal of Mathematical Sciences, 1994, 71:3, 2434–2485

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