Geodesic
Generic Structure of the Lagrangian Manifold in Chattering Problems
Matematičeskie zametki, Tome 95 (2014) no. 6, pp. 842-853

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This paper studies the structure of the singularity of Lagrangian manifolds in a neighborhood of the surface of singular extremals of second order in optimal control problems. For the Fuller classical problem, the structure of the Lagrangian manifold is explicitly constructed: it is shown that it has a singularity of conic type at the origin of coordinates. In the general case, it is proved that the Lagrangian manifold is a locally trivial fiber bundle over the surface of singular extremals with each fiber having a singularity of a similar conic type at the point of exit of the singular extremals.
Keywords: chattering problem, Lagrangian manifold, singular extremal, Fuller chattering problem, singular extremal, Hamiltonian system, singularity of conic type. 
L. V. Lokutsievskii. Generic Structure of the Lagrangian Manifold in Chattering Problems. Matematičeskie zametki, Tome 95 (2014) no. 6, pp. 842-853. http://geodesic.mathdoc.fr/item/MZM_2014_95_6_a5/
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