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. 
@article{MZM_2014_95_6_a5,
     author = {L. V. Lokutsievskii},
     title = {Generic {Structure} of the {Lagrangian} {Manifold} in {Chattering} {Problems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {842--853},
     publisher = {mathdoc},
     volume = {95},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_6_a5/}
}
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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/