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Generic Structure of the Lagrangian Manifold in Chattering Problems
L. V. Lokutsievskii M. V. Lomonosov Moscow State University
Abstract:
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.
DOI:
https://doi.org/10.4213/mzm10186
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English version:
Mathematical Notes, 2014, 95:6, 786–794
Bibliographic databases:
UDC:
517.974 Received: 01.11.2012
Citation:
L. V. Lokutsievskii, “Generic Structure of the Lagrangian Manifold in Chattering Problems”, Mat. Zametki, 95:6 (2014), 842–853; Math. Notes, 95:6 (2014), 786–794
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/mz10186https://doi.org/10.4213/mzm10186 http://mi.mathnet.ru/eng/mz/v95/i6/p842
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