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 Mat. Zametki, 2014, Volume 95, Issue 6, Pages 842–853 (Mi mz10186)

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.

 Funding Agency Grant Number Russian Foundation for Basic Research 11-01-00986-à

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

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
\Bibitem{Lok14} \by L.~V.~Lokutsievskii \paper Generic Structure of the Lagrangian Manifold in Chattering Problems \jour Mat. Zametki \yr 2014 \vol 95 \issue 6 \pages 842--853 \mathnet{http://mi.mathnet.ru/mz10186} \crossref{https://doi.org/10.4213/mzm10186} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3306222} \elib{http://elibrary.ru/item.asp?id=21826509} \transl \jour Math. Notes \yr 2014 \vol 95 \issue 6 \pages 786--794 \crossref{https://doi.org/10.1134/S000143461405023X} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000338338200023} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84903388870} 

• http://mi.mathnet.ru/eng/mz10186
• https://doi.org/10.4213/mzm10186
• http://mi.mathnet.ru/eng/mz/v95/i6/p842

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