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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-а


DOI: https://doi.org/10.4213/mzm10186

Full text: PDF file (479 kB)
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English version:
Mathematical Notes, 2014, 95:6, 786–794

Bibliographic databases:

Document Type: Article
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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