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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Volume 277, Pages 74–90 (Mi tm3381)  
This article is cited in 13 scientific papers (total in 13 papers)

Geometry of neighborhoods of singular trajectories in problems with multidimensional control

M. I. Zelikina, L. V. Lokutsievskiya, R. Hildebrandb

a Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
b Laboratoire Jean Kuntzmann, Université Joseph Fourier, Grenoble, France
Full-text PDF (261 kB) Citations (13)
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Abstract: It is shown that the order of a singular trajectory in problems with multidimensional control is described by a flag of linear subspaces in the control space. In terms of this flag, we construct necessary conditions for the junction of a nonsingular trajectory with a singular one in affine control systems. We also give examples of multidimensional problems in which the optimal control has the form of an irrational winding of a torus that is passed in finite time.
Received in May 2011
English version:
Proceedings of the Steklov Institute of Mathematics, 2012, Volume 277, Pages 67–83
DOI: https://doi.org/10.1134/S0081543812040062
Bibliographic databases:
Document Type: Article
UDC: 517.97
Language: Russian
Citation: M. I. Zelikin, L. V. Lokutsievskiy, R. Hildebrand, “Geometry of neighborhoods of singular trajectories in problems with multidimensional control”, Mathematical control theory and differential equations, Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko, Trudy Mat. Inst. Steklova, 277, MAIK Nauka/Interperiodica, Moscow, 2012, 74–90; Proc. Steklov Inst. Math., 277 (2012), 67–83
Citation in format AMSBIB
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\paper Geometry of neighborhoods of singular trajectories in problems with multidimensional control
\inbook Mathematical control theory and differential equations
\bookinfo Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko
\serial Trudy Mat. Inst. Steklova
\yr 2012
\vol 277
\pages 74--90
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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