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Mat. Sb., 2008, Volume 199, Number 4, Pages 143–158 (Mi msb3886)  

This article is cited in 4 scientific papers (total in 4 papers)

Codimension-two singularities in 3D affine control systems with a scalar control

A. O. Remizov

University of Porto

Abstract: Codimension-two singularities of the field of totally singular extremal trajectories in 3D affine control systems with scalar control are investigated. These singularities can be of two types: the first is related to singularities of the field of the Hamiltonian system of the maximum principle itself, while the second is related to the degenerate projection of the field of totally singular extremals onto the phase space. The fields of extremal trajectories occurring in these two cases have completely different normal forms and phase portraits.
Bibliography: 7 titles.

DOI: https://doi.org/10.4213/sm3886

Full text: PDF file (543 kB)
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English version:
Sbornik: Mathematics, 2008, 199:4, 613–627

Bibliographic databases:

UDC: 517.977
MSC: Primary 93C15, 93B27; Secondary 49K15
Received: 23.05.2007

Citation: A. O. Remizov, “Codimension-two singularities in 3D affine control systems with a scalar control”, Mat. Sb., 199:4 (2008), 143–158; Sb. Math., 199:4 (2008), 613–627

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. O. Remizov, “Geodesics on 2-surfaces with pseudo-Riemannian metric: singularities of changes of signature”, Sb. Math., 200:3 (2009), 385–403  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Ghezzi R., Remizov A.O., “On a class of vector fields with discontinuities of divide-by-zero type and its applications to geodesics in singular metrics”, J. Dyn. Control Syst., 18:1 (2012), 135–158  crossref  mathscinet  zmath  isi  scopus
    3. A. O. Remizov, “Geodesics in generalized Finsler spaces: singularities in dimension two”, J. Singul., 14 (2016), 172–193  mathscinet  zmath
    4. Ortiz-Bobadilla L. Rosales-Gonzalez E. Voronin S.M., “Analytic Classification of Foliations Induced By Germs of Holomorphic Vector Fields in (C-N,0) With Non-Isolated Singularities”, J. Dyn. Control Syst., 25:3 (2019), 491–516  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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