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.
\Bibitem{Rem08}
\by A.~O.~Remizov
\paper Codimension-two singularities in 3D affine control systems with a scalar control
\jour Sb. Math.
\yr 2008
\vol 199
\issue 4
\pages 613--627
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\crossref{https://doi.org/10.1070/SM2008v199n04ABEH003935}
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Linking options:
https://www.mathnet.ru/eng/sm3886
https://doi.org/10.1070/SM2008v199n04ABEH003935
https://www.mathnet.ru/eng/sm/v199/i4/p143
This publication is cited in the following 4 articles:
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
A. O. Remizov, “Geodesics in generalized Finsler spaces: singularities in dimension two”, J. Singul., 14 (2016), 172–193
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
A. O. Remizov, “Geodesics on 2-surfaces with pseudo-Riemannian metric: singularities of changes of signature”, Sb. Math., 200:3 (2009), 385–403
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