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Geometry of neighborhoods of singular trajectories in problems with multidimensional control

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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.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    M. I. Zelikin & L. V. Lokutsievskiy

  2. Laboratoire Jean Kuntzmann, Université Joseph Fourier, 51 rue des Mathématiques, Campus de Saint Martin d’Hères, BP 53, 38041, Grenoble cedex 09, France

    R. Hildebrand

Authors
  1. M. I. Zelikin
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  2. L. V. Lokutsievskiy
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  3. R. Hildebrand
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Correspondence to M. I. Zelikin.

Additional information

Original Russian Text © M.I. Zelikin, L.V. Lokutsievskiy, R. Hildebrand, 2012, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Vol. 277, pp. 74–90.

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Zelikin, M.I., Lokutsievskiy, L.V. & Hildebrand, R. Geometry of neighborhoods of singular trajectories in problems with multidimensional control. Proc. Steklov Inst. Math. 277, 67–83 (2012). https://doi.org/10.1134/S0081543812040062

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  • DOI: https://doi.org/10.1134/S0081543812040062

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