Geometry of neighborhoods of singular trajectories in problems with multidimensional control

  • M. I. Zelikin
  • L. V. Lokutsievskiy
  • R. Hildebrand


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.


Hamiltonian System STEKLOV Institute Optimal Trajectory Local Order Pontryagin Maximum Principle 
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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • M. I. Zelikin
    • 1
  • L. V. Lokutsievskiy
    • 1
  • R. Hildebrand
    • 2
  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Laboratoire Jean KuntzmannUniversité Joseph FourierGrenoble cedex 09France

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