• Michail I. Zelikin
  • Vladimir Borisov
Part of the Systems & Control: Foundations & Applications book series (SCFA)


The simplest nontrivial case admitting visualization is a three-dimensional space with a curve as a singular manifold. We consider two such examples. The first one (Problem 6.1) is a modification of Fuller’s problem. This is required to minimize the weighted mean-square deviation of a massive object from the origin. The role of the control belongs to a bounded force and the weight is the discounted factor e−αt. The second example (Problem 6.2) is a time-optimal problem for some control system of third order.


Manifold Torque Dition 


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Copyright information

© Birkhäuser Boston 1994

Authors and Affiliations

  • Michail I. Zelikin
    • 1
  • Vladimir Borisov
    • 2
  1. 1.Department of MathematicsMoscow State UniversityMoscowRussia
  2. 2.Department of MathematicsMoscow Technological InstituteMoscowRussia

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