On the time-optimal problem for three- and four-dimensional control systems

  • M. S. Nikol’skii


The paper is devoted to the time-optimal problem for three- and four-dimensional nonlinear control systems with one-dimensional control. We obtain sufficient conditions for a time-optimal control to be equivalent (in the Lebesgue sense) to a piecewise constant control that is also optimal, has a finite number of discontinuity points, and takes only extreme values. Such optimal controls are called bang-bang solutions and are of considerable interest in control theory and its applications.


STEKLOV Institute Nontrivial Solution Control Object Adjoint Equation Optimal Control Theory 
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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • M. S. Nikol’skii
    • 1
  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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