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Time-Optimal Control Problem for a Special Class of Control Systems: Optimal Controls and Approximation in the Sense of Time Optimality

Author

Listed:
  • Grigory M. Sklyar

    (University of Szczecin)

  • Svetlana Yu. Ignatovich

    (Kharkov National University)

  • Sergey E. Shugaryov

    (Kharkov National University)

Abstract

We consider the time-optimal control problem to the origin for a class of nonlinear systems, called dual-to-linear systems. We obtain the general description of possible optimal controls. In particular, we show that optimal controls take the values $$-1$$ - 1 , $$0$$ 0 , and $$+1$$ + 1 only and have a finite number of points of discontinuity. We describe a class of nonlinear affine control systems which can be approximated by dual-to-linear systems in the sense of time optimality.

Suggested Citation

  • Grigory M. Sklyar & Svetlana Yu. Ignatovich & Sergey E. Shugaryov, 2015. "Time-Optimal Control Problem for a Special Class of Control Systems: Optimal Controls and Approximation in the Sense of Time Optimality," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 62-77, April.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:1:d:10.1007_s10957-014-0607-6
    DOI: 10.1007/s10957-014-0607-6
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