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Properties of the Time-Optimal Feedback Control for a Pendulum-Like System

Author

Listed:
  • Sergey A. Reshmin

    (Russian Academy of Sciences)

  • Felix L. Chernousko

    (Russian Academy of Sciences)

Abstract

A time-optimal control problem for a pendulum-like system is considered. The system describes the dynamics of an inertial object under the action of a bounded control force and an external force which is periodic in coordinate. The terminal set consists of points on the abscissa axis of the phase plane, and the distance between two neighboring points is equal to the period of the external force. In the general case, the solution can be obtained only numerically. An estimate is found for the amplitude of the control for which the time-optimal feedback control has the simplest structure: the number of switchings is not greater than one for any initial conditions. For the estimated interval of the control constraints, we analyze the feedback control pattern.

Suggested Citation

  • Sergey A. Reshmin & Felix L. Chernousko, 2014. "Properties of the Time-Optimal Feedback Control for a Pendulum-Like System," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 230-252, October.
    • Handle: RePEc:spr:joptap:v:163:y:2014:i:1:d:10.1007_s10957-013-0480-8
    DOI: 10.1007/s10957-013-0480-8
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    Cited by:

    1. Yusheng Zhou & Zaihua Wang & Kwok-wai Chung, 2019. "Turning Motion Control Design of a Two-Wheeled Inverted Pendulum Using Curvature Tracking and Optimal Control Theory," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 634-652, May.

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