Time-Optimal Control for Pendulum-Like Systems in Case of Large Control Bounds

Abstract eng:
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. We suggest a numeric procedure that allows one to find an exact estimate 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. We consider the coordinate of the first terminal point as a parameter and find such estimate for different terminal positions in case of pendulum and earth satellite control problems.

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