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Conference Proceedings
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6th International Conference on Physics and Control (PhysCon 2013)
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Minimum-time damping of a physical pendulum
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We study the minimum-time damping of a physical pendulum by means of a

bounded control. In the similar problem for a linear oscillator each optimal trajectory possesses a

finite number of control switchings from the maximal to the minimal value. If one considers

simultaneously all optimal trajectories with any initial state, the number of switchings can be

arbitrary large. We show that for the nonlinear pendulum there is a uniform bound for the switching

number for all optimal trajectories. We find asymptotics for this bound as the control amplitude

goes to zero.

bounded control. In the similar problem for a linear oscillator each optimal trajectory possesses a

finite number of control switchings from the maximal to the minimal value. If one considers

simultaneously all optimal trajectories with any initial state, the number of switchings can be

arbitrary large. We show that for the nonlinear pendulum there is a uniform bound for the switching

number for all optimal trajectories. We find asymptotics for this bound as the control amplitude

goes to zero.