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

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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.

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Acknowledgements

This work was supported by the Presidential Program for the State Support of Leading Scientific Schools (Project No. NSh-369.2012.1) and the Russian Foundation for Basic Research Pproject Nos. 11-01-00378, 11-08-00435, and 11-01-00513).

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Authors and Affiliations

  1. Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

    Sergey A. Reshmin & Felix L. Chernousko

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  1. Sergey A. Reshmin
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  2. Felix L. Chernousko
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Correspondence to Sergey A. Reshmin.

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Reshmin, S.A., Chernousko, F.L. Properties of the Time-Optimal Feedback Control for a Pendulum-Like System. J Optim Theory Appl 163, 230–252 (2014). https://doi.org/10.1007/s10957-013-0480-8

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  • DOI: https://doi.org/10.1007/s10957-013-0480-8

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