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Controlling Transport and Synchronization in Non-identical Inertial Ratchets

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Abstract

In this paper, transport control and synchronization are investigated between two periodically driven non-identical, inertial ratchets that are able to exhibit directed transport. One of the two ratchets is acting as a drive system, while the other one represents the response system. Based on the Lyapunov stability theorem, the essential conditions, under which the error nonlinear system is transformed into an equivalent passive system and globally asymptotically stabilized at equilibrium points, are established. With these results, synchronization, not only between two non-identical ratchets with known parameters but also between two different uncertain ratchets, are realized via adaptive passive controllers and parameter update algorithm. The direction of transporting particles can be dominated along expected one and it is useful to control the motion of tiny particles, ratchetlike devices in nanoscience.

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Acknowledgements

This work is supported by the National Science Foundation of China under Grants 60904003, 60874011.

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Authors and Affiliations

  1. School of Automation, Beijing Institute of Technology, Beijing, 100081, China

    Pingli Lu & Qinghe Wu

  2. Department of Mechanics and Aerospace Technology, Peking University, Beijing, 100871, China

    Ying Yang

Authors
  1. Pingli Lu
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  2. Qinghe Wu
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  3. Ying Yang
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Corresponding author

Correspondence to Pingli Lu.

Additional information

Communicated by F.L. Chernousko.

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Lu, P., Wu, Q. & Yang, Y. Controlling Transport and Synchronization in Non-identical Inertial Ratchets. J Optim Theory Appl 157, 888–899 (2013). https://doi.org/10.1007/s10957-012-0187-2

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  • DOI: https://doi.org/10.1007/s10957-012-0187-2

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