Advertisement

Automation and Remote Control

, Volume 79, Issue 12, pp 2103–2113 | Cite as

Optimal Processes for Controllable Oscillators

  • B. AndresenEmail author
  • P. Salamon
  • K. H. Hoffmann
  • A. M. Tsirlin
Nonlinear Systems
  • 49 Downloads

Abstract

We consider the problem of optimal parametric control for a single oscillator or an ensemble of oscillators due to a change in one of the coefficients of the system of equations characterizing them. We obtain solutions for the problem of finding the maximal change in the energy of oscillations for a given time.

Keywords

parametric control single oscillator oscillator ensemble speed dependence 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Piccoli, B. and Kulkarni, J., Pumping a Swing by Standing and Squatting, IEEE Control Syst. Mag., 2005, no. 8, pp. 48–56.Google Scholar
  2. 2.
    Salamon, P., Hoffmann, K.H., Rezek, Y., and Kosloff, R., Maximum Work in Minimum Time from a Conservative Quantum System, Phys. Chem., 2009, no. 11, pp. 1013–1026.Google Scholar
  3. 3.
    Hoffmann, K.H., Andresen, B., and Salamon, P., Optimal Control of a Collection of Parametric Oscillators, Phys. Rev. E, 2013, no. 11, pp. 1027–1032.Google Scholar
  4. 4.
    Andresen, B., Hoffmann, K.H., Nulton, J., Tsirlin, A.M., and Salamon, P., Optimal Control of the Parametric Oscillator, Eur. J. Phys., 2011, no. 32, pp. 1–17.CrossRefzbMATHGoogle Scholar
  5. 5.
    Tsirlin, A.M., Salamon, P., and Hoffmann, K.H., Change of State Variables in the Problems of Parametric Control of Oscillators, Autom. Remote Control, 2011, vol. 72, no. 8, pp. 1627–1638.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Rozonoér, L.I. and Tsirlin, A.M., Optimal Control of Thermodynamic Processes, Autom. Remote Control, 1983, vol. 44, no. 1, part 1, pp. 55–62; no. 2, part 2, pp. 209–220; no. 3, part 1, pp. 314–326.Google Scholar
  7. 7.
    Gabasov, R.G. and Kirillova, F.M., Metody optimizatsii (Methods of Optimization), Minsk: Belarus. Gos. Univ., 1975.zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  • B. Andresen
    • 1
    Email author
  • P. Salamon
    • 2
  • K. H. Hoffmann
    • 3
  • A. M. Tsirlin
    • 4
  1. 1.University of CopenhagenCopenhagenDenmark
  2. 2.San Diego State UniversitySan DiegoUSA
  3. 3.Technical University of ChemnitzChemnitzGermany
  4. 4.Ailamazyan Program Systems InstituteRussian Academy of SciencesPereslavl-ZalesskyRussia

Personalised recommendations