Skip to main content
SpringerLink
Log in

Problem of optimal oscillator control for nulling its energy under bounded control action

  • Stochastic Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Consideration was given to the problem of optimal control based on two performance criteria with the aim of full oscillator stopping from the initial state.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Amel’kin, V.V. and Kalitin, B.S., Izokhronnye i impul’snye kolebaniya dvumernykh dinamicheskikh sistem (Isochronous and Pulse Oscillations of Two-dimensional Dynamic Systems), Moscow: URSS, 2006.

    Google Scholar 

  2. Fradkov, A., Control of Chaos: Methods and Applications, MIC2002, Innsbruck, 2002.

  3. Birkgof, D., Dinamicheskie sistemy. R&C Dynamics (Dynamic Systems. R&C Dynamics), Izhevsk: Udmurt. Univ., 1999.

    Google Scholar 

  4. Simiu, E., Khaoticheskie perekhody v determinirovannykh i stokhasticheskikh sistemakh (Chaotic Transitions in Deterministic and Stochastic Systems), Moscow: Fizmatlit, 2007.

    Google Scholar 

  5. Arnol’d, V.I., Matematicheskie metody klassicheskoi mekhaniki (Mathematical Methods of Classical Mechanics), Moscow: Nauka, 1974.

    Google Scholar 

  6. Galyaev, A.A. and Ignat’ev, A.A., Control of Distribution of Full Energy of the Mechanical System to Its Degrees of Freedom by the Nonlinear Feedback. Quantum Approach, Avtom. Telemekh., 2008, no. 3, pp. 17–28.

  7. Boltyanskii, V.G., Matematicheskie metody optimal’nogo upravleniya (Mathematical Methods of Optimal Control), Moscow: Nauka, 1969.

    Google Scholar 

  8. Davies, M.J. and Grisogono-Holstein, I., T-controllable Domains of the Soft Duffing Oscillator, J. Optimiz. Theory Appl., 1973, vol. 11, no. 3.

  9. Prourzin, V.A., A Constrained Scalar Control for the Motion of a System of Oscillators with Damping Residual Oscillations, J. Comput. Syst. Sci. Int., 2007, vol. 46, no. 4, pp. 521–531.

    Article  MathSciNet  Google Scholar 

  10. Reshmin, S.A. and Chernous’ko, F.L., A Time-optimal Control Synthesis for Nonlinear Pendulum, Izv. Ross. Akad. Nauk, Theor. Sist. Upravlen., 2007, no. 1, pp. 13–22.

  11. Reshmin, S.A., Finding the Principal Bifurcation Value of the Maximum Control Torque in the Problem of Optimal Control Synthesis for a Pendulum, J. Comput. Syst. Sci. Int., 2008, vol. 47, no. 2, pp. 163–178.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    A. A. Galyaev

Authors
  1. A. A. Galyaev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russion Text © A.A. Galyaev, 2009, published in Avtomatika i Telemekhanika, 2009, No. 3, pp. 24–33.

This work was supported by the Russian Foundation for Basic Research, project no. 07-08-00739-a.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Galyaev, A.A. Problem of optimal oscillator control for nulling its energy under bounded control action. Autom Remote Control 70, 366–374 (2009). https://doi.org/10.1134/S0005117909030047

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117909030047

PACS number

Search

Navigation