Skip to main content
Log in

On the problem of precise control of the system obeying the delay string equation

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

Abstract

Consideration was given to the problem of precise control of a system obeying the equation of string with integral “memory.” This system was proved to be reducible to the quiescent state in a finite time with the use of a distributed action bound in magnitude. The time to stop oscillations was also estimated.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Chernous’ko, F.L., Anan’evskii, I.M., and Reshmin, S.A., Metody upravleniya nelineinymi mekhanicheskimi sistemami (Methods to Control Nonlinear Mechanical Systems), Moscow: Fizmatlit, 2006.

    Google Scholar 

  2. Butkovskii, A.G., Teoriya optimal’nogo upravleniya sistemami s raspredelennymi parametrami (Theory of Optimal Control of the Distributed-Parameter Systems), Moscow: Nauka, 1985.

    Google Scholar 

  3. Lions, J.L., Exact Controllability, Stabilization and Perturbations for Distributed Systems, SIAM Rev., 1988, vol. 30, no. 1, pp. 1–68.

    Article  MathSciNet  MATH  Google Scholar 

  4. Ivanov, S. and Pandolfi, L., Heat Equations with Memory: Lack of Controllability to the Rest, J. Math. Anal. Appl., 2009, vol. 355, no. 1, pp. 1–11.

    Article  MathSciNet  MATH  Google Scholar 

  5. Lions, J.L. and Madgenes, E., Non-homogeneous Boundary Value Problems and Applications, New York: Springer, 1972, vol. 1. Translated under the title Neodnorodnye granichnye zadachi i ikh prilozheniya, Moscow: Fizmatlit, 1971.

    Book  Google Scholar 

  6. Rautian, N.A., On the Structure and Properties of Solutions of Integro-Differential Equations Arising in Thermal Physics and Acoustics, Mat. Zametki, 2011, vol. 90, no. 3, pp. 470–473.

    Article  MathSciNet  Google Scholar 

  7. Vlasov, V.V., Rautian, N.A., and Shamaev, A.S., Solvability and Spectral Analysis of the Integro-Differential Equations Arising in Thermal Physics and Acoustics, Dokl. Ross. Akad. Nauk, 2010, vol. 434, no. 1, pp. 12–15.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © I.V. Romanov, A.S. Shamaev, 2013, published in Avtomatika i Telemekhanika, 2013, No. 11, pp. 49–61.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Romanov, I.V., Shamaev, A.S. On the problem of precise control of the system obeying the delay string equation. Autom Remote Control 74, 1810–1819 (2013). https://doi.org/10.1134/S0005117913110040

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117913110040

Keywords

Navigation