Skip to main content
SpringerLink
Log in

Modification of the extremal shift method for delay systems

  • Control Theory
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We study a control problem for a delay differential equation in which one should construct a feedback control synthesis algorithm ensuring that the solution of the given equation tracks the solution of another equation generated by an unknown right-hand side. We indicate a noise-immune solution algorithm based on the extremal shift method well-known in guaranteed control theory.

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. Krasovskii, N.N. and Subbotin, A.I., Pozitsionnye differentsial’nye igry (Positional Differential Games), Moscow: Nauka, 1974.

    MATH  Google Scholar 

  2. Krasovskii, N.N. and Osipov, Yu.S., Linear Differential-Difference Games, Dokl. Akad. Nauk SSSR, 1971, vol. 197, no. 4, pp. 777–780.

    MathSciNet  Google Scholar 

  3. Osipov, Yu.S., Differential Games of Systems with Aftereffect, Dokl. Akad. Nauk SSSR, 1971, vol. 196, no. 4, pp. 779–782.

    MathSciNet  Google Scholar 

  4. Osipov, Yu.S., A Differential Guidance Game for Systems with Aftereffect, Prikl. Mat. Mekh., 1971, vol. 35, no. 1, pp. 123–131.

    MathSciNet  Google Scholar 

  5. Kryazhimskii, A.V., Maksimov, V.I., and Osipov, Yu.S., On Positional Simulation in Dynamic Systems, J. Appl. Math. Mech., 1983, vol. 47, no. 6, pp. 709–715.

    Article  MathSciNet  Google Scholar 

  6. Kadiev, A.M. and Maksimov, V.I., On the Reconstruction of Controls in a Parabolic Equation, Differ. Equ., 2007, vol. 43, no. 11, pp. 1585–1593.

    Article  MathSciNet  MATH  Google Scholar 

  7. Blizorukova, M.S. and Maksimov, V.I., On an Algorithm for Tracking the Motion of the Reference System with Aftereffect When Only Part of the Coordinates Is Measured, Differ. Equ., 2011, vol. 47, no. 3, pp. 412–418.

    Article  MathSciNet  MATH  Google Scholar 

  8. Banks, H.T. and Kappel, F., Spline Approximation for Functional-Differential Equations, J. Differential Equations, 1979, vol. 34, no. 3, pp. 406–522.

    Article  MathSciNet  Google Scholar 

  9. Bernier, C. and Manitius, A., On Semigroups in ℝn × L p Corresponding to Differential Equations with Delays, Canad. J. Math., 1978, vol. 14, pp. 897–914.

    Article  MathSciNet  Google Scholar 

  10. Maksimov, V.I., The Tracking of the Trajectory of a Dynamical System, J. Appl. Math. Mech., 2011, vol. 75, no. 6, pp. 667–674.

    Article  MathSciNet  MATH  Google Scholar 

  11. Samarskii, A.A., Vvedenie v teoriyu raznostnykh skhem (Introduction to the Theory of Difference Schemes), Moscow: Nauka, 1971.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

    V. I. Maksimov

  2. Ural Federal University, Yekaterinburg, Russia

    V. I. Maksimov

Authors
  1. V. I. Maksimov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. I. Maksimov.

Additional information

Original Russian Text © V.I. Maksimov, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 11, pp. 1517–1526.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maksimov, V.I. Modification of the extremal shift method for delay systems. Diff Equat 50, 1516–1525 (2014). https://doi.org/10.1134/S0012266114110093

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266114110093

Keywords

Search

Navigation