Skip to main content
Log in

Averaging of boundary-value problems of control over a standard system with delay

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

For the terminal problem of optimal control over systems of standard form with constant delay, according to the Pontryagin maximum principle, we study a boundary-value problem with deviating arguments with delay and anticipation. We justify an averaging method for an asymptotic solution of the boundary-value problem obtained.

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.

References

  1. R. Gabasov and F. M. Kirillova, Maximum Principle in the Theory of Optimal Control [in Russian], Nauka i Teknnika, Minsk (1974).

    Google Scholar 

  2. V. A. Plotnikov, Averaging Method in Problems of Control [in Russian], Lybid’, Kiev (1992).

    Google Scholar 

  3. V. P. Zheltikov and V. A. éfendiev, “Asymptotic solution of the problem of optimal control over a system of standard form with delay,” Kibernetika Sist. Anal., No. 5, 93–101 (1994).

    Google Scholar 

  4. A. N. Filatov and L. V. Sharova, Integral Inequalities and the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow 1976.

    MATH  Google Scholar 

  5. V. N. Filatov, Asymptotic Methods in the Theory of Differential Equations [in Russian], Fan, Tashkent 1974.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zheltikov, V.P., éfendiev, V.V. Averaging of boundary-value problems of control over a standard system with delay. Ukr Math J 48, 607–613 (1996). https://doi.org/10.1007/BF02390620

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02390620

Keywords

Navigation