Skip to main content
SpringerLink
Log in

Application of the Averaging Method to the Problems of Optimal Control for Ordinary Differential Equations on the Semiaxis

  • Published:
Ukrainian Mathematical Journal Aims and scope

Averaging method is applied to the nonlinear and linear (with respect to control) problems of optimal control on the semiaxis with small parameter and rapidly oscillating coefficients. It is shown that the solutions of the exact problem converge to the solutions of the averaged problem.

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. N. N. Bogolyubov, On the Some Statistical Methods in Mathematical Physics [in Russian], Akad. Nauk Ukr. SSR, Kiev (1945).

  2. A. M. Samoilenko and N. A. Perestyuk, “Second Bogolyubov theorem for systems of impulsive differential equations,” Differents. Uravn., 10, No. 11, 2001–2010 (1974).

    Google Scholar 

  3. G. Hale, Theory of Functional-Differential Equations, Springer, New York (1977).

    Book  Google Scholar 

  4. N. N. Moiseev, Elements of the Theory of Optimal Systems [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  5. N. N. Moiseev, Asymptotic Methods of Nonlinear Mechanics [in Russian], Nauka, Moscow (1981).

    Google Scholar 

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

  7. T. V. Nosenko and O. M. Stanzhyts’kyi, “Averaging method in some problems of optimal control,” Nelin. Kolyv., 11, No. 4, 512–519 (2008); English translation: Nonlin. Oscillat., 11, No. 4, 539–547 (2008).

  8. O. D. Kichmarenko, “Application of the averaging method to optimal control problem of system with fast parameters,” J. Pure Appl. Math., 115, No. 1, 93–114 (2017).

    MathSciNet  Google Scholar 

  9. A. M. Samoilenko and A. N. Stanzhitskii, “On the averaging of differential equations on infinite intervals,” Differents. Uravn., 42, No. 4, 476–482 (2006).

    MathSciNet  MATH  Google Scholar 

  10. A. N. Stanzhitskii and T. V. Dobrodzii, “Investigation of the problems of optimal control on the semiaxis by the averaging method,” Differents. Uravn., 47, No. 2, 264–277 (2011).

    MATH  Google Scholar 

  11. B. M. Makarov and A. N. Podkorytov, Lectures on Substantial Analysis [in Russian], BKHV-Petersburg, St.-Petersburg (2011).

    Google Scholar 

  12. E. B. Lee and L. Markus, Foundation of Optimal Control Theory, Wiley, London (1967).

    Google Scholar 

  13. K. Yosida, Functional Analysis, Springer, Berlin (1980).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechnikov Odessa National University, Odessa, Ukraine

    O. D. Kichmarenko

Authors
  1. O. D. Kichmarenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 5, pp. 642–654, May, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kichmarenko, O.D. Application of the Averaging Method to the Problems of Optimal Control for Ordinary Differential Equations on the Semiaxis. Ukr Math J 70, 739–753 (2018). https://doi.org/10.1007/s11253-018-1530-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-018-1530-z

Search

Navigation