Skip to main content
SpringerLink
Log in

Hamilton–Jacobi functional equations and differential games for neutral-type systems

  • Control Theory
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

The relation between a differential game for neutral-type systems and a Hamilton–Jacobi functional equation with coinvariant derivatives is established. The value functional of the game is proved to coincide with the minimax solution of this equation. Optimal strategies for the players are described.

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. Krasovskii and A. I. Subbotin, Game-Theoretical Control Problems (Nauka, Moscow, 1974; Springer-Verlag, New York, 1988).

    Google Scholar 

  2. N. N. Krasovskii, Control of a Dynamical System (Nauka, Moscow, 1985) [in Russian].

    Google Scholar 

  3. A. N. Krasovskii and N. N. Krasovskii, Control under Lack of Information (Birkhäuser, Berlin, 1995).

    Book  MATH  Google Scholar 

  4. Yu. S. Osipov, Dokl. Akad. Nauk SSSR 196 (4), 779–782 (1971).

    MathSciNet  Google Scholar 

  5. N. Yu. Lukoyanov, Dokl. Math. 61 (2), 301–304 (2000).

    MathSciNet  Google Scholar 

  6. N. Yu. Lukoyanov, Hamilton–Jacobi Functional Equations and Control Problems with Hereditary Information (Ural. Fed. Univ., Yekaterinburg, 2011) [in Russian].

    MATH  Google Scholar 

  7. M. I. Gomoyunov, N. Yu. Lukoyanov, and A. R. Plaksin, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk 22 (2), 101–112 (2016).

    Google Scholar 

  8. J. K. Hale and M. A. Cruz, Ann. Mat. Pura Appl. 85 (1), 63–81 (1970).

    Article  MathSciNet  Google Scholar 

  9. A. V. Kim, Functional Differential Equations: Application of i-Smooth Calculus (Kluwer, Dordrecht, 1999).

    Book  MATH  Google Scholar 

  10. A. I. Subbotin, Generalized Solutions of First-Order PDEs: The Dynamical Optimization Perspective (Birkhäuser, Boston, 1995).

    Book  MATH  Google Scholar 

  11. N. Yu. Lukoyanov, and A. R. Plaksin, Dokl. Math. 96 (2), (2017).

    Google Scholar 

  12. M. G. Crandall and P.-L. Lions, Trans. Am. Math. Soc. 277 (1), 1–42 (1983).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620990, Russia

    N. Yu. Lukoyanov, M. I. Gomoyunov & A. R. Plaksin

  2. Ural Federal University, Yekaterinburg, 620002, Russia

    N. Yu. Lukoyanov, M. I. Gomoyunov & A. R. Plaksin

Authors
  1. N. Yu. Lukoyanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. I. Gomoyunov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. R. Plaksin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Yu. Lukoyanov.

Additional information

Original Russian Text © N.Yu. Lukoyanov, M.I. Gomoyunov, A.R. Plaksin, 2017, published in Doklady Akademii Nauk, 2017, Vol. 477, No. 3, pp. 291–294.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lukoyanov, N.Y., Gomoyunov, M.I. & Plaksin, A.R. Hamilton–Jacobi functional equations and differential games for neutral-type systems. Dokl. Math. 96, 654–657 (2017). https://doi.org/10.1134/S1064562417060114

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562417060114

Search

Navigation