Skip to main content
SpringerLink
Log in

Stroboscopic Strategy in Dynamic Game Problems with Terminal Payoff Function and Integral Constraints on Controls

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

The paper considers linear differential games with terminal payoff function and integral constraints on controls. Sufficient conditions for game termination in a finite guaranteed time in the class of quasi-strategies are formulated. Two schemes of the method of resolving functions are proposed that ensure game termination in a final guaranteed time in the class of stroboscopic strategies. It is shown that without additional assumptions, this time coincides with the guaranteed time in the class of quasistrategies.

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. I. S. Rappoport and A. A. Chikrii, “Guaranteed result in a differential game with a terminal payoff function,” J. of Applied Math. and Mechanics, Vol. 59, No. 5, 685–690 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  2. I. S. Rappoport and A. A. Chikrii, “Guaranteed result in a differential game of group prosecution with terminal payoff function,” J. of Applied Math. and Mechanics, Vol. 61, No. 4, 567–576 (1997).

    Article  MathSciNet  Google Scholar 

  3. I. S. Rappoport, “Resolving functions method in the theory of conflict-controlled processes with terminal payoff function,” J. Autom. Inform. Sci., Vol. 48, Issue 5, 74–84 (2016).

    Article  Google Scholar 

  4. I. S. Rappoport, “Stroboscopic strategy in the method of resolving functions for game control problems withterminal payoff function,” Cybern. Syst. Analysis, Vol. 52, No. 4, 577–587 (2016).

    Article  MATH  Google Scholar 

  5. M. S. Nikol’skii, “Direct method in linear differential games with integral constraints,” Upravlyaemye Sistemy, Issue 2, 49–59 (1969).

  6. A. A. Chikrii and V. V. Bezmagorychnyi, “Metod of resolving functions in linear differential games with integral constraints,” Avtomatika, No. 4, 26–36 (1993).

  7. A. A. Chikrii and A. A. Belousov, “Linear differential games with integral constraints of approach,” Tr. IMM UrO RAN, Vol. 15, No. 4, 290–301 (2009).

    Google Scholar 

  8. B. T. Samatov, “Problems of group pursuit with integral constraints on controls of the players. I,” Cybern. Syst. Analysis, Vol. 49, No. 5, 756–767 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  9. I. S. Rappoport, “Resolving functions method for game problems of control with integral constraints,” Cybern. Syst. Analysis, Vol. 54, No. 5, 779–795 (2018).

    Article  MATH  Google Scholar 

  10. A. A. Chikrii, Conflict Controlled Processes, Springer Science and Business Media, Dordrecht–Boston–London (2013).

  11. A. A. Chikrii and I. S. Rappoport, “Method of resolving functions in the theory of conflict-controlled processes,” Cybern. Syst. Analysis, Vol. 48, No. 4, 512–531 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  12. A. A. Chikrii and V. K. Chikrii, “Image structure of multi-valued mappings in game problems of motion control,” J. Autom. Inform. Sci., Vol. 48, Issue 3, 20–35 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  13. I. S. Rappoport, “Sufficient conditions of the guaranteed result in differential game with a terminal payoff function,” J. Autom. Inform. Sci., Vol. 50, Issue 2, 14–27 (2018).

    Article  Google Scholar 

  14. O. Hajek, Pursuit Games, Vol. 12, Academic Press, New York (1975).

    MATH  Google Scholar 

  15. N. N. Krasovskii and A. I. Subbotin, Positional Differential Games [in Russsian], Nauka, Moscow (1974).

    MATH  Google Scholar 

  16. L. S. Pontryagin, Selected Scientific Works, Vol. 2 [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  17. M. S. Nikol’skii, The First Direct Pontryagin Method in Differential Games [in Russian], Izd. MGU, Moscow (1984).

    Google Scholar 

  18. M. V. Pittsyk and A. A. Chikrii, “On a group pursuit problem,” J. of Applied Math. and Mechanics, Vol. 46, No. 5, 584–589 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  19. A. A. Chikrii and S. F. Kalashnikova, “Pursuit of a group of evaders by a single controlled object,” Cybernetics, Vol. 23, No. 4, 437–445 (1987).

    Article  MATH  Google Scholar 

  20. A. A. Chikrii, “Multivalued mappings and their selections in game control problems,” J. of Autom. and Inform. Sci., Vol. 27, Issue 1, 27–38 (1995).

    MathSciNet  Google Scholar 

  21. A. A. Chikrii and S. D. Eidelman, “Generalized Mittag-Leffler matrix functions in game problems for evolutionary equations of fractional order,” Cybern. Syst. Analysis, Vol. 36, No. 3, 315–338 (2000).

    Article  MATH  Google Scholar 

  22. J. Albus, A. Meystel, A. A. Chikrii, A. A. Belousov, and A. J. Kozlov, “Analytical method for solution of the game problem of soft landing for moving object,” Cybern. Syst. Analysis, Vol. 37, No. 1, 75–91 (2001).

    Article  MATH  Google Scholar 

  23. A. A. Chikrii, “An analytical method in dynamic pursuit games,” in: Proc. of the Steklov Institute of Mathematics, Vol. 271, 69–85 (2010).

  24. A. A. Chikrii, “Game dynamic problems for systems with fractional derivatives,” Springer Optimization and its Applications, Vol. 17, 349–387 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  25. R. T. Rockafellar, Convex Analysis, Princeton Landmarks in Mathematics and Physics, (1973).

  26. A. F. Philippov, “Some problems from optimal control theory,” Ser. Matem., Mekhanika, Astronomiya, Fizika, Khimiya, No. 2, 25–32 (1959).

  27. E. S. Polovinkin, Elements of the Theory of Multi-Valued Mappings [in Russian], Izd. MFTI, Moscow (1982).

  28. J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser, Boston–Basel–Berlin (1990).

  29. A. D. Ioffe and V. M. Tikhomirov, Theory of Extremum Problems [in Russian], Nauka, Moscow (1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    J. S. Rappoport

Authors
  1. J. S. Rappoport
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. S. Rappoport.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 2, March–April, 2019, pp. 129–144.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rappoport, J.S. Stroboscopic Strategy in Dynamic Game Problems with Terminal Payoff Function and Integral Constraints on Controls. Cybern Syst Anal 55, 284–297 (2019). https://doi.org/10.1007/s10559-019-00133-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-019-00133-8

Keywords

Search

Navigation