Skip to main content
SpringerLink
Log in

On the question of the stability defect of sets in an approach game problem

  • Published:
Proceedings of the Steklov Institute of Mathematics Aims and scope Submit manuscript

Abstract

The stability property is studied in a game problem of approach of a conflictcontrol system to a target set at a fixed termination time. The notion of the stability defect of sets in the space of game positions is investigated.

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, Izv. Akad. Nauk SSSR, Ser. Tekhn. Kibernet. 5, 3 (1969).

    Google Scholar 

  2. N. N. Krasovskii and A. I. Subbotin, Dokl. Akad. Nauk SSSR 188(4), 745 (1969).

    MathSciNet  Google Scholar 

  3. N. N. Krasovskii, Game Problems on the Encounter of Motions (Nauka, Moscow, 1970) [in Russian].

    Google Scholar 

  4. N. N. Krasovskii and A. I. Subbotin, Dokl. Akad. Nauk SSSR 190(3), 523 (1969).

    MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  6. N. N. Krasovskii, Dokl. Akad. Nauk SSSR 226(6), 1260 (1976).

    MathSciNet  Google Scholar 

  7. N. N. Krasovskii, in Game Control Problems (Inst. Mat. Mekh. Ural’sk. Nauchn. Tsentra Akad. Nauk SSSR, Sverdlovsk, 1977), pp. 32–45 [in Russian].

    Google Scholar 

  8. H. G. Guseinov, A. I. Subbotin, and V. N. Ushakov, Problems Control Inform. Theory 14(6), 405 (1985).

    MathSciNet  Google Scholar 

  9. L. S. Pontryagin, Dokl. Akad. Nauk SSSR 175(4), 764 (1967).

    MathSciNet  Google Scholar 

  10. A. B. Kurzhanski and P. Varaiya, J. Optim. Theory Appl. 108(2), 227 (2001).

    Article  MathSciNet  Google Scholar 

  11. A. V. Kryazhimskii and Yu. S. Osipov, Prikl. Mat. Mekh. 37(1), 3 (1973).

    Google Scholar 

  12. A. G. Chentsov, Mat. Sb. 99(3), 394 (1976).

    MathSciNet  Google Scholar 

  13. A. I. Subbotin and A. G. Chentsov, Guarantee Optimization in Control Problems (Nauka, Moscow, 1981) [in Russian].

    MATH  Google Scholar 

  14. A. I. Subbotin and N. N. Subbotina, Dokl. Akad. Nauk SSSR 266(2), 294 (1982).

    MathSciNet  Google Scholar 

  15. V. I. Ukhobotov, Izv. Inst. Mat. Informat. Udmurtsk. Gos. Univ. 2(32), 23 (2005).

    Google Scholar 

  16. E. A. Isakova, G. V. Logunova, and V. S. Patsko, in Algorithms and Programs for Solving Linear Differential Games (Inst. Mat. Mekh. Ural’sk. Nauchn. Tsentra Akad. Nauk SSSR, Sverdlovsk, 1984), pp. 127–158 [in Russian].

    Google Scholar 

  17. A. M. Taras’ev and V. N. Ushakov, On Constructing Stable Bridges in a Minimax Game of Approach-Evasion (Sverdlovsk, 1983), Available from VINITI, No. 2454-83 [in Russian].

  18. A. M. Taras’ev, V. N. Ushakov, and A. P. Khripunov, Prikl. Mat. Mekh. 51(2), 216 (1987).

    MathSciNet  Google Scholar 

  19. V. N. Ushakov and Ya. A. Latushkin, Trudy Inst. Mat. Mekh. UrO RAN 12(2), 178 (2006).

    MathSciNet  Google Scholar 

  20. J. Warga, Optimal Control of Differential and Functional Equations (Academic, New York, 1972; Mir, Moscow, 1977).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Division of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    V. N. Ushakov & A. G. Malev

Authors
  1. V. N. Ushakov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. G. Malev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. N. Ushakov.

Additional information

Original Russian Text © V.N. Ushakov, A.G.Malev, 2010, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Vol. 16, No. 1.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ushakov, V.N., Malev, A.G. On the question of the stability defect of sets in an approach game problem. Proc. Steklov Inst. Math. 272 (Suppl 1), 229–254 (2011). https://doi.org/10.1134/S0081543811020179

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0081543811020179

Keywords

Search

Navigation