Skip to main content
SpringerLink
Log in

On the theory of three-person differential games

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

Abstract

A differential game of three players with dynamics described by linear differential equations under geometric constraints on the control parameters is considered. Sufficient conditions are obtained for the existence of the first player’s strategy guaranteeing that the trajectory of the game reaches a given target set for any admissible control of the second player and avoids the terminal set of the third player. An algorithm of constructing the first player’s strategy guaranteeing the game’s termination in finite time is suggested. A solution of a model example is given.

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, Berlin, 1988).

    Google Scholar 

  2. V. I. Blagodatskikh, Introduction to Optimal Control (Vyssh. Shkola, Moscow, 2001) [in Russian].

    Google Scholar 

  3. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, Mathematical Theory of Optimal Processes (Fizmatgiz, Moscow, 1961; Interscience, New York, 1962).

    Google Scholar 

  4. Yu. S. Osipov, F. P. Vasil’ev, and M. M. Potapov, Foundations of the Dynamical Regularization Method (Izd. MGU, Moscow, 1999) [in Russian].

    Google Scholar 

  5. L. S. Pontryagin and E. F. Mishchenko, Differents. Uravn. 7(3), 436 (1971).

    MATH  Google Scholar 

  6. E. S. Polovinkin and M. V. Balashov, Elements of Convex Analysis (Fizmatlit, Moscow, 2004) [in Russian].

    Google Scholar 

  7. A. V. Kryazhimskii and Yu. S. Osipov, Proc. Steklov Inst. Math., Suppl. 2, S91 (2004).

  8. M. S. Nikol’skii, Differents. Uravn. 31(11), 1866 (1995).

    Google Scholar 

  9. N. L. Grigorenko, Mathematical Methods of Control of Several Dynamical Processes (Izd. MGU, Moscow, 1990) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Vorob’evy Gory, 119992, Russia

    N. L. Grigorenko

Authors
  1. N. L. Grigorenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © N.L. Grigorenko, 2006, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2006, Vol. 12, No. 1.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grigorenko, N.L. On the theory of three-person differential games. Proc. Steklov Inst. Math. 253 (Suppl 1), S96–S104 (2006). https://doi.org/10.1134/S0081543806050087

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0081543806050087

Keywords

Search

Navigation