Automation and Remote Control

, Volume 67, Issue 4, pp 529–537 | Cite as

On some sufficient conditions for optimality of the pursuit time in the differential game with multiple pursuers

  • G. I. Ibragimov
  • B. B. Rikhsiev
Determinate Systems


Consideration was given to the problem of optimal pursuit of one object by multiple objects. The player’s moves obey the ordinary differential equations. Geometrical constraints are imposed on the player controls. Sufficient conditions were obtained for optimality of the pursuit time, and the optimal player strategies were constructed.

PACS number



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Isaaks, R., Differential Games. A Mathematical Theory with Applications to Warfare and Pursuit, Control, and Optimization, New York: Wiley, 1952. Translated under the title Differentsial’nye igry, Moscow: Mir, 1967.Google Scholar
  2. 2.
    Krasovskii, N.N., Upravlenie dinamicheskoi sistemoi (Control of the Dynamic System), Moscow: Nauka, 1985.Google Scholar
  3. 3.
    Subbotin, A.I. and Chentsov, A.G., Optimizatsiya garantii v zadachakh upravleniya (Optimization of Guarantee in Control Problems), Moscow: Nauka, 1981.Google Scholar
  4. 4.
    Petrosyan, L.A., Differentsial’nye igry presledovaniya (Differential Pursuit Games), Leningrad: Leningr. Gos. Univ., 1977.Google Scholar
  5. 5.
    Petrosyan, L.A. and Rikhsiev, B.B., Presledovanie na ploskosti (Planar Pursuuit), Moscow: Nauka, 1991.Google Scholar
  6. 6.
    Rikhsiev, B.B., Differentsial’nye igry s prostymi dvizheniyami (Differential Games with Simple Moves), Tashkent: Fan, 1989.Google Scholar
  7. 7.
    Ivanov, R.P. and Ledyaev, Yu.S., Optimality of the Pursuit Time in a Differential Game with Several Pursuers under Simple Motion, Tr. MIAN SSSR, 1981, vol. 158, pp. 87–97.MathSciNetGoogle Scholar
  8. 8.
    Pashkov, A.G. and Teorekhov, S.D., On a Game of Optimal Pursuit of One Object by Two Objects, Prikl. Mat. Mekh., 1983, vol. 47, no. 6, pp. 898–903.MathSciNetGoogle Scholar
  9. 9.
    Sinitsyn, A.V., Construction of the Cost Function in the Game of Pursuit by Several Objects, Prikl. Mat. Mekh., 1993, vol. 57, no. 1, pp. 52–57.zbMATHMathSciNetGoogle Scholar
  10. 10.
    Ibragimov, G.I., One Game of Optimal Pursuit of One Object by Two Objects, Prikl. Mat. Mekh., 1998, vol. 62, no. 2, pp. 199–205.zbMATHMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2006

Authors and Affiliations

  • G. I. Ibragimov
    • 1
  • B. B. Rikhsiev
    • 1
  1. 1.Romanovskii Institute of MathematicsTashkentUzbekistan

Personalised recommendations