Dynamic Games and Applications

, Volume 6, Issue 3, pp 409–425 | Cite as

On a Fixed Duration Pursuit Differential Game with Geometric and Integral Constraints

  • Mehdi SalimiEmail author
  • Gafurjan I. Ibragimov
  • Stefan Siegmund
  • Somayeh Sharifi


In this paper we investigate a differential game in which countably many dynamical objects pursue a single one. All the players perform simple motions. The duration of the game is fixed. The controls of a group of pursuers are subject to integral constraints, and the controls of the other pursuers and the evader are subject to geometric constraints. The payoff of the game is the distance between the evader and the closest pursuer when the game is terminated. We construct optimal strategies for players and find the value of the game.


Differential game Pursuer Evader Strategy  Value of the game 



The authors thank reviewers for their valuable comments and suggestions to improve the readability of the paper.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Mehdi Salimi
    • 1
    Email author
  • Gafurjan I. Ibragimov
    • 2
  • Stefan Siegmund
    • 1
  • Somayeh Sharifi
    • 3
  1. 1.Center for Dynamics and Institute for Analysis, Department of MathematicsTechnische Universität DresdenDresdenGermany
  2. 2.Department of Mathematics and Institute for Mathematical ResearchUniversiti Putra Malaysia (UPM)SerdangMalaysia
  3. 3.Young Researchers and Elite Club, Hamedan BranchIslamic Azad UniversityHamedanIran

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