Dynamic Games and Applications

, Volume 2, Issue 2, pp 228–257 | Cite as

Model Problem in a Line with Two Pursuers and One Evader

  • Sergey A. Ganebny
  • Sergey S. KumkovEmail author
  • Stéphane Le Ménec
  • Valerii S. Patsko


An antagonistic differential game is considered where motion occurs in a straight line. Deviations between the first and second pursuers and the evader are computed at the instants T 1 and T 2, respectively. The pursuers act in coordination. Their aim is to minimize the resultant miss, which is equal to the minimum of the deviations happened at the instants T 1 and T 2. Numerical study of value function level sets (Lebesgue sets) for qualitatively different cases is given. A method for constructing optimal feedback controls is suggested on the basis of switching lines. The results of a numerical simulation are shown.


Pursuit-evasion differential game Linear dynamics Value function Optimal feedback control 



This work was supported by the Russian Foundation for Fundamental Research under grants No. 10-01-96006, 11-01-12088, 12-01-00537.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Sergey A. Ganebny
    • 1
  • Sergey S. Kumkov
    • 1
    Email author
  • Stéphane Le Ménec
    • 2
  • Valerii S. Patsko
    • 1
  1. 1.Institute of Mathematics and MechanicsEkaterinburgRussia
  2. 2.EADS/MBDA FranceLe Plessis-Robinson CedexFrance

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