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. Kumkov
  • Stéphane Le Ménec
  • Valerii S. Patsko
Article

Abstract

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 T1 and T2, 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 T1 and T2. 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.

Keywords

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

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Sergey A. Ganebny
    • 1
  • Sergey S. Kumkov
    • 1
  • 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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