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Game with Two Pursuers and One Evader: Case of Weak Pursuers

  • Sergey KumkovEmail author
  • Valerii Patsko
  • Stéphane Le Ménec
Chapter
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 13)

Abstract

This paper deals with a zero-sum differential game, in which the first player controls two pursuing objects, whose aim is to minimize the minimum of the misses between each of them and the evader at some given instant. The case is studied when the pursuers have equal dynamic capabilities, but are less powerful than the evader. The first player’s control based on its switching lines is analyzed. Results of numeric application of this control are given.

Keywords

Pursuit differential games Fixed termination instant Positional control Switching lines 

Notes

Acknowledgments

We are grateful to the unknown reviewer for very helpful remarks.

This work was supported by Program of Presidium RAS “Dynamic Systems and Control Theory” under financial support of UrB RAS (project No.12-Π-1-1002) and also by the Russian Foundation for Basic Research under grant no.12-01-00537.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

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

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