Dynamic Games and Applications

, Volume 8, Issue 2, pp 352–378 | Cite as

Simple Motion Evasion Differential Game of Many Pursuers and Evaders with Integral Constraints

  • Gafurjan Ibragimov
  • Massimiliano Ferrara
  • Atamurat Kuchkarov
  • Bruno Antonio Pansera
Article
  • 67 Downloads

Abstract

We study a simple motion evasion differential game of many pursuers and evaders. Control functions of players are subjected to integral constraints. If the state of at least one evader does not coincide with that of any pursuer forever, then evasion is said to be possible in the game. The aim of the group of evaders is to construct their strategies so that evasion can be possible in the game and the aim of the group of pursuers is opposite. The problem is to find a sufficient condition of evasion. If the total energy of pursuers is less than or equal to that of evaders, then it is proved that evasion is possible, and moreover, evasion strategies are constructed explicitly.

Keywords

Differential game Many pursuers Many evaders Integral constraint Evasion Strategy 

Mathematics Subject Classification

Primary 91A23 Secondary 49N75 

Notes

Acknowledgements

The present research was partially supported by the National Fundamental Research Grant Scheme FRGS of Malaysia, 01-01-13-1228FR.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Institute for Mathematical ResearchUniversiti Putra MalaysiaSerdangMalaysia
  2. 2.Department of Law and EconomicsUniversity Mediterranea of Reggio CalabriaReggio CalabriaItaly
  3. 3.ICRIOSBocconi UniversityMilanItaly
  4. 4.Institute of MathematicsNational University of UzbekistanTashkentUzbekistan

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