Simultaneous Multiple Capture of Rigidly Coordinated Evaders

  • Aleksandr I. Blagodatskikh
  • Nikolai N. PetrovEmail author


Differential games of two players represent a very serious mathematical theory. Conflict-controlled processes with many objects (at least from one of the opposing sides) are a natural generalization of differential games of two players. Mathematical problems involving the conflict interaction between two groups of controlled objects are the most difficult to investigate. The specific nature of these problems requires new methods of research. The problem of pursuit of a group of rigidly coordinated evaders in a nonstationary conflict-controlled process with equal capabilities is examined. We say that a multiple capture in the problem of pursuit holds if a certain number of pursuers catch evaders possibly at different instants. In the nonstrict simultaneous multiple capture, there is a requirement of coinciding instants of capture. Simultaneous multiple capture means that the smallest instants of capture coincide. In this paper, sufficient and necessary conditions for simultaneous multiple capture of rigidly coordinated evaders are obtained for the case where pursuers use piecewise-program counterstrategies. Control of the pursuers which can guarantee simultaneous multiple capture not later than at a finite instant is constructed explicitly. A number of examples are considered.


Capture Multiple capture Simultaneous multiple capture Pursuit Evasion Differential games Conflict-controlled processes 

Mathematics Subject Classification

49N70 49N75 91A06 



The work of the second author was supported by the Russian Foundation for Basic Research (Grant 18-51-41005).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Udmurt State UniversityIzhevskRussia

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