Simultaneous Multiple Capture of Rigidly Coordinated Evaders

Aleksandr I. Blagodatskikh () and Nikolai N. Petrov ()
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Aleksandr I. Blagodatskikh: Udmurt State University
Nikolai N. Petrov: Udmurt State University

Dynamic Games and Applications, 2019, vol. 9, issue 3, No 3, 594-613

Abstract: Abstract 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.

Keywords: Capture; Multiple capture; Simultaneous multiple capture; Pursuit; Evasion; Differential games; Conflict-controlled processes; 49N70; 49N75; 91A06 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s13235-019-00300-8

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