Evasion Differential Game of Infinitely Many Evaders from Infinitely Many Pursuers in Hilbert Space

Idham Arif Alias (), Gafurjan Ibragimov () and Askar Rakhmanov ()
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Idham Arif Alias: Universiti Putra Malaysia
Gafurjan Ibragimov: Universiti Putra Malaysia
Askar Rakhmanov: Tashkent University of Information Technologies

Dynamic Games and Applications, 2017, vol. 7, issue 3, No 1, 347-359

Abstract: Abstract We consider a simple motion evasion differential game of infinitely many evaders and infinitely many pursuers in Hilbert space $$\ell _2$$ ℓ 2 . Control functions of the players are subjected to integral constraints. If the position of an evader never coincides with the position of any pursuer, then evasion is said to be possible. Problem is to find conditions of evasion. The main result of the paper is that if either (i) the total resource of evaders is greater than that of pursuers or (ii) the total resource of evaders is equal to that of pursuers and initial positions of all the evaders are not limit points for initial positions of the pursuers, then evasion is possible. Strategies for the evaders are constructed.

Keywords: Differential game; Hilbert space; Many players; Integral constraint; Evasion; Strategy; Primary 91A23; Secondary 49N75 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s13235-016-0196-0

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