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

被引：22

作者：

Alias, Idham Arif ^{[1
,2
]}

Ibragimov, Gafurjan ^{[1
,2
]}

Rakhmanov, Askar ^{[3
]}

机构：

[1] Univ Putra Malaysia, Dept Math, Serdang, Malaysia

[2] Univ Putra Malaysia, Inst Math Res, Serdang, Malaysia

[3] Tashkent Univ Informat Technol, Dept Informat, Tashkent, Uzbekistan

来源：

DYNAMIC GAMES AND APPLICATIONS | 2017年 / 7卷 / 03期

关键词：

Differential game; Hilbert space; Many players; Integral constraint; Evasion; Strategy; INTEGRAL CONSTRAINTS; EQUATIONS; SYSTEM;

D O I：

10.1007/s13235-016-0196-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a simple motion evasion differential game of infinitely many evaders and infinitely many pursuers in Hilbert space . 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.

引用

页码：347 / 359

页数：13

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