Construction of Strategies of Pursuers in a Differential Game of Many Players with State and Integral Constraints

Gafurjan Ibragimov (), Asqar Rahmanov () and Idham Arif Alias ()
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Gafurjan Ibragimov: Universiti Putra Malaysia, Institute for Mathematical Research
Asqar Rahmanov: Universiti Putra Malaysia, Department of Mathematics, Faculty of Science
Idham Arif Alias: Universiti Putra Malaysia, Institute for Mathematical Research

A chapter in International Conference on Mathematical Sciences and Statistics 2013, 2014, pp 37-43 from Springer

Abstract: Abstract The approach of a group of controlled objects, the pursuers, to another one, the evaders, is considered. The motions of all the objects are described by simple differential equations. The control functions of players are subjected to integral constraints. The amount of control resources such as fuel, energy etc. are described by such constraints. Given a non-empty convex subset of $$ {{\mathbb{R}}^{n}}, $$ all objects move in this set. If the position of each evader $${{y}_{j}},\text{ }j\in \{1,\,2,\,\text{ }...\,\text{ }k\},$$ coincides with the position of a pursuer $${{x}_{i}},\text{ }i\in \{1,\text{ }...\ ,m\},$$ at some time $${{t}_{j}}\text{, i}\text{.e}\text{. }{{x}_{i}}({{t}_{j}})={{y}_{j}}({{t}_{j}}),$$ then we say that pursuit can be completed. The total resource of the pursuers is assumed to be greater than that of the evaders. We show that pursuit can be completed in this differential game.

Keywords: Differential Games; Integral Constraints; Evader; Total Resources; Simple Differential Equation (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-981-4585-33-0_5

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