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

In: International Conference on Mathematical Sciences and Statistics 2013

Author

Listed:
  • Gafurjan Ibragimov

    (Universiti Putra Malaysia, Institute for Mathematical Research
    Universiti Putra Malaysia, Department of Mathematics, Faculty of Science)

  • Asqar Rahmanov

    (Universiti Putra Malaysia, Department of Mathematics, Faculty of Science
    Tashkent University of Information Technologies (TUIT), Department of Informatics)

  • Idham Arif Alias

    (Universiti Putra Malaysia, Institute for Mathematical Research
    Universiti Putra Malaysia, Department of Mathematics, Faculty of Science)

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.

Suggested Citation

  • Gafurjan Ibragimov & Asqar Rahmanov & Idham Arif Alias, 2014. "Construction of Strategies of Pursuers in a Differential Game of Many Players with State and Integral Constraints," Springer Books, in: Adem Kilicman & Wah June Leong & Zainidin Eshkuvatov (ed.), International Conference on Mathematical Sciences and Statistics 2013, edition 127, pages 37-43, Springer.
    • Handle: RePEc:spr:sprchp:978-981-4585-33-0_5
    DOI: 10.1007/978-981-4585-33-0_5
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