A Multiplayer Pursuit Differential Game on a Closed Convex Set with Integral Constraints
Joint Authors
Ibragimov, Gafurjan I.
Satimov, Nu'man
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-11-06
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
We study a simple motion pursuit differential game of many pursuers and many evaders on a nonempty convex subset of ℝn.
In process of the game, all players must not leave the given set.
Control functions of players are subjected to integral constraints.
Pursuit is said to be completed if the position of each evader yj, j∈{1,2,...k}, coincides with the position of a pursuer xi, i∈{1,...,m}, at some time tj, that is, xi(tj)=yj(tj).
We show that if the total resource of the pursuers is greater than that of the evaders, then pursuit can be completed.
Moreover, we construct strategies for the pursuers.
According to these strategies, we define a finite number of time intervals [θi−1,θi] and on each interval only one of the pursuers pursues an evader, and other pursuers do not move.
We derive inequalities for the resources of these pursuer and evader and, moreover, show that the total resource of the pursuers remains greater than that of the evaders.
American Psychological Association (APA)
Ibragimov, Gafurjan I.& Satimov, Nu'man. 2012. A Multiplayer Pursuit Differential Game on a Closed Convex Set with Integral Constraints. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-12.
https://search.emarefa.net/detail/BIM-473278
Modern Language Association (MLA)
Ibragimov, Gafurjan I.& Satimov, Nu'man. A Multiplayer Pursuit Differential Game on a Closed Convex Set with Integral Constraints. Abstract and Applied Analysis No. 2012 (2012), pp.1-12.
https://search.emarefa.net/detail/BIM-473278
American Medical Association (AMA)
Ibragimov, Gafurjan I.& Satimov, Nu'man. A Multiplayer Pursuit Differential Game on a Closed Convex Set with Integral Constraints. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-12.
https://search.emarefa.net/detail/BIM-473278
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-473278