Simple motion pursuit differential game of many pursuers and one evader on convex compact set
We study a differential game of many pursuers and single evader in nonempty closed bounded convex subset of ℝn. In this game, all players cannot leave the given set. Control parameters of all players are subjected to geometric constraints. Maximum speeds of all players are equal to 1. Pursuit is sai...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Academic Publications
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/56548/ http://psasir.upm.edu.my/id/eprint/56548/1/Simple%20motion%20pursuit%20differential%20game%20of%20many%20pursuers%20and%20one%20evader%20on%20convex%20compact%20set.pdf |
| _version_ | 1848853114407354368 |
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| author | Alias, Idham Arif Raja Ramli, Raja Noorsuria Ibragimov, Gafurjan Narzullaev, Anvar |
| author_facet | Alias, Idham Arif Raja Ramli, Raja Noorsuria Ibragimov, Gafurjan Narzullaev, Anvar |
| author_sort | Alias, Idham Arif |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We study a differential game of many pursuers and single evader in nonempty closed bounded convex subset of ℝn. In this game, all players cannot leave the given set. Control parameters of all players are subjected to geometric constraints. Maximum speeds of all players are equal to 1. Pursuit is said to be completed if geometric position of at least one pursuer coincides with that of the evader. Pursuers try to complete the pursuit. Problem is to find estimate for guaranteed pursuit time. To solve the problem, first, we study the same problem in an n-dimensional cube. Then, we reduce the main problem to the game in the cube. To this end, we use method of fictitious pursuers. In this paper, we improve the estimate for guaranteed pursuit time from O(n3) to O(n2). |
| first_indexed | 2025-11-15T10:48:49Z |
| format | Article |
| id | upm-56548 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:48:49Z |
| publishDate | 2015 |
| publisher | Academic Publications |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-565482017-08-01T08:55:48Z http://psasir.upm.edu.my/id/eprint/56548/ Simple motion pursuit differential game of many pursuers and one evader on convex compact set Alias, Idham Arif Raja Ramli, Raja Noorsuria Ibragimov, Gafurjan Narzullaev, Anvar We study a differential game of many pursuers and single evader in nonempty closed bounded convex subset of ℝn. In this game, all players cannot leave the given set. Control parameters of all players are subjected to geometric constraints. Maximum speeds of all players are equal to 1. Pursuit is said to be completed if geometric position of at least one pursuer coincides with that of the evader. Pursuers try to complete the pursuit. Problem is to find estimate for guaranteed pursuit time. To solve the problem, first, we study the same problem in an n-dimensional cube. Then, we reduce the main problem to the game in the cube. To this end, we use method of fictitious pursuers. In this paper, we improve the estimate for guaranteed pursuit time from O(n3) to O(n2). Academic Publications 2015 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/56548/1/Simple%20motion%20pursuit%20differential%20game%20of%20many%20pursuers%20and%20one%20evader%20on%20convex%20compact%20set.pdf Alias, Idham Arif and Raja Ramli, Raja Noorsuria and Ibragimov, Gafurjan and Narzullaev, Anvar (2015) Simple motion pursuit differential game of many pursuers and one evader on convex compact set. International Journal of Pure and Applied Mathematics, 102 (4). pp. 733-745. ISSN 1311-8080; ESSN: 1314-3395 http://www.ijpam.eu/contents/2015-102-4/11/ |
| spellingShingle | Alias, Idham Arif Raja Ramli, Raja Noorsuria Ibragimov, Gafurjan Narzullaev, Anvar Simple motion pursuit differential game of many pursuers and one evader on convex compact set |
| title | Simple motion pursuit differential game of many pursuers and one evader on convex compact set |
| title_full | Simple motion pursuit differential game of many pursuers and one evader on convex compact set |
| title_fullStr | Simple motion pursuit differential game of many pursuers and one evader on convex compact set |
| title_full_unstemmed | Simple motion pursuit differential game of many pursuers and one evader on convex compact set |
| title_short | Simple motion pursuit differential game of many pursuers and one evader on convex compact set |
| title_sort | simple motion pursuit differential game of many pursuers and one evader on convex compact set |
| url | http://psasir.upm.edu.my/id/eprint/56548/ http://psasir.upm.edu.my/id/eprint/56548/ http://psasir.upm.edu.my/id/eprint/56548/1/Simple%20motion%20pursuit%20differential%20game%20of%20many%20pursuers%20and%20one%20evader%20on%20convex%20compact%20set.pdf |