Optimal number of pursuers in differential games on the 1-skeleton of an orthoplex
We study a differential game of many pursuers and one evader. All the players move only along the one-skeleton graph of an orthoplex of dimension d+1. It is assumed that the maximal speeds of the pursuers are less than the speed of the evader. By definition, the pursuit is completed if the position...
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| Format: | Article |
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MDPI AG
2021
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| _version_ | 1796982985941057536 |
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| author | Azamov, Abdulla Ibragimov, Gafurjan Ibaydullaev, Tolanbay Alias, Idham Arif |
| author_facet | Azamov, Abdulla Ibragimov, Gafurjan Ibaydullaev, Tolanbay Alias, Idham Arif |
| author_sort | Azamov, Abdulla |
| collection | UPM |
| description | We study a differential game of many pursuers and one evader. All the players move only along the one-skeleton graph of an orthoplex of dimension d+1. It is assumed that the maximal speeds of the pursuers are less than the speed of the evader. By definition, the pursuit is completed if the position of a pursuer coincides with the position of the evader. Evasion is said to be possible in the game if the movements of players are started from some initial positions and the position of the evader never coincides with the position of any pursuer. We found the optimal number of pursuers in the game. The symmetry of the orthoplex plays an important role in the construction of the players’ strategies. |
| first_indexed | 2024-03-06T10:59:54Z |
| format | Article |
| id | upm.eprints-94444 |
| institution | Universiti Putra Malaysia |
| last_indexed | 2024-03-06T10:59:54Z |
| publishDate | 2021 |
| publisher | MDPI AG |
| record_format | dspace |
| spelling | upm.eprints-944442022-11-25T03:20:07Z http://psasir.upm.edu.my/id/eprint/94444/ Optimal number of pursuers in differential games on the 1-skeleton of an orthoplex Azamov, Abdulla Ibragimov, Gafurjan Ibaydullaev, Tolanbay Alias, Idham Arif We study a differential game of many pursuers and one evader. All the players move only along the one-skeleton graph of an orthoplex of dimension d+1. It is assumed that the maximal speeds of the pursuers are less than the speed of the evader. By definition, the pursuit is completed if the position of a pursuer coincides with the position of the evader. Evasion is said to be possible in the game if the movements of players are started from some initial positions and the position of the evader never coincides with the position of any pursuer. We found the optimal number of pursuers in the game. The symmetry of the orthoplex plays an important role in the construction of the players’ strategies. MDPI AG 2021-11 Article PeerReviewed Azamov, Abdulla and Ibragimov, Gafurjan and Ibaydullaev, Tolanbay and Alias, Idham Arif (2021) Optimal number of pursuers in differential games on the 1-skeleton of an orthoplex. Symmetry, 13 (11). art. no. 2170. pp. 1-8. ISSN 2073-8994 https://www.mdpi.com/2073-8994/13/11/2170/htm 10.3390/sym13112170 |
| spellingShingle | Azamov, Abdulla Ibragimov, Gafurjan Ibaydullaev, Tolanbay Alias, Idham Arif Optimal number of pursuers in differential games on the 1-skeleton of an orthoplex |
| title | Optimal number of pursuers in differential games on the 1-skeleton of an orthoplex |
| title_full | Optimal number of pursuers in differential games on the 1-skeleton of an orthoplex |
| title_fullStr | Optimal number of pursuers in differential games on the 1-skeleton of an orthoplex |
| title_full_unstemmed | Optimal number of pursuers in differential games on the 1-skeleton of an orthoplex |
| title_short | Optimal number of pursuers in differential games on the 1-skeleton of an orthoplex |
| title_sort | optimal number of pursuers in differential games on the 1 skeleton of an orthoplex |
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