Evasion differential game of infinitely many evaders from infinitely many pursuers in Hilbert space
We consider a simple motion evasion differential game of infinitely many evaders and infinitely many pursuers in Hilbert space ℓ2. Control functions of the players are subjected to integral constraints. If the position of an evader never coincides with the position of any pursuer, then evasion is sa...
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| Format: | Article |
| Language: | English |
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Springer
2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/56535/ http://psasir.upm.edu.my/id/eprint/56535/1/Evasion%20differential%20game%20of%20infinitely%20many%20evaders%20from%20infinitely%20many%20pursuers%20in%20Hilbert%20space.pdf |
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| author | Alias, Idham Arif Ibragimov, Gafurjan Rakhmanov, Askar |
| author_facet | Alias, Idham Arif Ibragimov, Gafurjan Rakhmanov, Askar |
| author_sort | Alias, Idham Arif |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We consider a simple motion evasion differential game of infinitely many evaders and infinitely many pursuers in Hilbert space ℓ2. Control functions of the players are subjected to integral constraints. If the position of an evader never coincides with the position of any pursuer, then evasion is said to be possible. Problem is to find conditions of evasion. The main result of the paper is that if either (i) the total resource of evaders is greater than that of pursuers or (ii) the total resource of evaders is equal to that of pursuers and initial positions of all the evaders are not limit points for initial positions of the pursuers, then evasion is possible. Strategies for the evaders are constructed. |
| first_indexed | 2025-11-15T10:48:46Z |
| format | Article |
| id | upm-56535 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:48:46Z |
| publishDate | 2017 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-565352017-08-01T08:54:21Z http://psasir.upm.edu.my/id/eprint/56535/ Evasion differential game of infinitely many evaders from infinitely many pursuers in Hilbert space Alias, Idham Arif Ibragimov, Gafurjan Rakhmanov, Askar We consider a simple motion evasion differential game of infinitely many evaders and infinitely many pursuers in Hilbert space ℓ2. Control functions of the players are subjected to integral constraints. If the position of an evader never coincides with the position of any pursuer, then evasion is said to be possible. Problem is to find conditions of evasion. The main result of the paper is that if either (i) the total resource of evaders is greater than that of pursuers or (ii) the total resource of evaders is equal to that of pursuers and initial positions of all the evaders are not limit points for initial positions of the pursuers, then evasion is possible. Strategies for the evaders are constructed. Springer 2017 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/56535/1/Evasion%20differential%20game%20of%20infinitely%20many%20evaders%20from%20infinitely%20many%20pursuers%20in%20Hilbert%20space.pdf Alias, Idham Arif and Ibragimov, Gafurjan and Rakhmanov, Askar (2017) Evasion differential game of infinitely many evaders from infinitely many pursuers in Hilbert space. Dynamic Games and Applications, 7 (3). pp. 347-359. ISSN 2153-0785; ESSN: 2153-0793 https://rd.springer.com/article/10.1007/s13235-016-0196-0 10.1007/s13235-016-0196-0 |
| spellingShingle | Alias, Idham Arif Ibragimov, Gafurjan Rakhmanov, Askar Evasion differential game of infinitely many evaders from infinitely many pursuers in Hilbert space |
| title | Evasion differential game of infinitely many evaders from infinitely many pursuers in Hilbert space |
| title_full | Evasion differential game of infinitely many evaders from infinitely many pursuers in Hilbert space |
| title_fullStr | Evasion differential game of infinitely many evaders from infinitely many pursuers in Hilbert space |
| title_full_unstemmed | Evasion differential game of infinitely many evaders from infinitely many pursuers in Hilbert space |
| title_short | Evasion differential game of infinitely many evaders from infinitely many pursuers in Hilbert space |
| title_sort | evasion differential game of infinitely many evaders from infinitely many pursuers in hilbert space |
| url | http://psasir.upm.edu.my/id/eprint/56535/ http://psasir.upm.edu.my/id/eprint/56535/ http://psasir.upm.edu.my/id/eprint/56535/ http://psasir.upm.edu.my/id/eprint/56535/1/Evasion%20differential%20game%20of%20infinitely%20many%20evaders%20from%20infinitely%20many%20pursuers%20in%20Hilbert%20space.pdf |