An optimal pursuit differential game problem with one evader and many pursuers
The objective of this paper is to study a pursuit differential game with finite or countably number of pursuers and one evader. The game is described by differential equations in l2 -space, and integral constraints are imposed on the control function of the players. The duration of the game is fixed...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/38261/ http://psasir.upm.edu.my/id/eprint/38261/1/38261.pdf |
| _version_ | 1848848830365171712 |
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| author | Ahmed, Idris Kumam, Poom Ibragimov, Gafurjan Rilwan, Jewaidu Kumam, Wiyada |
| author_facet | Ahmed, Idris Kumam, Poom Ibragimov, Gafurjan Rilwan, Jewaidu Kumam, Wiyada |
| author_sort | Ahmed, Idris |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The objective of this paper is to study a pursuit differential game with finite or countably number of pursuers and one evader. The game is described by differential equations in l2 -space, and integral constraints are imposed on the control function of the players. The duration of the game is fixed and the payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. However, we discuss the condition for finding the value of the game and construct the optimal strategies of the players which ensure the completion of the game. An important fact to note is that we relaxed the usual conditions on the energy resources of the players. Finally, some examples are provided to illustrate our result. |
| first_indexed | 2025-11-15T09:40:44Z |
| format | Article |
| id | upm-38261 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:40:44Z |
| publishDate | 2019 |
| publisher | MDPI |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-382612020-05-04T16:09:14Z http://psasir.upm.edu.my/id/eprint/38261/ An optimal pursuit differential game problem with one evader and many pursuers Ahmed, Idris Kumam, Poom Ibragimov, Gafurjan Rilwan, Jewaidu Kumam, Wiyada The objective of this paper is to study a pursuit differential game with finite or countably number of pursuers and one evader. The game is described by differential equations in l2 -space, and integral constraints are imposed on the control function of the players. The duration of the game is fixed and the payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. However, we discuss the condition for finding the value of the game and construct the optimal strategies of the players which ensure the completion of the game. An important fact to note is that we relaxed the usual conditions on the energy resources of the players. Finally, some examples are provided to illustrate our result. MDPI 2019 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/38261/1/38261.pdf Ahmed, Idris and Kumam, Poom and Ibragimov, Gafurjan and Rilwan, Jewaidu and Kumam, Wiyada (2019) An optimal pursuit differential game problem with one evader and many pursuers. Mathematics, 7 (9). art. no. 842. pp. 1-11. ISSN 2227-7390 https://www.mdpi.com/2227-7390/7/9/842 10.3390/math7090842 |
| spellingShingle | Ahmed, Idris Kumam, Poom Ibragimov, Gafurjan Rilwan, Jewaidu Kumam, Wiyada An optimal pursuit differential game problem with one evader and many pursuers |
| title | An optimal pursuit differential game problem with one evader and many pursuers |
| title_full | An optimal pursuit differential game problem with one evader and many pursuers |
| title_fullStr | An optimal pursuit differential game problem with one evader and many pursuers |
| title_full_unstemmed | An optimal pursuit differential game problem with one evader and many pursuers |
| title_short | An optimal pursuit differential game problem with one evader and many pursuers |
| title_sort | optimal pursuit differential game problem with one evader and many pursuers |
| url | http://psasir.upm.edu.my/id/eprint/38261/ http://psasir.upm.edu.my/id/eprint/38261/ http://psasir.upm.edu.my/id/eprint/38261/ http://psasir.upm.edu.my/id/eprint/38261/1/38261.pdf |