Simple motion pursuit and evasion differential games with many pursuers on manifolds with Euclidean metric
We consider pursuit and evasion differential games of a group of m pursuers and one evader on manifolds with Euclidean metric. The motions of all players are simple, and maximal speeds of all players are equal. If the state of a pursuer coincides with that of the evader at some time, we say that pur...
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/56540/1/56540.pdf |
| _version_ | 1796976499493961728 |
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| author | Kuchkarov, Atamurat Shamuratovich Ibragimov, Gafurjan Ferrara, Massimiliano |
| author_facet | Kuchkarov, Atamurat Shamuratovich Ibragimov, Gafurjan Ferrara, Massimiliano |
| author_sort | Kuchkarov, Atamurat Shamuratovich |
| collection | UPM |
| description | We consider pursuit and evasion differential games of a group of m pursuers and one evader on manifolds with Euclidean metric. The motions of all players are simple, and maximal speeds of all players are equal. If the state of a pursuer coincides with that of the evader at some time, we say that pursuit is completed. We establish that each of the differential games (pursuit or evasion) is equivalent to a differential game of m groups of countably many pursuers and one group of countably many evaders in Euclidean space. All the players in any of these groups are controlled by one controlled parameter. We find a condition under which pursuit can be completed, and if this condition is not satisfied, then evasion is possible. We construct strategies for the pursuers in pursuit game which ensure completion the game for a finite time and give a formula for this time. In the case of evasion game, we construct a strategy for the evader. |
| first_indexed | 2024-03-06T09:26:42Z |
| format | Article |
| id | upm.eprints-56540 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:26:42Z |
| publishDate | 2016 |
| publisher | Hindawi Publishing Corporation |
| record_format | dspace |
| spelling | upm.eprints-565402017-08-01T08:55:44Z http://psasir.upm.edu.my/id/eprint/56540/ Simple motion pursuit and evasion differential games with many pursuers on manifolds with Euclidean metric Kuchkarov, Atamurat Shamuratovich Ibragimov, Gafurjan Ferrara, Massimiliano We consider pursuit and evasion differential games of a group of m pursuers and one evader on manifolds with Euclidean metric. The motions of all players are simple, and maximal speeds of all players are equal. If the state of a pursuer coincides with that of the evader at some time, we say that pursuit is completed. We establish that each of the differential games (pursuit or evasion) is equivalent to a differential game of m groups of countably many pursuers and one group of countably many evaders in Euclidean space. All the players in any of these groups are controlled by one controlled parameter. We find a condition under which pursuit can be completed, and if this condition is not satisfied, then evasion is possible. We construct strategies for the pursuers in pursuit game which ensure completion the game for a finite time and give a formula for this time. In the case of evasion game, we construct a strategy for the evader. Hindawi Publishing Corporation 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/56540/1/56540.pdf Kuchkarov, Atamurat Shamuratovich and Ibragimov, Gafurjan and Ferrara, Massimiliano (2016) Simple motion pursuit and evasion differential games with many pursuers on manifolds with Euclidean metric. Discrete Dynamics in Nature and Society, 2016. art. no. 1386242. pp. 1-8. ISSN 1026-0226; ESSN: 1607-887X https://www.hindawi.com/journals/ddns/2016/1386242/abs/ 10.1155/2016/1386242 |
| spellingShingle | Kuchkarov, Atamurat Shamuratovich Ibragimov, Gafurjan Ferrara, Massimiliano Simple motion pursuit and evasion differential games with many pursuers on manifolds with Euclidean metric |
| title | Simple motion pursuit and evasion differential games with many pursuers on manifolds with Euclidean metric |
| title_full | Simple motion pursuit and evasion differential games with many pursuers on manifolds with Euclidean metric |
| title_fullStr | Simple motion pursuit and evasion differential games with many pursuers on manifolds with Euclidean metric |
| title_full_unstemmed | Simple motion pursuit and evasion differential games with many pursuers on manifolds with Euclidean metric |
| title_short | Simple motion pursuit and evasion differential games with many pursuers on manifolds with Euclidean metric |
| title_sort | simple motion pursuit and evasion differential games with many pursuers on manifolds with euclidean metric |
| url | http://psasir.upm.edu.my/id/eprint/56540/1/56540.pdf |
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