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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/1386242 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832568200852668416 |
|---|---|
| author | Atamurat Kuchkarov Gafurjan Ibragimov Massimiliano Ferrara |
| author_facet | Atamurat Kuchkarov Gafurjan Ibragimov Massimiliano Ferrara |
| author_sort | Atamurat Kuchkarov |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-26b51145956347f3b48d5cf8bb60ec74 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-26b51145956347f3b48d5cf8bb60ec742025-02-03T00:59:26ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/13862421386242Simple Motion Pursuit and Evasion Differential Games with Many Pursuers on Manifolds with Euclidean MetricAtamurat Kuchkarov0Gafurjan Ibragimov1Massimiliano Ferrara2Institute of Mathematics, National University of Uzbekistan, 100125 Tashkent, UzbekistanDepartment of Mathematics & Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, MalaysiaDepartment of Law and Economics, Mediterranea University of Reggio Calabria, 89127 Reggio Calabria, ItalyWe 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.http://dx.doi.org/10.1155/2016/1386242 |
| spellingShingle | Atamurat Kuchkarov Gafurjan Ibragimov Massimiliano Ferrara Simple Motion Pursuit and Evasion Differential Games with Many Pursuers on Manifolds with Euclidean Metric Discrete Dynamics in Nature and Society |
| 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://dx.doi.org/10.1155/2016/1386242 |
| work_keys_str_mv | AT atamuratkuchkarov simplemotionpursuitandevasiondifferentialgameswithmanypursuersonmanifoldswitheuclideanmetric AT gafurjanibragimov simplemotionpursuitandevasiondifferentialgameswithmanypursuersonmanifoldswitheuclideanmetric AT massimilianoferrara simplemotionpursuitandevasiondifferentialgameswithmanypursuersonmanifoldswitheuclideanmetric |