Linear Pursuit Differential Game under Phase Constraint on the State of Evader
We consider a linear pursuit differential game of one pursuer and one evader. Controls of the pursuer and evader are subjected to integral and geometric constraints, respectively. In addition, phase constraint is imposed on the state of evader, whereas pursuer moves throughout the space. We say that...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/1289456 |
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| _version_ | 1849306336612843520 |
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| author | Askar Rakhmanov Gafurjan Ibragimov Massimiliano Ferrara |
| author_facet | Askar Rakhmanov Gafurjan Ibragimov Massimiliano Ferrara |
| author_sort | Askar Rakhmanov |
| collection | DOAJ |
| description | We consider a linear pursuit differential game of one pursuer and one evader. Controls of the pursuer and evader are subjected to integral and geometric constraints, respectively. In addition, phase constraint is imposed on the state of evader, whereas pursuer moves throughout the space. We say that pursuit is completed, if inclusion y(t1)-x(t1)∈M is satisfied at some t1>0, where x(t) and y(t) are states of pursuer and evader, respectively, and M is terminal set. Conditions of completion of pursuit in the game from all initial points of players are obtained. Strategy of the pursuer is constructed so that the phase vector of the pursuer first is brought to a given set, and then pursuit is completed. |
| format | Article |
| id | doaj-art-2e8c26226c674de8bebf4bdd283d1920 |
| 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-2e8c26226c674de8bebf4bdd283d19202025-08-20T03:55:07ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/12894561289456Linear Pursuit Differential Game under Phase Constraint on the State of EvaderAskar Rakhmanov0Gafurjan Ibragimov1Massimiliano Ferrara2Department of Informatics, Tashkent University of Information Technologies, TUIT, Amir Temur Str. 108, 100202 Tashkent, UzbekistanDepartment of Mathematics & Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, MalaysiaDepartment of Law and Economics, University Mediterranea of Reggio Calabria, Reggio Calabria, ItalyWe consider a linear pursuit differential game of one pursuer and one evader. Controls of the pursuer and evader are subjected to integral and geometric constraints, respectively. In addition, phase constraint is imposed on the state of evader, whereas pursuer moves throughout the space. We say that pursuit is completed, if inclusion y(t1)-x(t1)∈M is satisfied at some t1>0, where x(t) and y(t) are states of pursuer and evader, respectively, and M is terminal set. Conditions of completion of pursuit in the game from all initial points of players are obtained. Strategy of the pursuer is constructed so that the phase vector of the pursuer first is brought to a given set, and then pursuit is completed.http://dx.doi.org/10.1155/2016/1289456 |
| spellingShingle | Askar Rakhmanov Gafurjan Ibragimov Massimiliano Ferrara Linear Pursuit Differential Game under Phase Constraint on the State of Evader Discrete Dynamics in Nature and Society |
| title | Linear Pursuit Differential Game under Phase Constraint on the State of Evader |
| title_full | Linear Pursuit Differential Game under Phase Constraint on the State of Evader |
| title_fullStr | Linear Pursuit Differential Game under Phase Constraint on the State of Evader |
| title_full_unstemmed | Linear Pursuit Differential Game under Phase Constraint on the State of Evader |
| title_short | Linear Pursuit Differential Game under Phase Constraint on the State of Evader |
| title_sort | linear pursuit differential game under phase constraint on the state of evader |
| url | http://dx.doi.org/10.1155/2016/1289456 |
| work_keys_str_mv | AT askarrakhmanov linearpursuitdifferentialgameunderphaseconstraintonthestateofevader AT gafurjanibragimov linearpursuitdifferentialgameunderphaseconstraintonthestateofevader AT massimilianoferrara linearpursuitdifferentialgameunderphaseconstraintonthestateofevader |