Optimal Pursuit Game of Two Pursuers and One Evader with the Grönwall-Type Constraints on Controls
We studied a simple motion differential game of two pursuers and one evader in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>2</mn...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/2/374 |
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| author | Gafurjan Ibragimov Ikrombek Yusupov Massimiliano Ferrara |
| author_facet | Gafurjan Ibragimov Ikrombek Yusupov Massimiliano Ferrara |
| author_sort | Gafurjan Ibragimov |
| collection | DOAJ |
| description | We studied a simple motion differential game of two pursuers and one evader in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>2</mn></msup></semantics></math></inline-formula>. The control functions of players are subjected to the Grönwall-type constraints. If the state of the evader coincides with the state of a pursuer, then the game is considered complete. The pursuers attempt to complete the game as earlier as possible. The evader attempts to avoid being captured or delays the capture time. We found an equation for the optimal pursuit time and construct the optimal strategies of players. |
| first_indexed | 2024-03-09T11:46:38Z |
| format | Article |
| id | doaj.art-8d1e4add032f43e3a2f13d4a4aeeee17 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:46:38Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8d1e4add032f43e3a2f13d4a4aeeee172023-11-30T23:21:18ZengMDPI AGMathematics2227-73902023-01-0111237410.3390/math11020374Optimal Pursuit Game of Two Pursuers and One Evader with the Grönwall-Type Constraints on ControlsGafurjan Ibragimov0Ikrombek Yusupov1Massimiliano Ferrara2Department of Digital Economics and Agrotechnologies, University of Digital Economics and Agrotechnologies, Tashkent 100022, UzbekistanDepartment of Mathematics, Andijan State University, Andijan 170100, UzbekistanDepartment of Law, Economics and Human Sciences and Decisions Lab, University Mediterranea of Reggio Calabria, 89125 Reggio Calabria, ItalyWe studied a simple motion differential game of two pursuers and one evader in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>2</mn></msup></semantics></math></inline-formula>. The control functions of players are subjected to the Grönwall-type constraints. If the state of the evader coincides with the state of a pursuer, then the game is considered complete. The pursuers attempt to complete the game as earlier as possible. The evader attempts to avoid being captured or delays the capture time. We found an equation for the optimal pursuit time and construct the optimal strategies of players.https://www.mdpi.com/2227-7390/11/2/374differential gameGrönwall constraintspursuersevaderoptimal pursuit timeoptimal strategy |
| spellingShingle | Gafurjan Ibragimov Ikrombek Yusupov Massimiliano Ferrara Optimal Pursuit Game of Two Pursuers and One Evader with the Grönwall-Type Constraints on Controls Mathematics differential game Grönwall constraints pursuers evader optimal pursuit time optimal strategy |
| title | Optimal Pursuit Game of Two Pursuers and One Evader with the Grönwall-Type Constraints on Controls |
| title_full | Optimal Pursuit Game of Two Pursuers and One Evader with the Grönwall-Type Constraints on Controls |
| title_fullStr | Optimal Pursuit Game of Two Pursuers and One Evader with the Grönwall-Type Constraints on Controls |
| title_full_unstemmed | Optimal Pursuit Game of Two Pursuers and One Evader with the Grönwall-Type Constraints on Controls |
| title_short | Optimal Pursuit Game of Two Pursuers and One Evader with the Grönwall-Type Constraints on Controls |
| title_sort | optimal pursuit game of two pursuers and one evader with the gronwall type constraints on controls |
| topic | differential game Grönwall constraints pursuers evader optimal pursuit time optimal strategy |
| url | https://www.mdpi.com/2227-7390/11/2/374 |
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