On some new results in a pursuit differential game with many pursuers and one evader
We study a simple motion differential game with many pursuers and one evader with equal capabilities in $ \mathbb{R}^n $. The control functions of the players are subject to the Grönwall-type constraints. If the state of the evader coincides with the state of a pursuer, then the game is considered c...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-01-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023332?viewType=HTML |
| _version_ | 1811176137504587776 |
|---|---|
| author | Gafurjan Ibragimov Omongul Egamberganova Idham Arif Alias Shravan Luckraz |
| author_facet | Gafurjan Ibragimov Omongul Egamberganova Idham Arif Alias Shravan Luckraz |
| author_sort | Gafurjan Ibragimov |
| collection | DOAJ |
| description | We study a simple motion differential game with many pursuers and one evader with equal capabilities in $ \mathbb{R}^n $. The control functions of the players are subject to the Grönwall-type constraints. If the state of the evader coincides with the state of a pursuer, then the game is considered completed. If the state of the evader does not coincide with the state of any pursuer at all times, then we say that evasion is possible. We show that pursuit can be completed if a condition on the convex hull of the initial states of the pursuers is satisfied. |
| first_indexed | 2024-04-10T19:47:19Z |
| format | Article |
| id | doaj.art-5a6972b3ab5b44fdaa2dc063a8478ee9 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T19:47:19Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-5a6972b3ab5b44fdaa2dc063a8478ee92023-01-29T02:18:03ZengAIMS PressAIMS Mathematics2473-69882023-01-01836581658910.3934/math.2023332On some new results in a pursuit differential game with many pursuers and one evaderGafurjan Ibragimov0Omongul Egamberganova 1 Idham Arif Alias2Shravan Luckraz31. Department of Digital Economics and Agrotechnologies, University of Digital Economics and Agrotechnologies, Tashkent 100022, Uzbekistan2. Faculty of Science, Universiti Putra Malaysia, Serdang, Selangor, Malaysia, & Department of Higher Mathematics, Tashkent Finance Institute, Tashkent, Uzbekistan3. Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia4. School of Public Finance and Taxation, Zhejiang University of Finance and Economics, Hangzhou 310018, ChinaWe study a simple motion differential game with many pursuers and one evader with equal capabilities in $ \mathbb{R}^n $. The control functions of the players are subject to the Grönwall-type constraints. If the state of the evader coincides with the state of a pursuer, then the game is considered completed. If the state of the evader does not coincide with the state of any pursuer at all times, then we say that evasion is possible. We show that pursuit can be completed if a condition on the convex hull of the initial states of the pursuers is satisfied.https://www.aimspress.com/article/doi/10.3934/math.2023332?viewType=HTMLdifferential gamegrönwall constraintspursuerevaderstrategy |
| spellingShingle | Gafurjan Ibragimov Omongul Egamberganova Idham Arif Alias Shravan Luckraz On some new results in a pursuit differential game with many pursuers and one evader AIMS Mathematics differential game grönwall constraints pursuer evader strategy |
| title | On some new results in a pursuit differential game with many pursuers and one evader |
| title_full | On some new results in a pursuit differential game with many pursuers and one evader |
| title_fullStr | On some new results in a pursuit differential game with many pursuers and one evader |
| title_full_unstemmed | On some new results in a pursuit differential game with many pursuers and one evader |
| title_short | On some new results in a pursuit differential game with many pursuers and one evader |
| title_sort | on some new results in a pursuit differential game with many pursuers and one evader |
| topic | differential game grönwall constraints pursuer evader strategy |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023332?viewType=HTML |
| work_keys_str_mv | AT gafurjanibragimov onsomenewresultsinapursuitdifferentialgamewithmanypursuersandoneevader AT omongulegamberganova onsomenewresultsinapursuitdifferentialgamewithmanypursuersandoneevader AT idhamarifalias onsomenewresultsinapursuitdifferentialgamewithmanypursuersandoneevader AT shravanluckraz onsomenewresultsinapursuitdifferentialgamewithmanypursuersandoneevader |