On some new results in a pursuit differential game with many pursuers and one evader

Gafurjan Ibragimov; Omongul Egamberganova; Idham Arif Alias; Shravan Luckraz; Gafurjan Ibragimov; Omongul Egamberganova; Idham Arif Alias; Shravan Luckraz

doi:10.3934/math.2023332

AIMS Mathematics

2023, Volume 8, Issue 3: 6581-6589. doi: 10.3934/math.2023332

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Research article

On some new results in a pursuit differential game with many pursuers and one evader

1.
Department of Digital Economics and Agrotechnologies, University of Digital Economics and Agrotechnologies, Tashkent 100022, Uzbekistan
2.
Faculty of Science, Universiti Putra Malaysia, Serdang, Selangor, Malaysia, & Department of Higher Mathematics, Tashkent Finance Institute, Tashkent, Uzbekistan
3.
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia
4.
School of Public Finance and Taxation, Zhejiang University of Finance and Economics, Hangzhou 310018, China

Received: 22 September 2022 Revised: 19 December 2022 Accepted: 25 December 2022 Published: 05 January 2023
MSC : Primary 05C57, Secondary 91A43

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.
- differential game,
- Grönwall constraints,
- pursuer,
- evader,
- strategy
Citation: Gafurjan Ibragimov, Omongul Egamberganova, Idham Arif Alias, Shravan Luckraz. On some new results in a pursuit differential game with many pursuers and one evader[J]. AIMS Mathematics, 2023, 8(3): 6581-6589. doi: 10.3934/math.2023332

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Abstract

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.

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