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Research Article | Open Access

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

Gafurjan Ibragimov1, Omongul Egamberganova2, Idham Arif Alias3, Shravan Luckraz4( )
Department of Digital Economics and Agrotechnologies, University of Digital Economics and Agrotechnologies, Tashkent 100022, Uzbekistan
Faculty of Science, Universiti Putra Malaysia, Serdang, Selangor, Malaysia, & Department of Higher Mathematics, Tashkent Finance Institute, Tashkent, Uzbekistan
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia
School of Public Finance and Taxation, Zhejiang University of Finance and Economics, Hangzhou 310018, China
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Abstract

We study a simple motion differential game with many pursuers and one evader with equal capabilities in 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.

Keywords

differential gameGrönwall constraintspursuerevaderstrategy
CLC number: Primary 05C57, Secondary 91A43

References

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AIMS Mathematics
Volume 8 Issue 3,
March 2023
Pages 6581-6589
DOI: 10.3934/math.2023332

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Cite this article:
Ibragimov G, Egamberganova O, Alias IA, et al. On some new results in a pursuit differential game with many pursuers and one evader. AIMS Mathematics, 2023, 8(3): 6581-6589. https://doi.org/10.3934/math.2023332

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Received: 22 September 2022
Revised: 19 December 2022
Accepted: 25 December 2022
Published: 15 March 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)