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

AIMS Mathematics

article

Gafurjan Ibragimov¹  Omongul Egamberganova²  Idham Arif Alias³  Shravan Luckraz⁴ 

[1] Department of Digital Economics and Agrotechnologies, University of Digital Economics and Agrotechnologies;Faculty of Science, Universiti Putra Malaysia, Serdang, Selangor, Malaysia, & Department of Higher Mathematics, Tashkent Finance Institute;Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia;School of Public Finance and Taxation, Zhejiang University of Finance and Economics

关键词: differential game;    Grönwall constraints;    pursuer;    evader;    strategy;   

DOI  :  10.3934/math.2023332

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY