A Pursuit Game in a Closed Convex Set on a Euclidean Space

This paper studies a pursuit differential game in a closed convex subset of the Euclidean space R n . Players of the game consist of finite number of pursuers chasing to catch a single evader both of which moves according to certain first order differential equation. The differential equations invol...

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Bibliographic Details
Published inDifferential equations and dynamical systems Vol. 32; no. 4; pp. 1215 - 1224
Main Authors Badakaya, Abbas Ja’afaru, Abdullahi, Hassan, Salimi, Mehdi
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.10.2024
Springer Nature B.V
Subjects
Computer Science
Convexity
Differential equations
Differential games
Engineering
Euclidean geometry
Mathematics
Mathematics and Statistics
Original Research
Players
Pursuit-evasion games
Pursuit-evasion game
Pursuer
Convex set
Evader
Coordinate-wise integral constraint
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Summary:This paper studies a pursuit differential game in a closed convex subset of the Euclidean space R n . Players of the game consist of finite number of pursuers chasing to catch a single evader both of which moves according to certain first order differential equation. The differential equations involve control functions through which players make their inputs in the game. Each of the player’s control function is subject to the coordinate-wise integral constraint. Pursuers are deemed to catch the evader when the geometric position of at least one pursuer coincides with that of the evader. We describe strategies of the pursuers in phases and give formula for computing the time span of each phase. Moreover, we provide and conditions that ensure evader’s catch.
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ISSN:0971-3514
0974-6870
DOI:10.1007/s12591-022-00621-y