EVASION IN A LINEAR DIFFERENTIAL GAME WITH MANY PURSUERS

Gafurjan Ibragimov; Tuychivoy Tursunaliev; Shravan Luckraz

doi:10.3934/dcdsb.2024072

EVASION IN A LINEAR DIFFERENTIAL GAME WITH MANY PURSUERS

Gafurjan Ibragimov, Tuychivoy Tursunaliev, Shravan Luckraz

School of Economics

Research output: Journal Publication › Article › peer-review

Abstract

We study a differential game of one evader and n pursuers on R^d, where the control sets are given by the unit ball for the pursuers and the ball of radius σ, where σ > 1, for the evader. Evasion is said to be possible if the state of the evader doesn’t coincide with that of any pursuer for all t. We propose a new evasion strategy which guarantees evasion from any initial positions of the players. We use the strategy to show that the number of approach times is bounded above by n(n + 1)/2.

Original language	English
Pages (from-to)	4929-4945
Number of pages	17
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	29
Issue number	12
DOIs	https://doi.org/10.3934/dcdsb.2024072
Publication status	Published - Dec 2024

Keywords

control
Differential game
evasion
evasion strategy
faster evader
many pursuers

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcdsb.2024072

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abstract = "We study a differential game of one evader and n pursuers on Rd, where the control sets are given by the unit ball for the pursuers and the ball of radius σ, where σ > 1, for the evader. Evasion is said to be possible if the state of the evader doesn{\textquoteright}t coincide with that of any pursuer for all t. We propose a new evasion strategy which guarantees evasion from any initial positions of the players. We use the strategy to show that the number of approach times is bounded above by n(n + 1)/2.",

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AB - We study a differential game of one evader and n pursuers on Rd, where the control sets are given by the unit ball for the pursuers and the ball of radius σ, where σ > 1, for the evader. Evasion is said to be possible if the state of the evader doesn’t coincide with that of any pursuer for all t. We propose a new evasion strategy which guarantees evasion from any initial positions of the players. We use the strategy to show that the number of approach times is bounded above by n(n + 1)/2.

KW - control

KW - Differential game

KW - evasion

KW - evasion strategy

KW - faster evader

KW - many pursuers

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JF - Discrete and Continuous Dynamical Systems - Series B

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ER -

EVASION IN A LINEAR DIFFERENTIAL GAME WITH MANY PURSUERS

Abstract

Keywords

ASJC Scopus subject areas

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