Game value for a pursuit-evasion differential game problem in a Hilbert space

Abbas Ja'afaru Badakaya; Aminu Sulaiman Halliru; Jamilu Adamu

doi:10.3934/jdg.2021019

Article Contents

2022, Volume 9, Issue 1: 1-12. Doi: 10.3934/jdg.2021019

This issue Previous Article Next Article Zero-sum games for pure jump processes with risk-sensitive discounted cost criteria

Game value for a pursuit-evasion differential game problem in a Hilbert space

1.
Department of Mathematical Sciences, Bayero University, Kano, Nigeria
2.
Federal University, Gashua, Yobe State, Nigeria

^* Corresponding author: Abbas Ja'afaru Badakaya
^* Corresponding author: Abbas Ja'afaru Badakaya

Received: December 2020

Revised: April 2021

Early access: May 2021

Published: January 2022

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Abstract

We consider a pursuit-evasion differential game problem with countable number pursuers and one evader in the Hilbert space $ l_{2}. $ Players' dynamic equations described by certain $ n^{th} $ order ordinary differential equations. Control functions of the players subject to integral constraints. The goal of the pursuers is to minimize the distance to the evader and that of the evader is the opposite. The stoppage time of the game is fixed and the game payoff is the distance between evader and closest pursuer when the game is stopped. We study this game problem and find the value of the game. In addition to this, we construct players' optimal strategies.

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Mathematics Subject Classification: Primary: 91A23; Secondary: 49N75.

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References

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