An infinite dimensional pursuit-evasion differential game with finite number of players

TL;DR

This paper analyzes a pursuit-evasion differential game in infinite-dimensional Hilbert space, providing explicit strategies for both pursuers and evader to guarantee pursuit or evasion.

Contribution

It introduces a novel solution to the pursuit-evasion game in infinite-dimensional space with explicit strategies for all players.

Findings

Explicit pursuit strategies guarantee pursuit.

Explicit evasion strategy guarantees evasion.

Game solution applicable in infinite-dimensional settings.

Abstract

We study a pursuit-evasion differential game with finite number of pursuers and one evader in Hilbert space with geometric constraints on the control functions of players. We solve the game by presenting explicit strategies for pursuers which guarantee their pursuit as well as an strategy for the evader which guarantees its evasion.