On extension for infinite horizon game of pursuit-evasion

TL;DR

This paper extends the infinite horizon pursuit-evasion game by constructing a projective limit of restricted games, analyzing the impact of target set sensitivity on optimal control existence, especially with joint and relaxed controls.

Contribution

It introduces a novel extension of infinite horizon pursuit-evasion games using projective limits and explores control existence conditions under joint and relaxed control frameworks.

Findings

Established the relation between target set sensitivity and control existence.

Developed a framework for pursuit-evasion with joint and relaxed controls.

Provided conditions for the existence of optimal controls in extended games.

Abstract

The extension of a conflict control problem with infinite horizon is constructed. This extension is the projective limit of restricted games. Relations between "sensitivity to target set" and the existence of the optimal control are studied. Special attention is paid to the pursuit-evasion game with "joint control/relaxed control".