A decomposition technique for pursuit evasion games with many pursuers

TL;DR

This paper introduces a decomposition method for solving pursuit-evasion differential games involving multiple pursuers by reducing problem complexity through target set decomposition and Hamilton-Jacobi theory.

Contribution

The paper presents a novel decomposition technique that simplifies multi-agent pursuit-evasion games by reducing problem dimensionality using geometric and Hamilton-Jacobi methods.

Findings

The technique effectively decomposes complex pursuit-evasion problems.

It establishes a relation between solution regularity and problem decomposability.

Applied to multi-agent pursuit-evasion, it enables more tractable solutions.

Abstract

Here we present a decomposition technique for a class of differential games. The technique consists in a decomposition of the target set which produces, for geometrical reasons, a decomposition in the dimensionality of the problem. Using some elements of Hamilton-Jacobi equations theory, we find a relation between the regularity of the solution and the possibility to decompose the problem. We use this technique to solve a pursuit evasion game with multiple agents.