On a fixed duration pursuit differential game with geometric and integral constraints

TL;DR

This paper analyzes a pursuit differential game with multiple pursuers and one evader, where players have geometric or integral control constraints, and determines optimal strategies and the game's value.

Contribution

It introduces a novel pursuit game model with mixed constraints and derives explicit optimal strategies and the game's value.

Findings

Optimal strategies for pursuers and evader are constructed.

The game's value, i.e., the minimal distance at termination, is explicitly determined.

The model extends previous pursuit game frameworks with mixed control constraints.

Abstract

In this paper we investigate a differential game in which countably many dynamical objects pursue a single one. All the players perform simple motions. The duration of the game is fixed. The controls of a group of pursuers are subject to geometric constraints and the controls of the other pursuers and the evader are subject to integral constraints. The payoff of the game is the distance between the evader and the closest pursuer when the game is terminated. We construct optimal strategies for players and find the value of the game.