Optimal Strategies for the Game of Protecting a Plane in 3-D

TL;DR

This paper develops optimal, robust strategies for a 3-D differential game where agents protect a target, providing explicit solutions and demonstrating their effectiveness through illustrative examples.

Contribution

It introduces new state-feedback saddle-point strategies and derives the value function as a solution to the Hamilton-Jacobi-Isaacs equation for the 3-D protection game.

Findings

Explicit saddle-point strategies derived for 3-D protection game

Value function shown to solve Hamilton-Jacobi-Isaacs equation

Strategies demonstrate robustness in illustrative examples

Abstract

A conflict between rational and autonomous agents is considered. The paper addresses a differential game of protecting a target in the 3-D space. This problem highlights the strong correlation between the highly dynamic scenario, the uncertainty on the behavior of the adversary, and the online and robust computation of state-feedback strategies which guarantee the required level of performance of each player. This work significantly expands previous results around this problem by providing the players' state-feedback saddle-point strategies. Additionally, the continuously differentiable Value function of the multi-agent differential game is obtained and it is shown to be the solution of the Hamilton-Jacobi-Isaacs equation. Finally, the Barrier surface is explicitly obtained and illustrative examples highlight the robustness properties and the guarantees provided by the saddle-point strategies obtained in this paper.