Optimal Strategies for the Game of Protecting a Plane in 3-D
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.
Keywords
Cite
@article{arxiv.2202.01826,
title = {Optimal Strategies for the Game of Protecting a Plane in 3-D},
author = {Eloy Garcia and Isaac Weintraub and David W. Casbeer and Meir Pachter},
journal= {arXiv preprint arXiv:2202.01826},
year = {2022}
}
Comments
9 pages, 9 figures