Title

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

Authors

Eloy Garcia, Control Science Center of Excellence, Air Force Research Laboratory
Isaac Weintraub, Control Science Center of Excellence, Air Force Research Laboratory
David W. Casbeer, Control Science Center of Excellence, Air Force Research Laboratory
Meir Pachter, Air Force Institute of TechnologyFollow

Document Type

Conference Proceeding

Publication Date

6-2022

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.

Comments

© 2022 American Automatic Control Council.

DOI

Version of Record: 10.23919/ACC53348.2022.9867567 ; [arxiv]: 10.48550/arXiv.2202.01826

Source Publication

Proceedings of the American Control Conference

Recommended Citation

Version of Record: E. Garcia, I. Weintraub, D. W. Casbeer and M. Pachter, "Optimal Strategies for the Game of Protecting a Plane in 3-D," 2022 American Control Conference (ACC), 2022, pp. 102-107, doi: 10.23919/ACC53348.2022.9867567. arXiv e-print: arXiv:2202.01826 [math.OC], https://doi.org/10.48550/arXiv.2202.01826