Optimal Strategies for the Game of Protecting a Plane in 3-D
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.
Version of Record: 10.23919/ACC53348.2022.9867567 ; [arxiv]: 10.48550/arXiv.2202.01826
Proceedings of the American Control Conference
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