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Mathematics > Optimization and Control

arXiv:2202.01826 (math)
[Submitted on 3 Feb 2022]

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

Authors:Eloy Garcia, Isaac Weintraub, David W. Casbeer, Meir Pachter
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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: 9 pages, 9 figures
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:2202.01826 [math.OC]
  (or arXiv:2202.01826v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2202.01826

Submission history

From: Eloy Garcia [view email]
[v1] Thu, 3 Feb 2022 20:12:49 UTC (612 KB)
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