IEEE Trans Cybern. 2022 May;52(5):3998-4011. doi: 10.1109/TCYB.2020.3015031. Epub 2022 May 19.
This article considers a subspace guarding game in high-dimensional space which consists of a play subspace and a target subspace. Two faster defenders as a team cooperate to protect the target subspace by capturing an attacker which strives to enter the target subspace from the play subspace without being captured. A closed-form solution is provided from the perspectives of kind and degree. Contributions of the work include the use of the attack subspace (AS) method to construct the barrier, by which the game winner can be perfectly predicted before the game starts. In addition to this inclusion, with the priori information about the game result, a critical payoff function is designed when the defenders can win the game. Then, the optimal strategy for each player is explicitly reformulated as a saddle-point equilibrium. Finally, we apply these theoretical results to two half-space and half-plane guarding games in 3-D space and 2-D plane, respectively. Since the entire achieved developments are analytical, they require a little memory without the computational burden and allow for real-time updates, beyond the capacity of the traditional Hamilton-Jacobi-Isaacs method. It is worth noting that this is the first time in the current work to consider the target guarding games for arbitrary high-dimensional space and in a fully analytical form.
本文考虑了高维空间中的子空间防御博弈，它由一个游戏子空间和一个目标子空间组成。两个更快的防御者作为一个团队合作，通过捕获从游戏子空间努力进入目标子空间而不被捕获的攻击者来保护目标子空间。从种类和程度的角度提供了一个闭式解。这项工作的贡献包括使用攻击子空间（AS）方法来构建障碍，通过这种方法，可以在游戏开始之前完美地预测游戏的获胜者。除了这一包含之外，根据游戏结果的先验信息，当防御者可以赢得比赛时，设计了一个临界收益函数。然后，作为鞍点均衡，明确地重新制定了每个玩家的最优策略。最后，我们将这些理论结果应用于三维空间中的两个半空间和半平面防御博弈，以及二维平面中的两个半空间和半平面防御博弈。由于整个开发过程都是分析性的，它们需要的内存很少，没有计算负担，并且允许实时更新，这超出了传统的哈密顿-雅可比-伊萨亚斯方法的能力。值得注意的是，这是首次在当前工作中以完全分析的形式考虑任意高维空间中的目标防御博弈。
