Solutions for Multiagent Pursuit-Evasion Games on Communication Graphs: Finite-Time Capture and Asymptotic Behaviors

In this paper, the multiagent pursuit-evasion (MPE) games are solved in order to obtain optimal strategic policies for all players. In these games, multiple pursuers attempt to intercept multiple evaders who try to avoid capture. A graph-theoretic approach is employed to study the interactions of the agents with limited sensing capabilities, such that distributed control policies are obtained for every agent. Furthermore, the minimization of performance indices associated with the goals of the agents is guaranteed. Nash equilibrium among the players is obtained by means of optimal policies that use the solutions of the Hamilton–Jacobi–Isaacs (HJI) equations of the game. Minmax strategies are also proposed to guarantee a security-level performance when the solutions of the HJI equations for Nash equilibrium do not exist. Scenarios for finite-time capture and for asymptotic rendezvous are analyzed, and emergent behaviors are obtained by means of modifications of the proposed general-case performance indices. The containment control results are shown to be special cases of the solutions of the MPE games.

在本文中，对多智能体追逃（MPE）博弈进行求解，以便为所有参与者获得最优策略。在这些博弈中，多个追击者试图拦截多个试图躲避抓捕的逃逸者。采用图论方法来研究具有有限感知能力的智能体之间的相互作用，从而为每个智能体获得分布式控制策略。此外，保证了与智能体目标相关的性能指标最小化。通过使用博弈的哈密顿 - 雅可比 - 艾萨克斯（HJI）方程的解的最优策略，在参与者之间获得纳什均衡。当纳什均衡的HJI方程无解时，还提出了极大极小策略以保证安全级别的性能。对有限时间捕获和渐近会合的情形进行了分析，并通过对所提出的一般情况性能指标进行修改获得了涌现行为。 containment控制结果被证明是MPE博弈解的特殊情况。