This article proposes an optimal-distributed control protocol for multivehicle systems with an unknown switching communication graph. The optimal-distributed control problem is formulated to differential graphical games, and the Pareto optimum to multiplayer games is sought based on the viability theory and reinforcement learning techniques. The viability theory characterizes the controllability of a wide range of constrained nonlinear systems; and the viability kernel and the capture basin are the pillars of the viability theory. The capture basin is the set of all initial states, in which there exist control strategies that enable the states to reach the target in finite time while remaining inside a set before reaching the target. In this regard, the feasible learning region is characterized by the reinforcement learner. In addition, the approximation of the capture basin provides the learner with prior knowledge. Unlike the existing works that employ the viability theory to solve control problems with only one agent and differential games with only two players, the viability theory, in this article, is utilized to solve multiagent control problems and multiplayer differential games. The distributed control law is composed of two parts: 1) the approximation of the capture basin and 2) reinforcement learning, which are computed offline and online, respectively. The convergence properties of the parameters' estimation errors in reinforcement learning are proved, and the convergence of the control policy to the Pareto optimum of the differential graphical game is discussed. The guaranteed approximation results of the capture basin are provided and the simulation results of the differential graphical game are provided for multivehicle systems with the proposed distributed control policy.

中文翻译：

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基于生存力理论的受限自动驾驶汽车微分图形游戏。

本文提出了一种具有未知切换通信图的多车辆系统的最优分布式控制协议。提出了针对差分图形游戏的最优分布控制问题，并基于生存力理论和强化学习技术，寻求了针对多人游戏的帕累托最优。生存力理论刻画了各种约束非线性系统的可控性。生存力核心和捕获盆地是生存力理论的基础。捕获盆地是所有初始状态的集合，其中存在控制策略，这些控制策略可使状态在有限的时间内达到目标，同时在达到目标之前保留在集合内。在这方面，可行的学习区域的特征在于强化学习者。此外，收集盆的近似为学习者提供了先验知识。与现有的采用生存能力理论来解决只有一个代理人的控制问题和只有两个参与者的差分博弈不同的是，本文中的生存力理论被用来解决多主体控制问题和多玩家的差分博弈。分布控制律由两部分组成：1）集水盆的逼近； 2）加固学习，分别是离线和在线计算的。证明了强化学习中参数估计误差的收敛性，讨论了控制策略对差分图形博弈的帕累托最优的收敛性。