In this paper, we explore aggregative games over networks of multi-integrator agents with coupled constraints. To reach the general Nash equilibrium of an aggregative game, a distributed strategy-updating rule is proposed by a combination of the coordination of Lagrange multipliers and the estimation of the aggregator. Each player has only access to partial-decision information and communicates with his neighbors in a weight-balanced digraph which characterizes players' preferences as to the values of information received from neighbors. We first consider networks of double-integrator agents and then focus on multi-integrator agents. The effectiveness of the proposed strategy-updating rules is demonstrated by analyzing the convergence of corresponding dynamical systems via the Lyapunov stability theory, singular perturbation theory and passive theory. Numerical examples are given to illustrate our results.

中文翻译：

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具有耦合约束的多积分系统聚合博弈的分布式策略更新规则

在本文中，我们探索了具有耦合约束的多积分代理网络上的聚合游戏。为了达到聚合博弈的一般纳什均衡，结合拉格朗日乘子的协调和聚合器的估计，提出了分布式策略更新规则。每个玩家只能访问部分决策信息，并在权重平衡有向图中与其邻居进行通信，该图描述了玩家对从邻居收到的信息值的偏好。我们首先考虑双积分代理网络，然后关注多积分代理。通过李雅普诺夫稳定性理论分析相应动力系统的收敛性，证明了所提出的策略更新规则的有效性，奇异摄动理论和被动理论。给出了数值例子来说明我们的结果。