For cooperative-antagonistic networks, the distributed control problem is solved owing to all static interactions among vertices, expressed conveniently by a communication graph whose edge weights are constant or time-varying numbers. The question asked in this paper is: whether and how can distributed control be achieved in the presence of dynamic interactions that are modeled as edge weights in terms of transfer functions on a communication graph? The answer is affirmative, and the nearest neighbor rule is effective for designing dynamic distributed controllers. Necessary and sufficient conditions are given for convergence of cooperative-antagonistic networks which can admit hybrid static and dynamic interactions. By defining a class of dynamic signed graphs and the related sign-indicator matrices, the structural balance/unbalance is proposed to describe the convergence conditions under dynamic interactions. Examples are provided to validate structure properties and convergence results of cooperative-antagonistic networks with dynamic interactions.

中文翻译：

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协同__对抗交互网络的动态分布式控制


对于合作对抗网络，由于顶点之间的所有静态交互，分布式控制问题得以解决，可以通过边权重为常数或时变数的通信图方便地表示。本文提出的问题是：在存在动态交互的情况下是否以及如何实现分布式控制，这些动态交互根据通信图上的传递函数被建模为边权重？答案是肯定的，最近邻规则对于设计动态分布式控制器是有效的。给出了允许静态和动态混合交互的合作对抗网络收敛的充要条件。通过定义一类动态符号图和相关符号指示矩阵，提出结构平衡/不平衡来描述动态相互作用下的收敛条件。提供了示例来验证具有动态交互的合作对抗网络的结构特性和收敛结果。