Large complex dynamical systems behave in ways that reflect their structure. There are many applications where we need to control these systems by bringing them from their current state to a desired state. Affecting the state of these systems is done by communications with its key elements, called driver nodes, in reference to their representation as a network of nodes. Over the past decades, much focus has been paid on analytical approaches to derive optimal control configurations based on the concept of Minimum Driver node Sets (MDSs) for directed complex networks. However, the underlying control mechanisms of many complex systems rely on quickly controlling a major subspace of a system. In this work, we ask how complex networks behave if driver nodes are randomly selected? We seek to understand and employ the statistical characteristics of MDSs to randomly select driver nodes and analyze the controllability properties of complex network. We propose an algorithm to build Random Driver node Sets (RDSs) and analyze their controllable subspace, the minimum time needed to control, and the cardinality of RDSs. Through our evaluations on a variety of synthetic and real-world networks, we show RDSs can quickly and effectively control a major subspace of networks.

中文翻译：

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使用统计随机抽样的复杂网络的可控性分析

大型复杂动力系统的行为方式反映了它们的结构。在许多应用程序中，我们需要通过将这些系统从当前状态变为所需状态来控制它们。影响这些系统的状态是通过与其关键元素（称为驱动节点）的通信来完成的，参考它们作为节点网络的表示。在过去的几十年中，基于有向复杂网络的最小驱动节点集 (MDS) 概念推导出最优控制配置的分析方法得到了很多关注。然而，许多复杂系统的底层控制机制依赖于快速控制系统的主要子空间。在这项工作中，我们问如果驱动节点是随机选择的，那么复杂的网络会如何表现？我们寻求理解和利用 MDS 的统计特性来随机选择驱动节点并分析复杂网络的可控性。我们提出了一种算法来构建随机驱动节点集 (RDS) 并分析它们的可控子空间、控制所需的最短时间以及 RDS 的基数。通过我们对各种合成和现实世界网络的评估，我们表明 RDS 可以快速有效地控制网络的主要子空间。