Feedback is one of the most powerful influences in dynamical systems, performing a fundamental function in self-regulating processes. However, it is not known whether the underlying control of networked systems is associated with feedback. Here, we analyze structural feedback, defined by adding directed links from controlled nodes to driver nodes, to determine the control energy requirement of networked systems. We show that feedback systems with positive links require less energy than feedback systems with negative links, and the control energies of positive and negative perturbed feedback systems with the same amplitudes display a universal symmetry for regular graphs. Then, we describe an algorithm to construct a structural feedback system enabling the control of both synthetic and empirical networks. Our results improve the understanding of feedback in determining the control energy of dynamical systems, thus providing a potential way to devise new feedback control schemes.<...

中文翻译：

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复杂网络控制中的结构反馈

反馈是动力系统中最强大的影响力之一，它在自我调节过程中起着基本作用。但是，尚不清楚网络系统的基础控制是否与反馈相关联。在这里，我们分析结构反馈，方法是通过添加从受控节点到驱动程序节点的有向链接来定义的，以确定网络系统的控制能量需求。我们显示，具有正连接的反馈系统比具有负连接的反馈系统需要更少的能量，并且具有相同幅度的正和负摄动反馈系统的控制能量对于规则图显示通用对称性。然后，我们描述了一种构建结构反馈系统的算法，该系统能够控制合成网络和经验网络。