Structural feedback in the control of complex networks

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.