Realizing actual feedback control of complex network

In this paper, we present the concept of feedbackability and how to identify the Minimum Feedbackability Set of an arbitrary complex directed network. Furthermore, we design an estimator and a feedback controller accessing one MFS to realize actual feedback control, i.e. control the system to our desired state according to the estimated system internal state from the output of estimator. Last but not least, we perform numerical simulations of a small linear time-invariant dynamics network and a real simple food network to verify the theoretical results. The framework presented here could make an arbitrary complex directed network realize actual feedback control and deepen our understanding of complex systems.