Control Energy of Directed Networks

This work studies the control energy for directed networks which are exactly controllable. By employing Jordan transformation, we derive a simplified formula to calculate the control energy of directed networks. We show that the control energy of directed networks is a decreasing function of the terminal time, indicating that the more time to control, the less energy to cost. Additionally, we investigate the control energy for the Price network model. We show that for Price networks the control energy is a decreasing function of network heterogeneity and an increasing function of network size.