Structural controllability and time-to-control of directed scale-free networks with minimum number of driver nodes

Abstract

In this paper we study structural controllability and time-to-control of directed scale-free networks, and propose algorithms to guarantee these properties with the minimum number of driver nodes. Structural controllability is a qualitative (i.e. topological) measure of the ability to steer the network to a desired state from an arbitrary initial state; while time-to-control measures how fast the above steering can be done. First, we develop an algorithm that generates directed scale-free networks which are provably structurally controllable with only one driver node. Moreover, considering the tradeoff between control cost (number of driver nodes) and control performance (time-to-control), we propose another algorithm that constructs directed scale-free networks which can be steered to a desired state within a prescribed time bound and with the minimum number of driver nodes.