Pinning Control on Directed Complex Network via Identifying Spanning Trees

Abstract

Previous works had proved that a directed complex network could be pinned to its equilibrium by a single controller if it had a spanning tree. But in fact, most of the real networks do not have spanning tree. In this paper, we study the pinning control of a general directed network without spanning tree. We prove that a general network could be divided into some sub-networks with spanning trees, and then the aggregation network is stabilized by stabilizing every sub-network with a single controller. As an illustrative example, a network without spanning tree is simulated to verify the effectiveness and convenience with the selective pinning control strategy.