Node-to-node pinning control of complex networks

In this paper, we study pinning controllability of oscillator networks. We present necessary conditions for network pinning controllability based on the spectral properties of the oscillator network and the individual oscillator dynamics. We define a performance metric for pinning-control systems based on the location of pinned sites, the pinning-control gains, and the network topology. We show that for any network structure, uniform pinning of all the network nodes maximizes the pinning-control performance. We propose the node-to-node pinning-control strategy to optimize the control performance while avoiding to simultaneously control all the network sites. In this novel strategy, the pinning-control action rapidly switches from one node to another with the goal of taming the oscillator network dynamics to the desired trajectory. We illustrate our findings through numerical simulations on networks of Rossler oscillators.