Pinning Controllability of Complex Network Systems with Noise

The ability of a network of nonlinear systems to synchronize onto the desired reference trajectory in the presence of one or more leader nodes is known as the pinning controllability problem. This paper studies the pinning controllability of multiagent networks subject to three different types of noise diffusion processes; namely, noise affecting the node dynamics, the communication links, and the pinning control action itself. Sufficient pinning controllability conditions are derived depending on the node dynamics, network structure, noise intensity, and control parameters. Counterintuitively, it is found that under some specific conditions noise may enhance the pinning controllability of the network making it easier to drive all agents toward the desired collective behavior. The effectiveness of the theoretical results is illustrated via two application examples arising in the context of gene regulatory networks and synchronization of chaotic systems.