Spatial Pinning Control

In this Letter, we introduce the concept of spatial pinning control for a network of mobile chaotic agents. In a planar space, N agents move as random walkers and interact according to a time-varying r-disk proximity graph. A control input is applied only to those agents which enter a given area, called control region. The control is effective in driving all the agents to a reference evolution and has better performance than pinning control on a fixed set of agents. We derive analytical conditions on the relative size of the control region and the agent density for the global convergence of the system to the reference evolution and study the system under different regimes inherited by the velocity.