Spatial pinning control of Vicsek's Agents

In this work we study a system of mobile agents that move in an anisotropic space and interact according to the Vicsek model. In particular, the space is divided in two regions: in the first one, agents obey to the traditional Vicsek model, while in the second one, called control region, a motion control law is added. The control law forces the pinned agents, that are the agents moving in the control region, to follow a criterion mediating between the tendency to adopt the average direction of neighboring agents, and that to follow an imposed preferential direction. We show that, for low and medium levels of noise in the system, the control law is effective to drive the system towards a global ordered state, while, for high levels of noise, a strong control action leads to a configuration, for some aspects paradoxical, where all the agents tend to avoid the control region and occupy for most of the time the remaining part of the space.