The relation between communication range and controllability of networked multi-agent systems

Recently, significant attention has been paid to the controllability problem of networked systems. In many real-world multi-agent systems, agents are spatially located in arbitrary positions and can only communicate with nearby agents. A natural problem of designing such a system is how to determine the necessary communication radius that ensures a certain degree of controllability. Taking advantage of the recent findings on network controllability, we obtain theoretical results that aid in choosing such a radius. We find that the critical communication radius, with which one can use only a negligible number of driver nodes to control the whole system, is proportional to the inverse of the square root of node density. Finally, we present how our conclusions apply to systems of different scales, ranging from very-large scale systems that have nearly infinite nodes to ones with only a limited number of nodes. The probability for the calculated critical communication radius to have a certain error is shown to be bounded.