Emergence of Power Laws in Networked Control Systems

In this paper we study multiple systems connected over an unreliable communication network. The links in the networks are modeled as drop-out channels. We consider the closed loop mean square stability of multi agent systems formations, and use our analysis result to evaluate the fragility of the networked system to packet losses or link drop-outs. We present a case where the packet drops can lead to loss of mean square stability. Systems that are not mean square stable have heavy tail distributions of their states. Simulations show the power law nature of such distributions. While having identical agents may lead to a simplified nominal stability analysis and to scalable solutions, it does not seem to reduce the complexity of the mean square stability analysis. We show that fading networks, which are spatially invariant in the mean, do not suffer from this limitation and allow for the maximal tolerable uncertainty to be distributed arbitrarily among the links