Distributed computation of the average of multiple time-varying reference signals

We present a distributed discontinuous control algorithm for a team of agents to track the average of multiple time-varying reference signals with bounded derivatives. We use tools from nonsmooth analysis to analyze the stability of the system. For time-invariant undirected connected network topologies, we prove that the states of all agents will converge to the average of the time-varying reference signals with bounded derivatives in finite time provided that the control gain is properly chosen. The validity of this result is also established for scenarios with switching undirected connected network topologies. For time-invariant directed network topologies with a directed spanning tree, we show that all agents will still reach a consensus in finite time, but the convergent value is generally not the average of the time-varying reference signals with bounded derivatives.