Multi-stage discrete time dynamic average consensus

In this paper we propose a novel local interaction protocol which solves the discrete time dynamic average consensus problem, i.e., the consensus problem on the average value of a set of time-varying input signals in an undirected graph. The proposed interaction protocol is based on a multi-stage cascade of consensus filters which tracks the average value of the inputs with small error. We characterize how the number of stages influences the steady state error. The main novelty of the proposed algorithm is that, with respect to other dynamic average consensus protocols, we do not exploit the k-th order derivatives of the inputs nor we require that the average of the network state is preserved to achieve convergence to the desired quantity, thus increasing the robustness of the method in several practical scenarios. In addition, the proposed design allows to trade-off convergence time with steady-state error by choosing a proper number of stages in the cascade. Finally, we provide a preliminary asynchronous and randomized version of the proposed protocol along with numerical examples to corroborate the theoretical findings.