Initialization-free Algorithm for Discrete-time Dynamic Average Consensus and Its Application to Distributed Optimization

In this paper, we address the problem of dynamic average consensus in a discrete-time setting. The objective of dynamic average consensus problem is for each state of agent to track the average of reference input signals of each agent in a distributed manner. Without initialization process, the proposed algorithm renders the state of each agent converge practically to the average of time-varying reference signals with any given bound. It is a simple time-domain algorithm based on two-time scale. Finally, by applying our algorithm to an distributed optimization problem, we provide two simulation results that converge correctly when the initial conditions are perturbed and that converge within certain amount of small error when numerical errors are injected every time step.