Dynamic Consensus on the Median Value in Open Multi-Agent Systems

In this paper we consider a dynamic consensus problem in continuous time where the state variables of the agents track with zero error the median value of a set of time-varying reference signals given as input to the agents in a time-varying, undirected network topology. Then, we consider the performance of the protocol in the framework of open multi-agent systems by proposing join and leave mechanisms, i.e., the scenario where agents may join and leave the network during the protocol execution. We characterize the finite-time convergence properties and tracking error of the considered protocol in the case of inputs with bounded variations. One notable feature of consensus on the median value is the robustness of the median, as opposed to the average, with respect to abnormal or outlier values of inputs which represent the outcome of a measurement or estimation process, thus significantly increasing the robustness of the estimation for large scale networks. We use non-smooth Lyapunov theory to provide convergence guarantees and simple tuning rules to adjust the algorithm parameters.