A Sensitivity Minimization Approach to the Distributed Average Tracking Problem

Abstract

This paper intends to present a novel sensitivity minimization perspective to the distributed average tracking (also called dynamic average consensus) problem, where the agents are expected to track the average of a set of reference signals. For the classic proportional-integral (PI) average tracking algorithm, we define a new network sensitivity function, which captures the evolution of the tracking error with respect to the reference signals. We show how to choose the parameters of the PI algorithm to minimize the H ∞ norm of the network sensitivity function, implying that the upper bound of the tracking error is minimized in the H ∞ norm sense for all reference signals of bounded power. Considering that the reference signals are generally of low frequency, we further study the weighted H ∞ optimization problem of the network sensitivity function and give conditions under which the PI algorithm will have a better tracking performance for low-frequency reference signals. Finally, simulation examples are presented to illustrate the effectiveness of the results.