  This paper studies the distributed average tracking problem pertaining to a
discrete-time linear time-invariant multi-agent network, which is subject to,
concurrently, input delays, random packet-drops, and reference noise. The
problem amounts to an integrated design of delay and packet-drop tolerant
algorithm and determining the ultimate upper bound of the tracking error
between agents' states and the average of the reference signals. The
investigation is driven by the goal of devising a practically more attainable
average tracking algorithm, thereby extending the existing work in the
literature which largely ignored the aforementioned uncertainties. For this
purpose, a blend of techniques from Kalman filtering, multi-stage consensus
filtering, and predictive control is employed, which gives rise to a simple yet
comepelling distributed average tracking algorithm that is robust to
initialization error and allows the trade-off between communication/computation
cost and stationary-state tracking error. Due to the inherent coupling among
different control components, convergence analysis is significantly
challenging. Nevertheless, it is revealed that the allowable values of the
algorithm parameters rely upon the maximal degree of an expected network, while
the convergence speed depends upon the second smallest eigenvalue of the same
network's topology. The effectiveness of the theoretical results is verified by
a numerical example.
