On Robustness Analysis of a Dynamic Average Consensus Algorithm to Communication Delay

TL;DR

This paper analyzes how communication delays affect the robustness of a dynamic average consensus algorithm on directed graphs, providing delay bounds and convergence guarantees for both continuous and discrete implementations.

Contribution

It characterizes admissible communication delay ranges and their impact on convergence and tracking error, linking delay bounds to graph degrees and topology.

Findings

Admissible delay bounds depend on graph degree and structure.

For static signals, perfect tracking is achieved within delay bounds.

Discrete-time algorithms tolerate at least one step delay on undirected graphs.

Abstract

This paper studies the robustness of a dynamic average consensus algorithm to communication delay over strongly connected and weight-balanced (SCWB) digraphs. Under delay-free communication, the algorithm of interest achieves a practical asymptotic tracking of the dynamic average of the time-varying agents' reference signals. For this algorithm, in both its continuous-time and discrete-time implementations, we characterize the admissible communication delay range and study the effect of the delay on the rate of convergence and the tracking error bound. Our study also includes establishing a relationship between the admissible delay bound and the maximum degree of the SCWB digraphs. We also show that for delays in the admissible bound, for static signals the algorithms achieve perfect tracking. Moreover, when the interaction topology is a connected undirected graph, we show that the discrete-time implementation is guaranteed to tolerate at least one step delay. Simulations demonstrate our results.