On Robustness Analysis of a Dynamic Average Consensus Algorithm to Communication Delay
For researchers in multi-agent systems and distributed control, this work provides a robustness analysis of a specific consensus algorithm to communication delays, but it is incremental as it extends existing results to a particular algorithm and topology class.
This paper characterizes the admissible communication delay range for a dynamic average consensus algorithm over strongly connected and weight-balanced digraphs, showing that within this bound, perfect tracking is achieved for static signals and the discrete-time implementation tolerates at least one step delay on connected undirected graphs.
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.