Distributed Average Consensus with Bounded Quantizer and Unbounded Input

TL;DR

This paper introduces a distributed averaging algorithm using a finite-bit bounded quantizer within the ADMM framework, ensuring convergence or cycling around the average with bounded error, and proposes an adaptive parameter strategy.

Contribution

It develops a novel distributed averaging method with bounded quantization, providing convergence analysis, error bounds, and an adaptive parameter selection strategy.

Findings

Agents converge to a common quantization level or cycle around the average.

Error bounds match those of unbounded rounding quantizers under certain conditions.

Adaptive parameter strategy accelerates convergence with guaranteed accuracy.

Abstract

This paper considers distributed average consensus using finite-bit bounded quantizer with possibly unbounded data. Under the framework of the alternating direction method of multipliers (ADMM), we develop distributed averaging algorithms where each node iteratively updates using only the local information and finitely quantized outputs from its neighbors. It is shown that all the agent variables either converge to the same quantization level or cycle around the data average after finite iterations. An error bound for the consensus value is established, which turns out to be the same as that of using the unbounded rounding quantizer provided that an algorithm parameter (i.e., ADMM step size) is small enough. We also analyze the effect of the algorithm parameter and propose an adaptive parameter selection strategy that only requires knowledge of the number of agents in order to accelerate the algorithm with certain consensus accuracy guarantee. Finally, simulations are performed to illustrate the effectiveness of the proposed algorithms.