Average Consensus with Dynamic Quantization Framing and Finite-Time Termination over Limited-Bandwidth Directed Networks

TL;DR

This paper introduces PP-ACDC, a distributed algorithm that achieves exact average consensus over directed networks using limited quantization bits, with finite-time termination and proven convergence.

Contribution

It presents a novel combination of push-pull consensus with dynamic quantization framing, enabling exact consensus with finite communication and termination in directed graphs.

Findings

Achieves asymptotic exact average consensus on strongly connected digraphs.

Provides a finite-time, fully distributed termination mechanism.

Demonstrates reliable consensus with minimal communication in simulations.

Abstract

This paper proposes a deterministic distributed algorithm, referred to as PP-ACDC, that achieves exact average consensus over possibly unbalanced directed graphs using only a fixed and a priori specified number of quantization bits. The method integrates Push-Pull (surplus) consensus dynamics with a dynamic quantization framing scheme combining zooming and midpoint shifting, enabling agents to preserve the true global average while progressively refining their quantization precision. We establish a rigorous convergence theory showing that PP-ACDC achieves asymptotic (exact) average consensus on any strongly connected digraph under appropriately chosen quantization parameters. Moreover, we develop a fully distributed and synchronized finite-time termination mechanism, and we provide a formal proof on the detection of $\epsilon$-convergence to the average within a finite number of iterations. Numerical simulations corroborate the theoretical results and demonstrate that PP-ACDC achieves reliable, communication-efficient, and precise average consensus even under very tight bit budgets, underscoring its suitability for large-scale and resource-constrained multi-agent systems operating over directed networks.