Optimal Memory Scheme for Accelerated Consensus Over Multi-Agent Networks

TL;DR

This paper investigates optimal memory schemes to accelerate consensus in multi-agent networks, showing that simple memory strategies are often sufficient, with some complex schemes only beneficial in specific network topologies.

Contribution

It introduces a general memory protocol, proves the sufficiency of one-tap node memory for optimal convergence, and identifies scenarios where additional memory improves performance.

Findings

One-tap node memory suffices for optimal convergence.

State deviation memory is unnecessary for the best results.

Two-tap state deviation memory benefits star networks.

Abstract

The consensus over multi-agent networks can be accelerated by introducing agent's memory to the control protocol. In this paper, a more general protocol with the node memory and the state deviation memory is designed. We aim to provide the optimal memory scheme to accelerate consensus. The contributions of this paper are three: (i) For the one-tap memory scheme, we demonstrate that the state deviation memory is useless for the optimal convergence. (ii) In the worst case, we prove that it is a vain to add any tap of the state deviation memory, and the one-tap node memory is sufficient to achieve the optimal convergence. (iii) We show that the two-tap state deviation memory is effective on some special networks, such as star networks. Numerical examples are listed to illustrate the validity and correctness of the obtained results.