Average Consensus on General Strongly Connected Digraphs

TL;DR

This paper introduces two distributed algorithms for average consensus in multi-agent systems over strongly connected directed graphs, extending previous results by removing the need for balanced or symmetric networks, and employs surplus variables for convergence.

Contribution

The paper presents novel linear algorithms for average consensus on arbitrary strongly connected digraphs, without requiring balanced or symmetric network conditions.

Findings

Guarantee state averaging on arbitrary strongly connected digraphs.

Algorithms work for both synchronous and asynchronous communication.

Use of surplus variables enables convergence analysis.

Abstract

We study the average consensus problem of multi-agent systems for general network topologies with unidirectional information flow. We propose two (linear) distributed algorithms, deterministic and gossip, respectively for the cases where the inter-agent communication is synchronous and asynchronous. Our contribution is that in both cases, the developed algorithms guarantee state averaging on arbitrary strongly connected digraphs; in particular, this graphical condition does not require that the network be balanced or symmetric, thereby extending many previous results in the literature. The key novelty of our approach is to augment an additional variable for each agent, called "surplus", whose function is to locally record individual state updates. For convergence analysis, we employ graph-theoretic and nonnegative matrix tools, with the eigenvalue perturbation theory playing a crucial role.