Average Consensus on Arbitrary Strongly Connected Digraphs with Time-Varying Topologies

TL;DR

This paper extends a surplus-based average consensus algorithm to time-varying strongly connected digraphs, providing a necessary and sufficient condition that is more general than previous results, requiring only joint strong connectivity.

Contribution

It introduces an extended surplus-based algorithm for time-varying topologies and establishes a broad graphical condition for convergence, surpassing previous restrictions like balance or symmetry.

Findings

The algorithm guarantees average consensus under joint strong connectivity.

The graphical condition is necessary and sufficient for convergence.

The approach applies to more general directed networks than prior methods.

Abstract

We have recently proposed a "surplus-based" algorithm which solves the multi-agent average consensus problem on general strongly connected and static digraphs. The essence of that algorithm is to employ an additional variable to keep track of the state changes of each agent, thereby achieving averaging even though the state sum is not preserved. In this note, we extend this approach to the more interesting and challenging case of time-varying topologies: An extended surplus-based averaging algorithm is designed, under which a necessary and sufficient graphical condition is derived that guarantees state averaging. The derived condition requires only that the digraphs be arbitrary strongly connected in a \emph{joint} sense, and does not impose "balanced" or "symmetric" properties on the network topology, which is therefore more general than those previously reported in the literature.