Average Consensus on General Strongly Connected Digraphs
This work solves a fundamental problem for multi-agent systems operating under general directed communication topologies, removing the restrictive balanced-graph assumption.
The paper addresses the average consensus problem in multi-agent systems with unidirectional communication, proposing deterministic and gossip algorithms that guarantee state averaging on arbitrary strongly connected digraphs without requiring balanced or symmetric networks, extending previous results.
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.