Consensus on the average in arbitrary directed network topologies with time-delays
This addresses the challenge of maintaining consensus in networked systems with delays, but it appears incremental as it builds on existing consensus algorithms with a focus on directed topologies.
The paper tackles the problem of achieving consensus on the average in arbitrary directed networks with time-delays by proposing an algorithm that adds a storage variable to preserve average information, proving stability for sufficiently small delays and providing simulations to estimate maximum allowable delays.
In this preliminary paper we study the stability property of a consensus on the average algorithm in arbitrary directed graphs with respect to communication/sensing time-delays. The proposed algorithm adds a storage variable to the agents' states so that the information about the average of the states is preserved despite the algorithm iterations are performed in an arbitrary strongly connected directed graph. We prove that for any network topology and choice of design parameters the consensus on the average algorithm is stable for sufficiently small delays. We provide simulations and numerical results to estimate the maximum delay allowed by an arbitrary unbalanced directed network topology.