Distributed stochastic consensus of multi-agent systems with noisy and delayed measurements

Networked systems are often subject to environmental uncertainties and communication delays, which make timely and accurate information exchange among neighbours difficult or impossible. This study investigates the distributed consensus problem of dynamical networks of multi-agents in which each agent can only obtain noisy and delayed measurements of the states of its neighbours. The authors consider consensus protocols that take into account both the noisy measurements and the communication time delays, and introduce the notions of almost sure average-consensus and pth moment average-consensus. Using a convergence theorem for continuous-time semimartingales and moment inequality techniques for stochastic delay differential equations, the authors establish sufficient conditions for both almost sure and moment average-consensus. These results naturally generalise to networks with arbitrary and Markovian switching topologies. The consensus protocol considered here can be applied to networks with arbitrary bounded communication delays, which appears to the first consensus algorithm that is both average preserving and robust to arbitrarily sized delays. Numerical simulations are also provided to demonstrate the theoretical results.