Stochastic consensus seeking with communication delays

This paper investigates the consensus problem of dynamical networks of multi-agents where each agent can only obtain noisy and delayed measurements of the states of its neighbors due to environmental uncertainties and communication delays. We consider general networks with fixed topology and with switching (dynamically changing) topology, propose consensus protocols that take into account both the noisy measurements and the communication time-delays, and study mean square average-consensus for multi-agent systems networked in an uncertain environment and with uniform communication time-varying delays. Using tools from differential equations and stochastic calculus, together with results from matrix theory and algebraic graph theory, we establish sufficient conditions under which the proposed consensus protocols lead to mean square average-consensus. Simulations are also provided to demonstrate the theoretical results.