Convergence time of average consensus with heterogeneous random link failures

Abstract

Average consensus algorithms have attracted considerable attention in recent years. Communication impairments make the network suffer from random link failures. In this paper, for networks with heterogeneous random link failures, we investigate the convergence time of the average consensus problem and consider the impacts of event-triggered communication on the consensus performances. We introduce (α,γ)-convergence time to evaluate how fast the algorithm converges in probability γ to the value at most α away from the average. And we derive the dynamical range of the consensus parameter that guarantees the convergence, together with the upper and lower bounds of the closed-form expression for (α,γ)-convergence time. Then, the impact of the event-trigger communication on the convergence accuracy is analyzed, and an upper bound of finite (α,γ)-convergence time is further derived, which can be employed to calculate the triggering parameters with guaranteed convergence time. Finally, extensive simulations are conducted to verify the results.