Asymptotic consensus of multi-agent systems under binary-valued observations and observation uncertainty

This paper investigates a multi-agent asymptotic consensus problem with binary-valued observations and observation uncertainty. This uncertainty is described by an additive random noise, whose variance could follow a polynomial-type rate of increase, and even tend to infinity. A stochastic approximation-type asymptotic consensus algorithm is proposed: firstly, to handle simultaneously quantized observation and observation uncertainty, each agent estimates its neighbors' states through an online estimation algorithm; secondly, based on the estimated states of neighbors and its own state, every agent designs its consensus control in real-time. Under suitable conditions, the above estimation algorithm in the mean square sense can ensure that the estimations of unknown neighbors' states converge to the true values. And the states of the agents can achieve an asymptotic consensus effect by this asymptotic consensus algorithm. In addition, to characterize the impact of observation uncertainty on the consensus speed and the convergence speed, two quantitative relationships between observation uncertainty and these two speeds are given, respectively, which have not been considered before. Finally, two simulations are given to verify the above theoretical results.