On the benefits of saturating information in consensus networks with noise

In a consensus network subject to non-zero mean noise, the system state may be driven away even when the disagreement exhibits a bounded response. This is unfavourable in applications since the nodes may not work properly and even be faulty outside their operating region. In this paper, we propose a new control algorithm to mitigate this issue by assigning each node a favourite interval that characterizes the nodes desired convergence region. The algorithm is implemented in a self-triggered fashion. If the nodes do not share a global clock, the network operates in a fully asynchronous mode. By this algorithm, we show that the state evolution is confined around the favourite interval and the node disagreement is bounded by a simple linear function of the noise magnitude, without requiring any priori information on the noise. We also show that if the nodes share some global information, then the algorithm can be adjusted to make the nodes evolve into the favourite interval, improve on the disagreement bound and achieve asymptotic consensus in the noiseless case.