Dealing with uncertainty in consensus protocols

Recent results on consensus protocols for networks are presented. The basic tools and the main contribution available in the literature are considered, together with some of the related challenging aspects: estimation in networks and how to deal with disturbances is considered. Motivated by applications to sensor, peer-to-peer, and ad hoc networks, many papers have considered the problem of estimation in a consensus fashion. Here, the Unknown But Bounded (UBB) noise affecting the network is addressed in details. Because of the presence of UBB disturbances convergence to equilibria with all equal components is, in general, not possible. The solution of the ε-consensus problem, where the states converge in a tube of ray ε asymptotically or in finite time, is described. In solving the ε-consensus problem a focus on linear protocols and a rule for estimating the average from a compact set of candidate points, the lazy rule, is shown.