Distributed synchronization of noisy non-identical double integrators

In this paper we present a novel synchronization protocol to synchronize a network of controlled discrete-time double integrators which are non-identical, with unknown model parameters and subject to additive measurement and process noise. This framework is motivated by the typical problem of synchronizing a network of clocks whose speeds are non-identical and are subject to variations. This synchronization protocol is formally studied in its synchronous implementation. In particular, we provide a completely distributed strategy that guarantees convergence for any undirected connected communication graph, and we also propose an optimal convex design strategy when the underlaying communication graph is known. Moreover, this protocol can be readily used to study the effect of noise and external disturbances on the steady-state performance. Finally, some simulations including also asynchronous implementation of the proposed algorithm are presented.