A Randomized Linear Algorithm for Clock Synchronization in Multi-Agent Systems

A broad family of randomized clock synchronization protocols based on a second order consensus algorithm is proposed. Under mild conditions on the graph connectivity, it is proved that the parameters of the algorithm can always be tuned in such a way that the clock synchronization is achieved in the probabilistic mean-square sense. This family of algorithms contains, as particular cases, several known approaches which range from distributed asynchronous to hierarchical synchronous protocols. This is illustrated by specializing the algorithm for the well-known broadcast and gossip scenarios in wireless communications, and for the standard hierarchical protocol used in the context of wired communications in data networks. In these cases, we show how the feasible range for the algorithm parameters can be explicitly computed. Finally, the performance of this strategy is validated by actual implementation in a real testbed and by numerical simulations.