A PI Consensus Controller for Networked Clocks Synchronization

n this paper we propose a novel distributed clock synchronization protocol for networks of clocks which have different initial offsets and internal clock speeds. The algorithm is based on an PI-like consensus protocol where the proportional (P) part compensates the different clock speeds while the integral part (I) eliminates the different clock offsets. This synchronization protocol is formally studied in its synchronous implementation and we provide both convergence guarantees as well optimal design using standard optimization tools when the underlaying communication graph is known. We also show how this protocol can be readily used to study the effect of noise and external disturbances on the steady-state performance. Finally, some simulations are presented.