Pulse-Coupled Synchronization With Guaranteed Clock Continuity

Clock synchronization is a widely discussed topic in the engineering literature. Ensuring that individual clocks are closely aligned is important in network systems, since the correct timing of various events in a network is usually necessary for proper system implementation. However, many existing clock synchronization algorithms update clock values abruptly and instantaneously, resulting in discontinuous clocks, which have been shown to lead to undesirable behavior. In this paper, we explore the generalization of the pulse-coupled oscillator model to guarantee clock continuity, achieving continuous phase evolution in any pulse-coupled oscillator network. We provide rigorous mathematical proof for pulse-coupled synchronization under the proposed phase continuity methods, along with analysis of the time to synchronization under phase continuity. Two simple methods to achieve the desired continuity are presented. We further provide simulation and experimental results supporting these proofs, analyzing the effects of the phase continuity methods to convergence. We also investigate the convergence behavior of other pulse-coupled oscillator synchronization algorithms using the proposed methods.