Event-triggered control for synchronization of coupled harmonic oscillators

This paper addresses the synchronization problem of coupled harmonic oscillators by event-triggered control. A centralized event-triggered control strategy is first developed and is further extended to a decentralized counterpart, in which the control protocol and event-triggering conditions only require local information. With the event-triggered control strategies, controllers update at the discrete instants when the related measurement errors exceed some proper state-dependent thresholds, which can reduce the computation and transmission costs. By the tools from nonsmooth analysis, it is shown that the proposed event-triggered control strategies synchronize asymptotically all oscillator states. Furthermore, a decentralized event-triggered strategy with a fixed threshold is proposed for the sake of excluding the Zeno behavior. The effectiveness of the proposed strategies is illustrated by numerical simulations.