This paper proposes a class of distributed event-triggered algorithms that solve the average consensus problem in multi-agent systems. By designing events such that a specifically chosen Lyapunov function is monotonically decreasing, event-triggered algorithms succeed in reducing communications among agents while still ensuring that the entire system converges to the desired state. However, depending on the chosen Lyapunov function the transient behaviours can be very different. Moreover, performance requirements also vary from application to application. Consequently, we are instead interested in considering a class of Lyapunov functions such that each Lyapunov function produces a different event-triggered coordination algorithm to solve the multi-agent average consensus problem. The proposed class of algorithms all guarantee exponential convergence of the resulting system and exclusion of Zeno behaviours. This allows us to easily implement different algorithms that all guarantee correctness to meet varying performance needs. We show that our findings can be applied to the practical clock synchronisation problem in wireless sensor networks (WSNs) and further corroborate their effectiveness with simulation results.

本文提出了一类分布式事件触发算法，用于解决多智能体系统中的平均共识问题。通过设计事件以使特定选择的 Lyapunov 函数单调递减，事件触发算法成功地减少了代理之间的通信，同时仍确保整个系统收敛到所需状态。然而，根据所选择的 Lyapunov 函数，瞬态行为可能会有很大不同。此外，性能要求也因应用程序而异。因此，我们感兴趣的是考虑一类 Lyapunov 函数，这样每个 Lyapunov 函数都会产生不同的事件触发协调算法来解决多智能体平均共识问题。所提出的算法类都保证了结果系统的指数收敛并排除了 Zeno 行为。这使我们能够轻松实现不同的算法，这些算法都可以保证正确性以满足不同的性能需求。我们表明，我们的研究结果可以应用于无线传感器网络 (WSN) 中的实际时钟同步问题，并通过仿真结果进一步证实了它们的有效性。