This paper addresses an event-triggered distributed convex optimisation problem over networks with time-varying delays. The communication between agents is triggered by conditions monitored by nodes. The proposed triggering condition is decentralised and does not require continuous communications among agents to calculate the threshold. By constructing a new Lyapunov–Krasovskii function, the optimisation problem is solved, and the explicit sufficient condition for the maximum admissible time delay is derived. Moreover, the Zeno behaviour of the closed-loop system is excluded. Finally, a simulation example is provided to verify the results obtained in this paper.

中文翻译：

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具有时变通信延迟的事件触发零梯度和分布式优化算法

本文解决了具有时变延迟的网络上的事件触发分布式凸优化问题。代理之间的通信由节点监控的条件触发。提议的触发条件是分散的，不需要代理之间的持续通信来计算阈值。通过构造一个新的Lyapunov-Krasovskii函数，求解了优化问题，并推导出了最大容许时滞的显式充分条件。此外，闭环系统的芝诺行为被排除在外。最后，提供了一个仿真实例来验证本文获得的结果。