标题： 关于传输延迟下的双速率一致性问题 显示英文标题

标题： On dual-rate consensus under transmission delays

摘要： 本文研究了存在传输延迟情况下的双速率一致性问题，其中控制更新以比接收测量值更快的速率发生。 我们假设测量值存在固定延迟，并证明对于所有延迟和速率，系统达到一致性的充要条件是代理通信图连通且控制增益被选择在一个特定区间内。 基于这些结果，我们进一步深入研究收敛特性，并探讨当改变发送测量值的速率时收敛如何变化。 我们观察到，在某些情况下，存在一个最佳点来选择测量值的采样率，这可以提高向一致性点的收敛速度。 然后我们构建了一个优化问题，以找到改进收敛速度的采样率，并提供了该问题有限最优解存在的充要条件。 我们的结果通过数值模拟得到了验证。 显示英文摘要

摘要： In this paper, we investigate the problem of dual-rate consensus under transmission delays, where the control updates happen at a faster rate than the measurements being received. We assume that the measurements are delayed by a fixed delay and show that for all delays and rates, the system reaches a consensus if and only if the communication graph of the agents is connected and the control gain is chosen in a specific interval. Based on these results we dive deeper into the convergence properties and investigate how the convergence changes when we change the rate for sending measurements. We observe that in certain cases there exists a sweet spot for choosing the sampling rate of the measurements, which can improve the convergence to the consensus point. We then formulate an optimization problem to find a sampling rate to improve the convergence speed and provide a necessary and sufficient condition for the existence of a finite optimizer of this problem. Our results are verified with numerical simulations.