A Study on Accelerating Average Consensus Algorithms Using Delayed Feedback
A Study on Accelerating Average Consensus Algorithms Using Delayed Feedback
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DOI：
10.1109/tcns.2022.3188481
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发表时间：
2019-12
影响因子：
4.2
通讯作者：
Hossein Moradian;Solmaz S. Kia
中科院分区：
文献类型：
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作者：
Hossein Moradian;Solmaz S. Kia
本文研究通过将传统的无延迟分歧反馈分解为当前项和过时项的加权求和来加速基于拉普拉斯的动态平均共识算法。在确定加权和时，存在一定范围的时间延迟，这会导致算法具有较高的收敛速度。对于这样的权重，使用Lambert $W$函数，我们获得时间延迟的速率增加范围，获得最大可达速率，并表征相应的最大化延迟的值。我们还研究了使用过时的反馈对智能体控制工作的影响。我们表明，仅对于即时反馈和过时反馈的某些特定仿射组合，代理的控制工作不会超出无延迟算法的控制工作。此外，我们证明使用过时的反馈不会增加平均共识算法的稳态跟踪误差。最后，我们确定当前和过时反馈权重的最佳组合，以在不增加智能体控制工作的情况下实现收敛速度的最大提高。我们通过数值示例展示我们的结果。
This article studies accelerating a Laplacian-based dynamic average consensus algorithm by splitting the conventional delay-free disagreement feedback into a weighted summation of current and outdated terms. When determining the weighted sum, there is a range of time delay that results in a higher convergence rate for the algorithm. For such weights, using the Lambert $W$ function, we obtain the rate-increasing range of the time delay, obtain the maximum reachable rate, and characterize the value of the corresponding maximizer delay. We also study the effect of using the outdated feedback on the control effort of the agents. We show that only for some specific affine combination of the immediate and outdated feedback, the control effort of the agents does not go beyond that of the delay-free algorithm. In addition, we demonstrate that using outdated feedback does not increase the steady-state tracking error of the average consensus algorithm. Finally, we determine the optimum combination of the current and the outdated feedback weights to achieve the maximum increase in the rate of convergence without increasing the control effort of the agents. We demonstrate our results through a numerical example.