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arXiv 1111.4825eess.SYcs.DCcs.MAcs.SY
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切比雪夫多项式在分布式共识中的应用

Chebyshev Polynomials in Distributed Consensus Applications

Universidad de Zaragoza(萨拉戈萨大学)

Eduardo Montijano, Juan I. Montijano, Carlos Sagues

AI总结:

本文利用切比雪夫多项式的性质提出一种基于线性迭代的分布式共识算法,通过二阶差分方程更新规则,显著减少迭代次数,适用于固定和切换通信拓扑,提高了收敛速度。

摘要:

本文分析了切比雪夫多项式在分布式共识中的应用。我们研究了这些多项式的性质,提出了一种快速达成共识的分布式算法。该算法以线性迭代形式表达,每一步中,智能体只需向邻居传输当前状态。与先前方法的不同之处在于,网络使用的更新规则基于描述第一类切比雪夫多项式的二阶差分方程。因此,我们证明我们的算法使用远少于其他方法的迭代次数达成共识。我们表征了该算法在固定和切换通信拓扑下的主要性质。本文的主要贡献是研究了切比雪夫多项式在分布式共识应用中的性质,提出了一种相对于现有方法提高收敛速度的算法。理论结果以及合成数据实验都显示了使用我们算法的优势。

英文摘要:

In this paper we analyze the use of Chebyshev polynomials in distributed consensus applications. We study the properties of these polynomials to propose a distributed algorithm that reaches the consensus in a fast way. The algorithm is expressed in the form of a linear iteration and, at each step, the agents only require to transmit their current state to their neighbors. The difference with respect to previous approaches is that the update rule used by the network is based on the second order difference equation that describes the Chebyshev polynomials of first kind. As a consequence, we show that our algorithm achieves the consensus using far less iterations than other approaches. We characterize the main properties of the algorithm for both, fixed and switching communication topologies. The main contribution of the paper is the study of the properties of the Chebyshev polynomials in distributed consensus applications, proposing an algorithm that increases the convergence rate with respect to existing approaches. Theoretical results, as well as experiments with synthetic data, show the benefits using our algorithm.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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