Adaptive consensus and algebraic connectivity estimation in sensor networks with chebyshev polynomials
Adaptive consensus and algebraic connectivity estimation in sensor networks with chebyshev polynomials
复制标题
具有切比雪夫多项式的传感器网络中的自适应一致性和代数连通性估计
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
C. Sagüés
中科院分区：
文献类型：
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作者：
E. Montijano;J. I. Montijano;C. Sagüés
在最近几年中，大量的努力一直致力于寻找分布式算法，实现快速共识的问题。多项式的分布式求值在保持标准方法良好性质的基础上，提高了收敛速度。使用多项式的缺点是，它们通常需要一些关于网络的知识，以便具有良好的收敛特性。本文考虑了基于Chebyshev多项式的一致性方法，并给出了一个算法，以分布式的方式计算使该方法获得最优收敛速度的参数。其中一个参数与权重矩阵的第二大特征值一致，即，的代数连通性，我们证明了算法的收敛性。我们还提出了三种变体的算法收敛到这个参数，以更快的方式，并考虑在通信拓扑结构的变化。我们评估我们的算法在一个模拟的环境中显示其性能在广泛的网络。
In the recent years a lot of effort has been devoted to the problem of finding distributed algorithms that achieve a fast consensus. The distributed evaluation of polynomials improves the convergence speed to the consensus keeping the good properties of standard methods. The drawback about using polynomials is that they usually require some knowledge about the network in order to have good convergence properties. In this paper we consider the consensus method using Chebyshev polynomials and present an algorithm to compute, in a distributed way, the parameters that make the method get the optimal convergence rate. One of the parameters coincides with the second largest eigenvalue of the weight matrix, i.e., the algebraic connectivity, and we prove the convergence of the algorithm to it. We also present three variants of the algorithm to converge to this parameter in a faster way and to consider changes in the communication topology. We evaluate our algorithm in a simulated environment showing its performance in a wide set of networks.