Growing Linear Dynamical Networks Endowed by Spectral Systemic Performance Measures
Growing Linear Dynamical Networks Endowed by Spectral Systemic Performance Measures
复制标题
由谱系统性能测量赋予的不断增长的线性动态网络
DOI：
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复制
发表时间：
2018
影响因子：
6.8
通讯作者：
N. Motee
中科院分区：
文献类型：
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作者：
Milad Siami;N. Motee
通过引入系统性能测度的概念，提出了一种公理化的方法来设计和分析噪声线性一致性网络。这类测度是网络的拉普拉斯特征值的谱函数，这些特征值是单调的、凸的，并且相对于网络的拉普拉斯矩阵正交不变。它表明，现有的几个金标准和广泛使用的性能指标在文献中属于这一类新的措施。我们建立在这个新的概念，并通过最小化一个给定的系统性能指标来研究线性共识网络增长的组合问题的一般形式。设计了两种有效的多项式时间近似算法来解决这个网络综合问题：基于线性化的方法和基于秩一更新的简单贪婪算法。几个理论上的基本限制的组合问题的最佳可实现的性能，帮助我们评估我们提出的算法的最优性差距。详细的复杂性分析证实了我们的算法处理大规模共识网络的有效性和可行性。
We propose an axiomatic approach for design and performance analysis of noisy linear consensus networks by introducing a notion of systemic performance measure. This class of measures are spectral functions of Laplacian eigenvalues of the network that are monotone, convex, and orthogonally invariant with respect to the Laplacian matrix of the network. It is shown that several existing gold-standard and widely used performance measures in the literature belong to this new class of measures. We build upon this new notion and investigate a general form of the combinatorial problem of growing a linear consensus network via minimizing a given systemic performance measure. Two efficient polynomial-time approximation algorithms are devised to tackle this network synthesis problem: a linearization-based method and a simple greedy algorithm based on rank-one updates. Several theoretical fundamental limits on the best achievable performance for the combinatorial problem are derived that assist us to evaluate optimality gaps of our proposed algorithms. A detailed complexity analysis confirms the effectiveness and viability of our algorithms to handle large-scale consensus networks.