Scalable analysis of linear networked systems via chordal decomposition
Scalable analysis of linear networked systems via chordal decomposition
复制标题
通过弦分解对线性网络系统进行可扩展分析
DOI：
10.23919/ecc.2018.8550409
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
A. Papachristodoulou
中科院分区：
文献类型：
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作者：
Yang Zheng;M. Kamgarpour;Aivar Sootla;A. Papachristodoulou
介绍了线性网络系统可伸缩分析的弦分解方法，包括稳定性、数学上的{H_2}}和数学上的{H_(INFTY)}性能。我们的主要策略是利用这些分析问题中的任何稀疏性并使用弦分解。我们首先证明了Grone和Agler定理可以推广到具有任意划分的分块矩阵。这有助于网络系统分析，允许人们只关注网络系统的物理连接，以利用可伸缩性。然后，通过选择具有适当稀疏模式的Lyapunov函数，我们根据系统图的最大团将所有分析问题中的大的半正定约束分解成多个较小的约束。通过最近的一阶算法，这使得解的计算效率更高。数值实验证明了该方法的有效性和可扩展性。
This paper introduces a chordal decomposition approach for scalable analysis of linear networked systems, including stability, $\mathcal{H_{2}}$ and $\mathcal{H_{\infty}}$ performance. Our main strategy is to exploit any sparsity within these analysis problems and use chordal decomposition. We first show that Grone’s and Agler’s theorems can be generalized to block matrices with any partition. This facilitates networked systems analysis, allowing one to solely focus on the physical connections of networked systems to exploit scalability. Then, by choosing Lyapunov functions with appropriate sparsity patterns, we decompose large positive semidefinite constraints in all of the analysis problems into multiple smaller ones depending on the maximal cliques of the system graph. This makes the solutions more computationally efficient via a recent first-order algorithm. Nu- merical experiments demonstrate the efficiency and scalability of the proposed method.