Data-Driven Sparse System Identification
Data-Driven Sparse System Identification
复制标题
数据驱动的稀疏系统识别
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
S. Sojoudi
中科院分区：
文献类型：
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作者：
S. Fattahi;S. Sojoudi
本文研究稀疏线性定常系统的系统辨识问题。我们提出了一个稀疏性促进拉索型估计，以确定只有有限数量的输入状态数据样本的系统的动态。利用当代高维统计的结果，我们证明了$Omega（k_{max}log（m+n））$数据样本足以可靠地估计系统动态，其中n和m分别是状态和输入的数目，$k_{max}$是输入和状态矩阵行中非零元素的最大数目.在发达国家的估计样本的数量显着小于稀疏系统的问题的维度，但它提供了一个小的估计误差进入明智的。此外，我们表明，与最近著名的最小二乘估计系统识别问题，在这项工作中开发的方法是能够准确恢复的基本稀疏结构的系统与上述数量的数据样本。综合生成的系统和物理质量弹簧网络的广泛的案例研究，证明所提出的方法的有效性。
In this paper, we study the system identification porblem for sparse linear time-invariant systems. We propose a sparsity promoting Lasso-type estimator to identify the dynamics of the system with only a limited number of input-state data samples. Using contemporary results on high-dimensional statistics, we prove that $Omega(k_{max}log(m+n))$ data samples are enough to reliably estimate the system dynamics, where n and m are the number of states and inputs, respectively, and $k_{max}$ is the maximum number of nonzero elements in the rows of input and state matrices. The number of samples in the developed estimator is significantly smaller than the dimension of the problem for sparse systems, and yet it offers a small estimation error entry-wise. Furthermore, we show that, unlike the recently celebrated least-squares estimators for system identification problems, the method developed in this work is capable of exact recovery of the underlying sparsity structure of the system with the aforementioned number of data samples. Extensive case studies on synthetically generated systems and physical mass-spring networks are offered to demonstrate the effectiveness of the proposed method.