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Sparse System Identification in Pairs of Pulse and Takenaka--Malmquist Bases
SIAM Journal on Control and Optimization ( IF 2.2 ) Pub Date : 2020-03-30 , DOI: 10.1137/18m1217474
Dan Xiong , Li Chai , Jingxin Zhang

SIAM Journal on Control and Optimization, Volume 58, Issue 2, Page 965-985, January 2020.
This paper considers the identification of a rational transfer function with sparse coefficients, under a pair of pulse and Takenaka--Malmquist (TM) bases and from a limited number of linear frequency domain measurements. We propose to concatenate pulse and TM basis functions in the representation of the transfer function, and prove the uniqueness of the sparse representation. We provide the sufficient condition under which the sparse system can be identified by $\ell_1$ optimization from random samples with high probability, and also provide the computation algorithm. Numerical examples show that the concatenated pulse and TM bases give a much sparser representation, with much lower reconstruction order compared to using only pulse basis functions and less dependency on the knowledge of the true system poles compared to using only TM basis functions.


中文翻译:

脉冲和Takenaka-Malmquist基对中的稀疏系统识别

SIAM控制与优化杂志,第58卷,第2期,第965-985页,2020年1月。
本文考虑了在一对脉冲和Takenaka-Malmquist(TM)基准下以及从有限数量的线性频域测量中识别出稀疏系数的有理传递函数。我们建议在传递函数的表示中串联脉冲和TM基函数,并证明稀疏表示的唯一性。我们提供了充分的条件,在该条件下可以通过高概率从随机样本中通过$ \ ell_1 $优化来识别稀疏系统,并提供了计算算法。数值示例表明,级联脉冲和TM基数给出了更稀疏的表示,
更新日期:2020-03-30
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