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Basis pursuit for frequency‐domain identification
Author(s) -
Mi Wen,
Qian Tao,
Li Shuang
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3498
Subject(s) - basis pursuit , mathematics , basis (linear algebra) , domain (mathematical analysis) , frequency domain , stability (learning theory) , identification (biology) , matrix (chemical analysis) , algorithm , system identification , computer science , matching pursuit , compressed sensing , machine learning , data mining , mathematical analysis , botany , geometry , materials science , composite material , biology , measure (data warehouse)
W. Sprößig In this paper, we propose a new adaptive method for frequency‐domain identification problem of discrete LTI systems. It is based on a dictionary that is consisting of normalized reproducing kernels. We prove that the singular values of the matrix generated by this dictionary converge to zero rapidly; this makes it quite efficient in representing the original systems with only a few elements. For different systems, it results in different selected sequences from the dictionary, that is, its adaptivity. Meanwhile, the stability of results is automatically guaranteed according to the structure of the dictionary. Two examples are presented to illustrate the idea. Copyright © 2016 John Wiley & Sons, Ltd.