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Subspace Identi cation using Nuclear Norm Minimization


M. Graf Plessen

Master Thesis, HS 13 (10301)

Subspace identi cation is a method to build discrete-time linear time-invariant state-space models based on measurements of the input and output signals of the underlying dynamic system. The nuclear norm is a convex heuristic for the rank of a matrix. This master thesis presents the algorithmic implementation via the alternating direction method of multipliers (ADMM) of recently developed frequency domain subspace identi cation methods for non-uniformly spaced frequency samples using nuclear norm minimization and Hankel matrix realizations. In addition, theory and the corresponding algorithms are developed for the time domain equivalent. Besides ADMM, the dual accelerated gradient-projection (DAGP) method plays an important role for the solution of nuclear norm minimization problems. Furthermore, for both the frequency and time domain, alternative subspace identi cation methods using nuclear norm minimization are formulated. Some of them are computationally implemented, others are readily described for numerical implementation, and more methods are suggested but are missing one link that potentially prevents an implementation. In a variety of examples, involving arti cially created test systems as well as real-world applications, for both the frequency and time domain, all numerically implemented optimization-based subspace identi cation methods presented in this thesis are compared to existing state-of-the-art software, Matlab's n4sid.


Type of Publication:

(12)Diploma/Master Thesis

T. A. Wood

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2014:IFA_4735
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