A Branch and Bound Approach to System Identification based on Fixed-rank Hankel Matrix Optimization

We consider identification of linear systems with a certain order from a set of noisy input-output observations. We utilize the fact that the system order corresponds to the rank of the Hankel matrix associated with the system impulse response. Then, the system identification problem is formulated a...

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Bibliographic Details
Published inIFAC-PapersOnLine Vol. 51; no. 15; pp. 96 - 101
Main Authors Sadeghi, Mostafa, Rojas, Cristian R., Wahlberg, Bo
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 2018
Subjects
bound method
branch
Hankel matrix
rank minimization
System identification
Hankel matrix
rank minimization
System identification
branch
bound method
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Summary:We consider identification of linear systems with a certain order from a set of noisy input-output observations. We utilize the fact that the system order corresponds to the rank of the Hankel matrix associated with the system impulse response. Then, the system identification problem is formulated as the minimization of the output error subject to a rank constraint on a Hankel matrix. As this problem is non-convex, we propose a branch and bound (BB) solver, which is a powerful tool for solving non-convex problems to optimality. The main ingredients of the proposed BB method are a convex relaxation problem and a local minimizer of the original non-convex problem. We illustrate the promising performance of the proposed scheme in a system identification problem. The results demonstrate the higher accuracy and stability of our method in estimating the true system compared to the standard output error (OE) algorithm.
ISSN:2405-8963
2405-8971
2405-8963
DOI:10.1016/j.ifacol.2018.09.097