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Nuclear norm subspace identification (N2SID) for short data batches
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
2014 (English)In: Proceedings of IFAC 2014 World Congress, Cape Town, 2014, 9528-9533 p.Conference paper (Refereed)
Abstract [en]

Subspace identification is revisited in the scope of nuclear norm minimization methods. It is shown that essential structural knowledge about the unknown data matrices in the data equation that relates Hankel matrices constructed from input and output data can be used in the first step of the numerical solution presented. The structural knowledge comprises the low rank property of a matrix that is the product of the extended observability matrix and the state sequence and the Toeplitz structure of the matrix of Markov parameters (of the system in innovation form). The new subspace identification method is referred to as the N2SID (twice the N of Nuclear Norm and SID for Subspace IDentification) method. In addition to include key structural knowledge in the solution it integrates the subspace calculation with minimization of a classical prediction error cost function. The nuclear norm relaxation enables us to perform such integration while preserving convexity. The advantages of N2SID are demonstrated in a numerical open- and closed-loop simulation study. Here a comparison is made with another widely used SID method, i.e. N4SID. The comparison focusses on the identification with short data batches, i.e. where the number of measurements is a small multiple of the system order.

Place, publisher, year, edition, pages
Cape Town, 2014. 9528-9533 p.
Keyword [en]
Subspace system identification, Nuclear norm optimization, Rank constraint, Short
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-129293DOI: 10.3182/20140824-6-ZA-1003.00386OAI: oai:DiVA.org:liu-129293DiVA: diva2:937579
Conference
Preprints of the 19th World Congress The International Federation of Automatic Control. Cape Town, South Africa. August 24-29, 2014
Available from: 2016-06-15 Created: 2016-06-15 Last updated: 2016-06-29

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Verhaegen, MichelHansson, Anders
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Automatic ControlFaculty of Science & Engineering
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ReferencesLink to record
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