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Algorithms for deterministic balanced subspace identification

Algorithms for deterministic balanced subspace identification
Algorithms for deterministic balanced subspace identification
New algorithms for identification of a balanced state space representation are proposed. They are based on a procedure for the estimation of impulse response and sequential zero input responses directly from data. The proposed algorithms are more efficient than the existing alternatives that compute the whole Hankel matrix of Markov parameters. It is shown that the computations can be performed on Hankel matrices of the input–output data of various dimensions. By choosing wider matrices, we need persistency of excitation of smaller order. Moreover, this leads to computational savings and improved statistical accuracy when the data is noisy. Using a finite amount of input–output data, the existing algorithms compute finite time balanced representation and the identified models have a lower bound on the distance to an exact balanced representation. The proposed algorithm can approximate arbitrarily closely an exact balanced representation. Moreover, the finite time balancing parameter can be selected automatically by monitoring the decay of the impulse response. We show what is the optimal in terms of minimal identifiability condition partition of the data into “past” and “future”.
Exact deterministic subspace identification, Balanced model reduction, Approximate system identification, MPUM
0005-1098
755-766
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
Willems, Jan C.
3a5841a4-3cdb-4d99-8cb8-dd02ca641e87
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
de Moor, Bart L.M.
6aba7d23-1605-4d40-b3bd-a5374c813f44
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
Willems, Jan C.
3a5841a4-3cdb-4d99-8cb8-dd02ca641e87
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
de Moor, Bart L.M.
6aba7d23-1605-4d40-b3bd-a5374c813f44

Markovsky, Ivan, Willems, Jan C., Rapisarda, Paolo and de Moor, Bart L.M. (2005) Algorithms for deterministic balanced subspace identification. Automatica, 41, 755-766.

Record type: Article

Abstract

New algorithms for identification of a balanced state space representation are proposed. They are based on a procedure for the estimation of impulse response and sequential zero input responses directly from data. The proposed algorithms are more efficient than the existing alternatives that compute the whole Hankel matrix of Markov parameters. It is shown that the computations can be performed on Hankel matrices of the input–output data of various dimensions. By choosing wider matrices, we need persistency of excitation of smaller order. Moreover, this leads to computational savings and improved statistical accuracy when the data is noisy. Using a finite amount of input–output data, the existing algorithms compute finite time balanced representation and the identified models have a lower bound on the distance to an exact balanced representation. The proposed algorithm can approximate arbitrarily closely an exact balanced representation. Moreover, the finite time balancing parameter can be selected automatically by monitoring the decay of the impulse response. We show what is the optimal in terms of minimal identifiability condition partition of the data into “past” and “future”.

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Published date: 2005
Keywords: Exact deterministic subspace identification, Balanced model reduction, Approximate system identification, MPUM
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 262202
URI: https://eprints.soton.ac.uk/id/eprint/262202
ISSN: 0005-1098
PURE UUID: abbdbf16-ef0a-4b8c-83d7-fe3e2064e736

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Date deposited: 29 Mar 2006
Last modified: 19 Jul 2019 22:32

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