A subspace algorithm for balanced state space system identification

Moonen, Marc; Ramos, José A.

doi:10.1109/9.262050

Cited by 32 publications

(22 citation statements)

References 11 publications

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“…It turns out that this task is greatly simplified if the local models are converted to a suitable balanced form. In order to clarify this point, the main properties of internally balanced realisations have to be briefly summarised ( [21], [22]). …”

Section: B Balancing Of the Identified Modelsmentioning

confidence: 99%

Identification for gain-scheduling: a balanced subspace approach

Lovera

Mercère

2007

2007 American Control Conference

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Abstract-The problem of deriving MIMO parameterdependent models for gain-scheduling control design from data generated by local identification experiments is considered and a numerically sound approach is proposed, based on subspace identification ideas combined with the use of suitable properties of balanced state space realisations. Simulation examples are used to demonstrate the performance of the proposed approach.

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Section: B Balancing Of the Identified Modelsmentioning

confidence: 99%

Identification for gain-scheduling: a balanced subspace approach

Lovera

Mercère

2007

2007 American Control Conference

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“…of order n(B), and that σ + (Σ) = m(B); then Proposition 6 implies that, if the matrix K satisfying (12) Remark 8. Approaches to the identification of balanced state models in the deterministic case similar to the one presented in this paper are studied in Moonen and Ramos (1993) and in Chapter 5 of Van Overschee and De Moor (1996); and in a combined deterministic-stochastic setting in Van Overschee and De Moor (1995). On the related topic of stochastic balancing of autoregressive systems, see Dahlén and Scherrer (2004).…”

Section: Given Sequence and Assume That U Is Pe Of Order N(b) Thementioning

confidence: 99%

Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

Rapisarda

Trentelman

2011

Automatica

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a b s t r a c tWe illustrate procedures to identify a state-space representation of a lossless or dissipative system from a given noise-free trajectory; important special cases are passive systems and bounded-real systems. Computing a rank-revealing factorization of a Gramian-like matrix constructed from the data, a state sequence can be obtained; the state-space equations are then computed by solving a system of linear equations. This idea is also applied to perform model reduction by obtaining a balanced realization directly from data and truncating it to obtain a reduced-order model.

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“…In Moonen and Ramos (1993); Van Overschee and De Moor (1996), it is not mentioned that the Hankel matrix of Markov parameters H is computed. Also in Moonen and Ramos (1993), it is not mentioned that the matrix Y 0 of sequential zero input responses is computed. In the present paper, we interpret these algorithms as implementations of the above basic algorithm and reveal their structure.…”

Section: Note 2 (Model Reduction)mentioning

confidence: 99%

“…The balanced state-space identification problem is studied in Moonen and Ramos (1993) and Van Overschee and De Moor (1996, Chapter 5). The proposed algorithms fit in the outline given below, which will be called the basic algorithm.…”

Section: Introductionmentioning

confidence: 99%

Algorithms for deterministic balanced subspace identification

et al. 2005

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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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A subspace algorithm for balanced state space system identification

Cited by 32 publications

References 11 publications

Identification for gain-scheduling: a balanced subspace approach

Identification for gain-scheduling: a balanced subspace approach

Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

Algorithms for deterministic balanced subspace identification

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