Convergence Analysis of Instrumental Variable Recursive Subspace Identification Algorithms

Mercère, Guillaume; Lovera, Marco

doi:10.3182/20060329-3-au-2901.00039

Cited by 7 publications

(9 citation statements)

References 21 publications

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“…The complex-valued case is motivated by the fact that observations in some communication systems are complex-valued. As mentioned in [42], the propagator method and the SREIV-PAST algorithm differ in the exact subspace vectors they are tracked. However, the subspace estimated are fundamentally identical.…”

Section: ) Vff Recursive Eiv Algorithm For Estimating a A A And C C Cmentioning

confidence: 99%

A Variable Regularized Recursive Subspace Model Identification Algorithm With Extended Instrumental Variable and Variable Forgetting Factor

2020

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This paper proposes a new smoothly clipped absolute deviation (SCAD) regularized recursive subspace model identification algorithm with square root(SR) extended instrumental variable (EIV) and locally optimal variable forgetting factor (LOFF). The proposed algorithm is based on a new local polynomial modeling (LPM)-based variable FF EIV projection approximation subspace tracking (PAST) and multivariate recursive least squares algorithms for estimating respectively the subspace of the extended observability matrix, and the input matrix and feedthrough matrix. The SREIV-PAST algorithm offers improved resilience to additive noise over the PAST algorithm and it is implemented using the more stable square-root form. The asymptotic mean square error of the corresponding LPM-based model is derived and minimized at each time instant to obtain the proposed LOFF for improving the convergence speed and steady state error. A recursive bi-iteration singular value decomposition (SVD) algorithm is also proposed for recursive computation of the pseudo-inverse of the state transition matrix and its eigenvalues. This facilitates online estimation of its model order using classical model selection criteria. Moreover, a new criterion based on the percentage of explained variance is also proposed with improved performance. The SCAD regularization is proposed for automatic model selection of the input and feedthrough matrices, as it is asymptotically unbiased. Efficient techniques for incorporating SCAD and estimating other required quantities are also developed. The proposed algorithms are evaluated using computer simulations under stationary and nonstationary environments and a real dataset on wing flutter data. Results show that the proposed algorithms offer improved convergence speed and steady state performance over the conventional algorithms and it also provides an online estimate of the system model order. INDEX TERMS Recursive subspace model identification (RSI), variable forgetting factor (VFF), SCAD regularization, extended instrumental variable (EIV), local polynomial modeling (LPM), model order estimation.

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Section: ) Vff Recursive Eiv Algorithm For Estimating a A A And C C Cmentioning

confidence: 99%

A Variable Regularized Recursive Subspace Model Identification Algorithm With Extended Instrumental Variable and Variable Forgetting Factor

2020

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“…In the case of all the involved matrices are nonsingular (see (Mercère and Lovera, 2007)) the argument of minimizing Eq. 21is given by (Mercère et al, 2008):…”

Section: I) Qr Factorization Updatingmentioning

confidence: 99%

Parametric Fault Detection in Nonlinear Systems - A Recursive Subspace-based Approach

Gil

Santos²,

Cardoso

et al. 2013

Proceedings of the 10th International Conference on Informatics in Control, Automation and Robotics

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This paper deals with the problem of detecting nolinear systems' parametric faults modeled as changes in the eigenvalues of a local linear state-space model. The linear state-space model approximations are obtained by recursive subspace system identification techniques, from which the eigenvalues are extracted at each sampling time. Residuals are generated by comparing the eigenvalues against those associated with a local nominal model derived from a neural network predictor describing the nonlinear plant dynamics in free fault conditions. Parametric fault symptoms are generated from the eigenvalues residuals, whenever a given predefined threshold is exceeded. The feasibility and effectiveness of the proposed framework is demonstrated in a practical case study.

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“…The most important step in RSMI is the recursive update of the observability subspace (Gustafsson et al [1998], Oku & Kimura [2002], Mercère et al [2007]). The basic idea of solving this procedure is to use the close relationship between SMI and sensor array signal processing (SAP) problems.…”

Section: Rsmi Based On Varx and Pastmentioning

confidence: 99%

“…The recursive subspace identification problem has received much attention in the literature (Gustafsson et al [1998], Oku & Kimura [2002], Mercère et al [2007]). RSMI methods are mostly inspired by the off-line versions of subspace model identification techniques.…”

Section: Introductionmentioning

confidence: 99%

Recursive Subspace Model Identification Based On Vector Autoregressive Modelling

Yang

Song

2008

IFAC Proceedings Volumes

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Recursive subspace model identification (RSMI) has been developed for a decade. Most of RSMIs are only applied for open loop data. In this paper, we propose a new recursive subspace model identification which can be applied under open loop and closed loop data. The key technique of this derivation of the proposed algorithm is to bring the Vector Auto Regressive with eXogenous input (VARX) models into RSMI. Numerical studies on a closed loop identification problem show the effectiveness of the proposed algorithm.

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Convergence Analysis of Instrumental Variable Recursive Subspace Identification Algorithms

Cited by 7 publications

References 21 publications

A Variable Regularized Recursive Subspace Model Identification Algorithm With Extended Instrumental Variable and Variable Forgetting Factor

A Variable Regularized Recursive Subspace Model Identification Algorithm With Extended Instrumental Variable and Variable Forgetting Factor

Parametric Fault Detection in Nonlinear Systems - A Recursive Subspace-based Approach

Recursive Subspace Model Identification Based On Vector Autoregressive Modelling

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