Subspace identification with eigenvalue constraints

Miller, Daniel N.; Callafon, Raymond A. de

doi:10.1016/j.automatica.2013.04.028

Cited by 62 publications

(46 citation statements)

References 9 publications

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“…Moreover, one of the main strength of our method is that it is possible to impose the poles location through LMI constraints for every considered operating point. This is also proposed in this article as an extension of what have been done in [8] and [9] in the LTI case only.…”

Section: Introductionmentioning

confidence: 87%

Identification of parametric models in the frequency-domain through the subspace framework under LMI constraints

Kergus

Demourant

Poussot-Vassal

2018

International Journal of Control

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An extension of standard subspace-based algorithms to identify parametric systems from frequency response samples is presented. This algorithm uses arbitrary frequency spacing and allows frequency weighting. It offers the possibility to impose the model's poles location through LMI constraints. This technique is applied to a numerical example and to real industrial frequency-domain data originating from an openchannel flow for hydroelectricity production.

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Section: Introductionmentioning

confidence: 87%

Identification of parametric models in the frequency-domain through the subspace framework under LMI constraints

Kergus

Demourant

Poussot-Vassal

2018

International Journal of Control

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“…The first stabilization technique is based on formulating stability of the model (8) as a constraint on the eigenvalues of the companion matrix of A(z) in (9). This constraint can be characterized in terms of Linear Matrix Inequalities (LMI) as discussed in [10], and used later on in [11] to enforce stable models in subspace identification, thus leading to:…”

Section: Stabilization Via Lmi Constraintmentioning

confidence: 99%

“…According to [11,Theorem 1], which presents small variations w.r.t the original central theorem in [10], we define the companion matrix of f as Ψ(f ) ∈ R p×p . Therefore,…”

Section: Formulation Of the Lmi Constraintmentioning

confidence: 99%

Identification of stable models via nonparametric prediction error methods

Romeres

Pillonetto

Chiuso

2015

2015 European Control Conference (ECC)

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Abstract-A new Bayesian approach to linear system identification has been proposed in a series of recent papers. The main idea is to frame linear system identification as predictor estimation in an infinite dimensional space, with the aid of regularization/Bayesian techniques. This approach guarantees the identification of stable predictors based on the prediction error minimization. Unluckily, the stability of the predictors does not guarantee the stability of the impulse response of the system. In this paper we propose and compare various techniques to address this issue. Simulations results comparing these techniques will be provided. I. INTRODUCTIONRecent approaches for linear system identification describe the unknown system directly in terms of impulse response, thus describing an infinite dimensional model class. Needless to say, this is not entirely free of difficulties, since an alternative way to control the model complexity, i.e., to face the so called-bias variance tradeoff [1], [2], need to be found. It has been shown in the recent literature that the apparatus of Reproducing Kernel Hilbert Spaces (RHKS) or, equivalently, Bayesian Statistics provide powerful tools to face this tradeoff.The paper [3] has shown how these infinite dimensional model classes can be used for identification of linear systems in the framework of prediction error methods, leading naturally to stable predictors. Yet stability of the predictor model does not necessarily guarantee stability of the so called "forward" (or simulation) model. As a matter of fact, we faced this stability issue when performing identification on a real data set from EEG recordings. Physical insight in this case suggests that the transfer function describing the link between potentials in different brain locations are expected to be stable, while the identified models where not.Therefore, motivated by this real-world application, in this paper we shall tackle the problem of identifying stable (simulation) models when nonparametric prediction error methods [3] are used. We shall describe and compare, through an extensive simulation study, four possible solutions to this problem.The paper is structured as follows: Section II formulates the problem. Sections III-V introduce four different approaches to guarantee stability of the identified models. Experimental results are described in Section VI and conclusions are drawn in Section VII.Notation: Given a matrix M , M shall denote its transpose, σ(M ) will be its eigenvalues. If A(z) is a polynomial, σ(A(z)) will denote the set of roots of A(z). Given two discrete time jointly stationary stochastic process y(t) and z(t), the symbol E[y(t)|z(s), s < t] shall denote the linear

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“…-(19), if c max → 0 and r max → 1, then a → 1 and b → 1. Conversely, if ζ min → 1 in (14)-(15), then c max → e −1 and r max → 0. Likewise, we have a → and b → 0.…”

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confidence: 99%

Mapping prior information onto LMI eigenvalue‐regions for discrete‐time subspace identification

Ricco

Teixeira

2020

IET Control Theory & Applications

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In subspace identification, prior information can be used to constrain the eigenvalues of the estimated state-space model by defining corresponding LMI regions. In this paper, first we argue on what kind of practical information can be extracted from historical data or step-response experiments to possibly improve the dynamical properties of the corresponding model and, also, on how to mitigate the effect of the uncertainty on such information. For instance, prior knowledge regarding the overshoot, the period between damped oscillations and settling time may be useful to constraint the possible locations of the eigenvalues of the discrete-time model. Then, we show how to map the prior information onto LMI regions and, when the obtaining regions are non-convex, to obtain convex approximations.

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Subspace identification with eigenvalue constraints

Cited by 62 publications

References 9 publications

Identification of parametric models in the frequency-domain through the subspace framework under LMI constraints

Identification of parametric models in the frequency-domain through the subspace framework under LMI constraints

Identification of stable models via nonparametric prediction error methods

Mapping prior information onto LMI eigenvalue‐regions for discrete‐time subspace identification

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