L&lt;inf&gt;1&lt;/inf&gt; - L&lt;inf&gt;2&lt;/inf&gt; robust estimation in prediction error system identification

Corbier, Ch.; Carmona, J.C.; Alvarado, Victor M.

doi:10.1109/iceee.2009.5393561

Cited by 5 publications

(4 citation statements)

References 7 publications

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“…related to the identification of a real system, namely, an acoustic duct plant, in order to estimate and validate reduced order models, using estimators. We compare the estimation results with those given by Huber's [28,29], LSAD, LSE [24], and ∞ estimators (̂∞ = min max | ( )|). As shown in Figure 3, we have to find discrete-time dynamical models with reduced orders of the plant including the secondary loudspeaker, its amplifier, the acoustic secondary path, the measurement microphone, and its amplifier/antialiasing filter.…”

Section: Presentation This Section Presents Different Resultsmentioning

confidence: 99%

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MixedLpEstimators Variety for Model Order Reduction in Control Oriented System Identification

Corbier

Carmona²

2015

Mathematical Problems in Engineering

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A new family of MLE typeLpestimators for model order reduction in dynamical systems identification is presented in this paper. A family ofLpdistributions proposed in this work combinesLp2(1<p2<2) andLp1(0<p1<1) distributions which are quantified by four parameters. The main purpose is to show that these parameters add degrees of freedom (DOF) in the estimation criterion and reduce the estimated model complexity. Convergence consistency properties of the estimator are analysed and the model order reduction is established. Experimental results are presented and discussed on a real vibration complex dynamical system and pseudo-linear models are considered.

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Section: Presentation This Section Presents Different Resultsmentioning

confidence: 99%

“…The second one is to use a symmetrix convex Huber's function [27]. Recently, in [28,29], the identification of the same plant, using 2 − 1 estimators with low values of the scaling factor in Huber's function, proposes OE-2 − 1 models with complexity M equal to 17.…”

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confidence: 99%

MixedLpEstimators Variety for Model Order Reduction in Control Oriented System Identification

Corbier

Carmona²

2015

Mathematical Problems in Engineering

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“…-matrix and the limit hessian of the PREC and then the !-asymptotic covariance matrix of the robust estimator. Moreover, in this L 2 L 1 -estimation context [23][24][25], we propose a new decisional tool for the models validation, named L 1 -contribution function.This paper is organized as follows: Section 2 describes the context of complex systems control. In Section 3, we summarize the mathematical background related to the Output Error model, the !corrupted distribution models and the Huber's M-estimates.…”

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Extension of the tuning constant in the Huber's function for robust modeling of piezoelectric systems

Corbier

Carmona

2014

Adaptive Control & Signal

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This paper proposes a new modeling approach that is experimentally validated on piezoelectric systems in order to provide a black-box pseudolinear model for complex systems control. Most of the time, one uses physical based approaches. However, sometimes complex phenomena occur in the system due to atypical changes of the process behavior, output noise or some hard nonlinearities. Therefore, we adopt identification methods to achieve the modeling task. The microdisplacements of the piezoelectric systems generate atypical data named outliers, leading to large estimated prediction errors. Since these errors disturb the classical normal probability density function, we choose here, as corrupted distribution model, the gross error model (GEM). In order to deal more efficiently with the outliers, we use the Huber's function, as mixed L 2 =L 1 norms in which the tuning threshold named scaling factor is extended. From this function, a cost function also named PREC as parameterized robust estimation criterion is established. The identification is performed by choosing an Output Error model structure. In order to express the asymptotic covariance matrix of the robust estimator, we present a L finite Taylor's expansion to linearize the gradient and the hessian of the PREC. Experimental results are presented and discussed.

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Robust Black-Box Modeling of Piezoelectric Actuators for Vibration Drilling Control

Corbier

Carmona

2014

J Intell Robot Syst

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L<inf>1</inf> - L<inf>2</inf> robust estimation in prediction error system identification

Cited by 5 publications

References 7 publications

MixedLpEstimators Variety for Model Order Reduction in Control Oriented System Identification

MixedLpEstimators Variety for Model Order Reduction in Control Oriented System Identification

Extension of the tuning constant in the Huber's function for robust modeling of piezoelectric systems

Robust Black-Box Modeling of Piezoelectric Actuators for Vibration Drilling Control

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