Sequential approximation of feasible parameter sets for identification with set membership uncertainty

Vicino, Antonio; Zappa, G.

doi:10.1109/9.506230

Cited by 171 publications

(94 citation statements)

References 19 publications

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“…When F (k, θ) is linear, boxes, parallelotopes, ellipsoids or zonotopes are used to characterize the AFPS [25][26] [27]. In the nonlinear case, a minimum outer box can be determined by means of a set of optimization problems [24].…”

Section: Set-membership Parameter Estimation Problemmentioning

confidence: 99%

Non‐linear set‐membership identification approach based on the Bayesian framework

Canti

Tornil-Sin

Blesa

et al. 2015

IET Control Theory & Applications

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This paper deals with the problem of set-membership identication of nonlinear-in-the-parameters models. To solve this problem, the paper illustrates how the Bayesian approach can be used to determine the feasible parameter set (FPS) by assuming uniform distributed estimation error and at model prior probability distributions. The key point of the methodology is the interval evaluation of the likelihood function and the result is a set of boxes with associated credibility indexes. For each box, the credibility index is in the interval (0,1] and gives information about the amount of consistent models inside the box. The union of the boxes with credibility value equal to one provides an inner approximation of the FPS, whereas the union of all boxes provides an outer estimation. The boxes with credibility value smaller than one are located around the boundary of the FPS and their credibility index can be used to iteratively rene the inner and outer approximations up to a desired precision. The main issues and performance of the developed algorithms are discussed and illustrated by means of examples.

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Section: Set-membership Parameter Estimation Problemmentioning

confidence: 99%

Non‐linear set‐membership identification approach based on the Bayesian framework

Canti

Tornil-Sin

Blesa

et al. 2015

IET Control Theory & Applications

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“…Such vertices can e.g. be found by using outer parallellotopic approximations as in (Vicino and Zappa, 1996). Each of the ¾ÄÒ Ö cases can now be determined by simple arithmetic operations, except when Ó Ò ÚÎ µ is split by a hyperplane, when LPs still has to be solved.…”

Section: On-line Search Treementioning

confidence: 99%

Evaluation of piecewise affine control via binary search tree

2003

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We present an algorithm for generating a binary search tree that allows efficient evaluation of piecewise affine (PWA) functions defined on a polyhedral partitioning. This is useful for PWA control approaches, such as explicit model predictive control (MPC), as it allows the controller to be implemented online with small computational effort. The computation time is logarithmic in the number of regions in the PWA function.

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“…However, exact computation of FPS and nominal model parameters is a laborious task and requires a large amount of numerical computation, and hence is not usable in practical situations [25,26,27]. An alternative is to outbound the FPS by simple geometrical shapes such as "Ellipsoid" and "Parallelotope" (Fig.1) and consider their centre as the parameters of the nominal model [8,9,10,14]. Then, these shapes are mapped to the frequency domain (e.g.…”

Section: Non-statistical Based Robust Identification Of a Lightly Dammentioning

confidence: 99%

“…Both parametric and nonparametric uncertainties can be easily considered in SM identification problems. In [8], [9], [10] and [11] just parametric uncertainties are considered while [1], [4], [11], [13], [14], [15] and [16] deal with both parametric and non-parametric uncertainties. This approach to robust identification is more popular than SE and other statistical based approaches, since:…”

Section: Introductionmentioning

confidence: 99%

Non-Statistical Based Robust Identification of a Lightly Damped Flexible Beam Using Kautz Orthonormal Basis Functions

Esmaeilsabzali

Montazeri

Poshtan

et al. 2008

Journal of Low Frequency Noise, Vibration and Active Control

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Robust identification of a lightly damped flexible beam with parametric and non-parametric uncertainties is presented; however, the main concern is about non-parametric uncertainties which are high-frequency high-amplitude unmodeled dynamics. Our approach is based on worst-case estimation theory in which uncertainties are assumed to be unknown but bounded and produces socalled hard bounds on model errors. Based on this theory, two methods named "Set Member-sip" and "Model Error Modeling" has been applied. We have also examined two outbounding algorithms (ellipsoidal and parallelotopic) to solve the Set Membership identification problem. In order to properly deal with highamplitude non-parametric uncertainties, the proposed methods are compared. It is shown that the combination of Set Membership approach with Model Error Modeling technique will result in superior identification in that it can better handle high-frequency high-amplitude non-parametric uncertainties. For each method the mode obtained and its associated uncertainty bound is mapped to the frequency plane so that it can be utilised by robust controller design methods such as H∞.

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Sequential approximation of feasible parameter sets for identification with set membership uncertainty

Cited by 171 publications

References 19 publications

Non‐linear set‐membership identification approach based on the Bayesian framework

Non‐linear set‐membership identification approach based on the Bayesian framework

Evaluation of piecewise affine control via binary search tree

Non-Statistical Based Robust Identification of a Lightly Damped Flexible Beam Using Kautz Orthonormal Basis Functions

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