A local identification method for linear parameter-varying systems based on interpolation of state-space matrices and least-squares approximation

This paper proposes a novel state-space matrix interpolation technique to generate linear parameter-varying (LPV) models starting from a set of local linear time-invariant (LTI) models estimated at fixed operating conditions. Since the state-space representation of LTI models is unique up to a simil...

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Published in:	Mechanical systems and signal processing Vol. 82; pp. 478 - 489
Main Authors:	Ferranti, Francesco, Rolain, Yves
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.01.2017 Elsevier
Subjects:	Approximation Electronics Engineering Sciences Interpolation Least squares method Linear parameter-varying (LPV) systems Mathematical analysis Mathematical models Mechanical systems Similarity State-space matrices System identification Transformations Interpolation System identification State-space matrices Linear parameter-varying (LPV) systems State-space matrice
ISSN:	0888-3270, 1096-1216
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Abstract	This paper proposes a novel state-space matrix interpolation technique to generate linear parameter-varying (LPV) models starting from a set of local linear time-invariant (LTI) models estimated at fixed operating conditions. Since the state-space representation of LTI models is unique up to a similarity transformation, the state-space matrices need to be represented in a common state-space form. This is needed to avoid potentially large variations as a function of the scheduling parameters of the state-space matrices to be interpolated due to underlying similarity transformations, which might degrade the accuracy of the interpolation significantly. Underlying linear state coordinate transformations for a set of local LTI models are extracted by the computation of similarity transformation matrices by means of linear least-squares approximations. These matrices are then used to transform the local LTI state-space matrices into a form suitable to achieve accurate interpolation results. The proposed LPV modeling technique is validated by pertinent numerical results. •We present a novel local approach to model linear parameter-varying (LPV) systems.•Linear state coordinate transformations extracted for a set of local LTI models.•Similarity transformation matrices computed by linear least-squares approximations.•Least-squares-based algorithms with fixed and dynamic reference state trajectories.•This LPV modeling method is easy-to-implement and relies on robust numerical tools.
AbstractList	This paper proposes a novel state-space matrix interpolation technique to generate linear parameter-varying (LPV) models starting from a set of local linear time-invariant (LTI) models estimated at fixed operating conditions. Since the state-space representation of LTI models is unique up to a similarity transformation, the state-space matrices need to be represented in a common state-space form. This is needed to avoid potentially large variations as a function of the scheduling parameters of the state-space matrices to be interpolated due to underlying similarity transformations, which might degrade the accuracy of the interpolation significantly. Underlying linear state coordinate transformations for a set of local LTI models are extracted by the computation of similarity transformation matrices by means of linear least-squares approximations. These matrices are then used to transform the local LTI state-space matrices into a form suitable to achieve accurate interpolation results. The proposed LPV modeling technique is validated by pertinent numerical results. This paper proposes a novel state-space matrix interpolation technique to generate linear parameter-varying (LPV) models starting from a set of local linear time-invariant (LTI) models estimated at fixed operating conditions. Since the state-space representation of LTI models is unique up to a similarity transformation, the state-space matrices need to be represented in a common state-space form. This is needed to avoid potentially large variations as a function of the scheduling parameters of the state-space matrices to be interpolated due to underlying similarity transformations, which might degrade the accuracy of the interpolation significantly. Underlying linear state coordinate transformations for a set of local LTI models are extracted by the computation of similarity transformation matrices by means of linear least-squares approximations. These matrices are then used to transform the local LTI state-space matrices into a form suitable to achieve accurate interpolation results. The proposed LPV modeling technique is validated by pertinent numerical results. •We present a novel local approach to model linear parameter-varying (LPV) systems.•Linear state coordinate transformations extracted for a set of local LTI models.•Similarity transformation matrices computed by linear least-squares approximations.•Least-squares-based algorithms with fixed and dynamic reference state trajectories.•This LPV modeling method is easy-to-implement and relies on robust numerical tools.
Author	Ferranti, Francesco Rolain, Yves
Author_xml	– sequence: 1 givenname: Francesco surname: Ferranti fullname: Ferranti, Francesco email: francesco.ferranti@vub.ac.be – sequence: 2 givenname: Yves surname: Rolain fullname: Rolain, Yves
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Cites_doi	10.1109/CDC.1995.478600 10.1109/ACC.2007.4282899 10.1109/TCST.2014.2300510 10.1115/1.2802444 10.1109/TAC.1981.1102563 10.1016/j.ymssp.2015.01.007 10.1243/09544100JAERO28 10.1016/j.automatica.2007.02.027 10.1109/37.165527 10.1109/CDC.2004.1429336 10.1109/ACC.2003.1239782 10.1109/TADVP.2009.2029242 10.1007/978-3-642-13812-6 10.1109/TCST.2010.2078509 10.1016/j.electacta.2004.01.050 10.3182/20120711-3-BE-2027.00065 10.1016/j.ymssp.2009.04.007 10.1016/j.automatica.2005.03.027
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Keywords	Interpolation System identification State-space matrices Linear parameter-varying (LPV) systems State-space matrice
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SubjectTerms	Approximation Electronics Engineering Sciences Interpolation Least squares method Linear parameter-varying (LPV) systems Mathematical analysis Mathematical models Mechanical systems Similarity State-space matrices System identification Transformations
Title	A local identification method for linear parameter-varying systems based on interpolation of state-space matrices and least-squares approximation
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