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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:0888-3270
1096-1216
DOI:10.1016/j.ymssp.2016.05.037