Nonlinear Model Reduction in the Loewner Framework

We introduce a novel method of model reduction for nonlinear systems by extending the Loewner framework developed for linear time-invariant systems. This objective is achieved by defining Loewner functions obtained by utilizing a state-space interpretation of the Loewner matrices. A Loewner equivale...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2021-12, Vol.66 (12), p.5711-5726
Main Authors: Simard, Joel David, Astolfi, Alessandro
Format: Article
Language:English
Subjects:
Center manifold
Interconnected systems
Interpolation
Loewner matrices
Mathematical model
Model reduction
Nonlinear systems
Reduced order models
Reduced order systems
Time invariant systems
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Summary:We introduce a novel method of model reduction for nonlinear systems by extending the Loewner framework developed for linear time-invariant systems. This objective is achieved by defining Loewner functions obtained by utilizing a state-space interpretation of the Loewner matrices. A Loewner equivalent model using these functions is derived. This allows constructing reduced order models achieving interpolation in the Loewner sense.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2021.3110809