Model Reduction by Moment Matching for Linear and Nonlinear Systems

2010/03/24 by Alessandro Astolfi · 356 citations
Engineering · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Computer science #Control Systems and Identification #Control theory (sociology) #Covariance #Hydraulic and Pneumatic Systems #Interpolation (computer graphics) #Linear model #Linear system #Matching (statistics) #Mathematical analysis #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Moment (physics) #Nonlinear system #Projection (relational algebra) #Reduction (mathematics)

paper · doi:10.1109/tac.2010.2046044

published in IEEE Transactions on Automatic Control 55(10), 2321-2336 (Institute of Electrical and Electronics Engineers)

openalex publication_date 2010/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

The model reduction problem for (single-input, single-output) linear and nonlinear systems is addressed using the notion of moment. A re-visitation of the linear theory allows to obtain novel results for linear systems and to develop a nonlinear enhancement of the notion of moment. This, in turn, is used to pose and solve the model reduction problem by moment matching for nonlinear systems, to develop a notion of frequency response for nonlinear systems, and to solve model reduction problems in the presence of constraints on the reduced model. Connections between the proposed results, projection methods, the covariance extension problem and interpolation theory are presented. Finally, the theory is illustrated by means of simple worked out examples and case studies.

Citations

• Principal component analysis in linear systems: Controllability, observability, and model reduction
• Dissipative dynamical systems part I: General theory
• Balanced Model Reduction via the Proper Orthogonal Decomposition

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