Abstract
We propose a projection based multi-moment matching method for model order reduction of quadratic-bilinear systems. The goal is to construct a reduced system that ensures higher-order moment matching for the multivariate transfer functions appearing in the input-output representation of the non-linear system. An existing technique achieves this for the first two multivariate transfer functions, in what is called the symmetric form of the multivariate transfer functions. We extend this framework to an equivalent and simplified form, the regular form, which allows us to show moment matching for the first three multivariate transfer functions. Numerical results for three benchmark examples of quadratic-bilinear systems show that the proposed framework exhibits better performance with reduced computational cost in comparison to existing techniques.
Highlights
We consider the problem of model order reduction for a single-input single-output (SISO) quadratic-bilinear descriptor system of the form ( ) = ( ) + ( ) ( ) + ( ) ⊗ ( ) + ( ), (1.1)
We propose a multi-moment matching technique that utilises the regular form of the multivariate transfer functions (2.8) and is, easy to be extended to higher multi-moments
It is a well-used example for model order reduction of nonlinear systems, where a non-linear RC circuit as shown in Figure 1 is considered for model reduction
Summary
An extension to two-sided projection has been presented in Benner and Breiten (2015) that refines the quality of the approximations in term of accuracy It is observed in Ahmad, Benner and Jaimoukha (2016) that a simplified and equivalent representation of the multivariate transfer functions can be identified, for which it is relatively easy to extend the moment matching concept to higher multivariate transfer functions. The construction of the projection matrices and requires the use of the matrices and from the nonlinear terms, and will result in more accurate reduced-order system This is different from Benner and Breiten (2012), where multi-moment matching of the first two transfer functions is discussed.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
