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Interpolatory model reduction for quadratic-bilinear systems using error estimators

Mian Ilyas Ahmad (Research Center for Modeling and Simulation, National University of Science and Technology, Islamabad, Pakistan)
Peter Benner (Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany, and Faculty of Mathematics, Otto von Guericke University Magdeburg, Magdeburg, Germany)
Lihong Feng (Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany)

Engineering Computations

ISSN: 0264-4401

Article publication date: 7 January 2019

Issue publication date: 8 February 2019




The purpose of this paper is to propose an interpolation-based projection framework for model reduction of quadratic-bilinear systems. The approach constructs projection matrices from the bilinear part of the original quadratic-bilinear descriptor system and uses these matrices to project the original system.


The projection matrices are constructed by viewing the bilinear system as a linear parametric system, where the input associated with the bilinear part is treated as a parameter. The advantage of this approach is that the projection matrices can be constructed reliably by using an a posteriori error bound for linear parametric systems. The use of the error bound allows us to select a good choice of interpolation points and parameter samples for the construction of the projection matrices by using a greedy-type framework.


The results are compared with the standard quadratic-bilinear projection methods and it is observed that the approximations through the proposed method are comparable to the standard method but at a lower computational cost (offline time).


In addition to the proposed model order reduction framework, the authors extend the one-sided moment matching parametric model order reduction (PMOR) method to a two-sided method that doubles the number of moments matched in the PMOR method.



Ahmad, M.I., Benner, P. and Feng, L. (2019), "Interpolatory model reduction for quadratic-bilinear systems using error estimators", Engineering Computations, Vol. 36 No. 1, pp. 25-44.



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