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MOR by Rewriting to (Quadratic)Bilinear System Order Reduction
Researcher:
 Tobias Breiten
Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg,
Computational Methods in Systems and Control Theory,
Tel: +49 (0)3916110806
Email: breiten@mpimagdeburg.mpg.de
Project Description
An important tool in the analysis of complex physical phenomena is the
simulation of the underlying mathematical models which are often given
by systems of ordinary and/or partial differential equations. As one
is interested in models as accurate as possible, linear models are often
insufficient such that one is faced with largescale nonlinear systems.
Frequently, these cannot be handled efficiently, necessitating model order
reduction, i.e., the construction of a smaller system approximating the
original one.
While most existing nonlinear reduction methods like proper orthogonal decomposition (POD)
and trajectory piecewise linear (TPWL) require specific training inputs and thus are input
dependent, here we study Krylovbased reduction techniques for socalled quadraticbilinear systems
which overcome this drawback.
The advantage of quadraticbilinear systems is that they allow the exact
representation of a large class of nonlinear systems. Moreover, the quadraticbilinearization
is often achieved with an acceptable increase of the state dimension. The initial idea using quadraticbilinear systems
for nonlinear model reduction emerged quite recently and can be found in
[1].
Duration and Funding
 since September 2010: MPI Magdeburg
Related Publications
References
Dynamic, Analysis and Control of Anaerobic Digestions Processes for Biogas Production
Researcher:
 Astrid Bornhöft
OttovonGuericke University Magdeburg,
Chair Process Systems Engineering,
Tel: +49 (0)391 6754637
Email: abornhoeft@mpimagdeburg.mpg.de
 Tobias Breiten
Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg,
Computational Methods in Systems and Control Theory,
Tel: +49 (0)3916110806
Email: breiten@mpimagdeburg.mpg.de
 Richard HankeRauschenbach
OttovonGuericke University Magdeburg,
Chair Process Systems Engineering,
Tel: +49 (0)391 6754630
Email: hankerauschenbach@mpimagdeburg.mpg.de
Project Description
In cooperation with the group of Prof. Dr. Kai Sundmacher, we investigate the above mentioned nonlinear model reduction technique
by means of a reallife application arising in digstion processes in the context of biogas production. Before applying model order reduction, as a
first step the nonlinear dynamics have to be transformed into a qudraticbilinear control systems with additional algebraic constraints that
make the reduction itself more complicated. Subsequently, we want to apply the model reduction approach and give an interpretation of the reduced system.
Duration and Funding
 since September 2010: MPI Magdeburg
Related Publications

Steadystate analysis of the anaerobic digestion model No. 1 (ADM1);
A. Bornhöft, R. HankeRauschenbach, and K. Sundmacher; submitted to Journal of Biotechnology;
2011. 