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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)391-6110-806
E-mail: breiten@mpi-magdeburg.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 large-scale 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 Krylov-based reduction techniques for so-called quadratic-bilinear systems
which overcome this drawback.
The advantage of quadratic-bilinear systems is that they allow the exact
representation of a large class of nonlinear systems. Moreover, the quadratic-bilinearization
is often achieved with an acceptable increase of the state dimension. The initial idea using quadratic-bilinear 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
Otto-von-Guericke University Magdeburg,
Chair Process Systems Engineering,
Tel: +49 (0)391 67-54637
E-mail: abornhoeft@mpi-magdeburg.mpg.de
- Tobias Breiten
Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg,
Computational Methods in Systems and Control Theory,
Tel: +49 (0)391-6110-806
E-mail: breiten@mpi-magdeburg.mpg.de
- Richard Hanke-Rauschenbach
Otto-von-Guericke University Magdeburg,
Chair Process Systems Engineering,
Tel: +49 (0)391 67-54630
E-mail: hanke-rauschenbach@mpi-magdeburg.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 real-life 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 qudratic-bilinear 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
|
Steady-state analysis of the anaerobic digestion model No. 1 (ADM1);
A. Bornhöft, R. Hanke-Rauschenbach, and K. Sundmacher;
submitted to Journal of Biotechnology;
2011. |
