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Multivariate Interpolationsmethoden zur parametrischen Modellreduktion

DFG Projekt MIM4PMOR

Projektkoordinator:

  • Prof. Dr. Peter Benner
    Max-Planck-Institut für Dynamik komplexer technischer Systeme Magdeburg,
    Computational Methods in Systems and Control Theory,
    Tel: +49 (0)391-6110-451
    E-mail: benner@mpi-magdeburg.mpg.de

Mitarbeiter:

  • Tobias Breiten
    Max-Planck-Institut für Dynamik komplexer technischer Systeme Magdeburg,
    Computational Methods in Systems and Control Theory,
    Tel: +49 (0)391-6110-806
    E-mail: breiten@mpi-magdeburg.mpg.de

Projekt Beschreibung

Many computer-aided engineering problems involve analyzing large-scale parameter-dependent dynamical processes. Here, one can, e.g., think of optimization of geometry and topology in MEMS design. Model order reduction (MOR) techniques are often required to allow multiple simulations for varying parameter values in design studies or optimization algorithms. In case of parameters staying constant during one simulation cycle, there exist several generalizations of linear MOR methods like moment-matching, balanced truncation and rational interpolation, respectively. However, the situation becomes rather complicated if the parameters vary in time. Here, efficient reduction methods are still an open question.

In this project, we investigate a beneficial connection between linear parameter-varying (LPV) control systems and so-called bilinear control systems. Although the latter ones formally belong to the class of nonlinear control systems, many linear reduction techniques have been shown to possess bilinear analogues. Moreover, embedding LPV systems in the class of bilnear control systems allows for studying parametric model reduction techniques that automatically take care of a desired structure preservation of the underyling parametric process.

Duration and Funding

  • Januar 2010 - August 2010: Technische Universität Chemnitz
  • seit September 2010: MPI Magdeburg, gefördert durch DFG (seit 2012)

Zugehörige Publikationen