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Model Reduction for Dynamical Systems SS2012
Schedule -
Further Information -
Contents -
Certificates -
References -
Exercises -
Lecture material
Schedule
Lectures: |
Thursday, |
01:00 pm - 03:00 pm (1. Lecture on 04/12/2012) |
|
V0.05-2+3 (MPI) |
|
Exercises: |
Tuesday, |
11:00 am - 01:00 pm (1. Exercise on 04/24/2012) |
|
V0.05-2+3 (MPI) |
|
Further Information
- Course description.
- Important: Lecture instead of exercise session on April 17, 2012!
- Important: no lecture/exericse session on June 19/21, 2012!
Contents
- Basics of linear systems and control theory.
- Model reduction methods for linear and nonlinear systems:
- modal truncation (eigenvalue-based methods),
- balanced truncation (SVD-based methods),
- Padé approximation / rational interpolation (Krylov subspace based methods),
- proper orthogonal decomposition (POD),
- dimension reduction via central/inertial manifolds (slow/fast decomposition).
- Applications of model reduction in computational science and engineering.
- Model reduction for parametric systems.
Certificate for successful participation
Criteria for getting a certificate for successful participation:
- Reasonable execution of at least 50% of the homework exercises.
- Demonstration of at least two homework exercises in the tutorial class.
Further information on exams will be given in the lecture.
References
- A.C. Antoulas: Approximation of Large-Scale Dynamical Systems, SIAM, Philadelphia, 2005.
- P. Benner, V. Mehrmann, D.C. Sorensen: Dimension Reduction of Large-Scale Systems, Springer-Verlag, Berlin/Heidelberg, June 2005.
- P. Benner, M. Hinze, E.J.W. ter Maten: Model Reduction for Circuit Simulation, Springer-Verlag, 2011.
- P. Benner: Numerical Linear Algebra for Model Reduction in Control and Simulation, GAMM Mitteilungen, 2006.
- R.W. Freund: Model reduction methods based on Krylov subspaces, Acta Numerica, 2003.
- G. Obinata, B.D.O. Anderson: Model Reduction for Control System Design, Springer-Verlag, 2000.
- W.H. Schilders, H.A. van der Vorst, J. Rommes Model Order Reduction: Theory, Research Aspects and Applications, Springer-Verlag, 2008.
Exercises
Lecture material