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) 

V0.052+3 (MPI) 

Exercises: 
Tuesday, 
11:00 am  01:00 pm (1. Exercise on 04/24/2012) 

V0.052+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 (eigenvaluebased methods),
 balanced truncation (SVDbased methods),
 PadÃ© 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 LargeScale Dynamical Systems, SIAM, Philadelphia, 2005.
 P. Benner, V. Mehrmann, D.C. Sorensen: Dimension Reduction of LargeScale Systems, SpringerVerlag, Berlin/Heidelberg, June 2005.
 P. Benner, M. Hinze, E.J.W. ter Maten: Model Reduction for Circuit Simulation, SpringerVerlag, 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, SpringerVerlag, 2000.
 W.H. Schilders, H.A. van der Vorst, J. Rommes Model Order Reduction: Theory, Research Aspects and Applications, SpringerVerlag, 2008.
Exercises
Lecture material