Computational Methods in Systems and Control Theory: Teaching: MOR

Model Reduction for Dynamical Systems SS2012

Lectures:	Prof. Dr. Peter Benner	Office Hours:	on appointment
Exercises:	Tobias Breiten	Office Hours:	on appointment

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.

• P. Benner Model Reduction for Linear Dynamical Systems, Summer School on Numerical Linear Algebra for Dynamical and High-Dimensional Problem, 2011.

Exercises

• Exercise 1, dom_md_c.mat (compressed dom.tar)

• Exercise 2, CDPlayer.mat

• Exercise 3, LyapSol.mat

• Exercise 4, beam.mat, lyap_sgn_fac.m

• Exercise 5

• Exercise 6

• Exercise 7

Lecture material

• Lecture 1

• Lecture 2

• Lecture 5

• Lecture 6

• Lecture 7

• Lecture 8

• Lecture 9

• Lecture 10

• Lecture 11

• Lecture 12

• Chapter VI: Model Reduction using Center and Inertial Manifolds