| Lecturer: |
Lena
Scholz (Consultation hour: Tue 15-16 MA
463) |
|
| Lecture: |
Tue 10-12 in MA 645 |
|
Thu 12-14 in MA 142 |
Exams:
Dates for the next oral exams:
Please register for the exam in the examination office
(Prüfungsamt).
After registration arrange the time for the exam in the office MA
4-5 (Mrs. Ullrich, Room MA 471). The confirmation of the
registration ("gelber Zettel") is necessary.
The modeling of complex physical and technical processes often
leads to systems of ordinary differential equations with several
millions of equations and variables. The numerical simulation,
real-time and optimal control of such large-scale systems is very
time-consuming and expensive due to high computing times and high
memory requirements, and sometimes even impossible. The goal of
model order reduction is to approximate highly dimensional systems
with systems of smaller dimension. Hereby, crucial physical
properties of the system should be preserved in the reduced order
model, while simultaneously the approximation error should be small,
and the methods should be stable and efficient.
Previous Knowledge:
- Linear Algebra I, II
- basic knowledge in the Theory of Ordinary Differential
Equations
- basic knowledge in Numerical Analysis is recommended
Material:
- Example: heat propagation (pdf)
- Examples: Model order reduction by balanced truncation (pdf)
- Examples: Model order reduction by moment matching (pdf)
- A.C. Antoulas. Approximation of Large-Scale Dynamical Systems.
SIAM, Philadelphia, PA, 2005.
- H.W. Knobloch, H. Kwakernaak. Lineare Kontrolltheorie.
Springer-Verlag, Berlin, 1985.
- Script ''Kontrolltheorie'' by Volker Mehrmann. (pdf)
- Script ''Mathematische System- und Regelungstheorie'' by Peter
Benner. (pdf)