Model Reduction for Dynamical Systems (Summer Semester 2023)

This course deals with Model Order Reduction (MOR) for the efficient simulation, analysis, control, and optimization of large-scale dynamical systems. A large variety of MOR methods will be introduced and discussed, including both frequency-domain and time-domain methods. MOR methods applied to real-world problems will be presented in order to highlight the necessity and usefulness of model reduction.

Contents -  Schedule -  Certification -  Lectures -  Exercises -  Homework -  References


  1. Basics of Linear Systems and Control Theory
    • Singular Value Decomposition
    • Input and Output Dynamical Systems
    • Frequency Domain Behavior and Transfer Functions
    • Gramians and Energy Functionals
  2. System-theoretic Model Reduction
    • Balanced Truncation
    • Pade Approximation
    • Interpolation-based Model Reduction
  3. Model Reduction of Nonlinear Systems
    • Proper Orthogonal Decomposition (POD)
    • Discrete Empirical Interpolation Method (DEIM)
  4. Model Reduction of Parametric Systems
    • Multi-moment Matching
    • Reduced Basis (RB) Method
  5. Data-Driven Methods for Dynamical Systems
    • Eigenvalue Realization Algorithm (ERA)
    • Loewner Framework
    • Dynamic Mode Decomposition
    • Operator Inference

The content of this lecture is summarized in the follwoing slides.





Exercise:  TBA

Certificate for successful participation

Will be announced in the lecture


  • Week 1 (12/04 and 14/04): 



Recomended Literature


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