Supplementing material like lecture overview and slides
Switch branches/tags
Nothing to show
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Permalink
Failed to load latest commit information.
GugSW-properimproper.png
README.md
concept-daense.tex
concept-lti.tex
concept-sysnorms.tex
lecture_notes.pdf
main-concepts.tex
stylefyle.tex

README.md

Introductory Course on Model Order Reduction

Please download the lecture notes -- updates after every lecture

Abstract:

I will start my short course by introducing the class of Linear Time Invariant (LTI) systems and the control related system theory for them. Although LTI systems can be used to model many real life processes, the mathematical theory for control is very general. The second lecture will be on the fundamental motivations and mathematical notions of model reduction in general and for LTI in particular. This lecture will provide some illustrative examples for the use and results of model reduction. In the third lecture, I will introduce the fundamental model reduction approach that uses projections and explain several ways to compute these projections. A mathematical well understood projection method is Balanced Truncation (BT). The 4th lecture will introduce BT and discuss how it can be applied in practice. The last lecture contains some example on how the LTI related theory can be extended to so called differential-algebraic equations (DAEs) or descriptor systems. After introducing some basic concepts, I will show and explain recent results concerning the control of Navier-Stokes equations.

Course of the Lecture

  1. Introduction to Linear Time Invariant (LTI) Systems, Sep. 2nd
  2. Introduction to Model Reduction of LTI Systems, Sep. 7th
  3. Model Reduction of LTI Systems via Projection, Sep. 9th
  4. Balanced Truncation, Sep. 14th
  5. Model Reduction for DAEs and Navier-Stokes Equations, Sep. 15th

Little Chinese Dictionary

Hello 你好
Matrix 矩阵
Vector 向量
Eigenvalue 特征值
Projection 投影
Subspace 子空间
Interpolation 插值
Model 模型
System 系统
Transfer function 传递函数
Stable 稳定
Truncation 截断

1. Introduction to the Control Theory of Linear Time Invariant (LTI) Systems

Requirements

  • Basic notions from Linear Algebra
  • Basic notions from linear ODEs
  • Laplace transform

Contents of the lecture

  • Examples of LTI systems
  • State space representation
  • Transfer functions
  • Realizations
  • Controllability, Observability

2. Introduction to Model Reduction of LTI Systems

Requirements

  • LTI systems
  • Basic notions from Linear Algebra

Contents of the lecture

  • Examples of successful MOR
  • Basic concepts and ideas of model reduction
  • Norms of systems

3. Model Reduction of LTI Systems via Projection

Requirements

  • LTI systems
  • Basic notions from Linear Algebra

Contents of the lecture

  • Projectors and projections
  • A projected model interpolates the transferfunction
  • Modal truncation
  • Dominant poles

4. Balanced Truncation

Requirements

  • LTI systems
  • Realizations
  • MOR via projection

Contents of the lecture

  • System Gramians and Lyapunov Equations
  • Balanced Realizations
  • Hankel Singular Values
  • Balanced Truncation
  • Hankel Operator

5. Model Reduction for DAEs and Navier-Stokes Equations

Requirements

  • LTI Systems
  • Balanced Truncation

Contents of the lecture

  • DAEs as LTI systems
  • Decouplings of DAEs
  • (Linearized) Navier-Stokes Equations
  • Balanced Truncation for linear Navier-Stokes Equations
  • Application to stabilization of flows