Introductory Course on Model Order Reduction

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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

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Contents of the lecture

2. Introduction to Model Reduction of LTI Systems

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Contents of the lecture

3. Model Reduction of LTI Systems via Projection

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Contents of the lecture

4. Balanced Truncation

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Contents of the lecture

5. Model Reduction for DAEs and Navier-Stokes Equations

Requirements

Contents of the lecture