Model Order Reduction (MOR) in Control System

Author: Pengcen Jiang, Yi Gu, Shibo Hao Course: DSC 210: Linear Algebra/Data Science, FA22@UCSD Instructor: Dr. Tsui-wei Weng

Instructions

• Ensure that the following libraries are installed in python 3 environment:
  • numpy
  • torch
  • matplotlib
  • scipy
• Open MOR_in_control_system.ipynb and run all the cells of the notebook.

Repository Structure

• DynamicSystem.py: Contains the basic classes of a dynamic system, and a linear dynamic system.
• models.py: Contains classes of neural network models.
• MOR.py: The implementation of two MOR methods. They are encapsulated as subclass of a dynamic system.
• util.py: Helper functions.
• MOR_in_control_system.ipynb: A notebook for conducting experiment and presenting the results.

Primary Results

Here we show all the numeric and figurative results. Please refer to our report for the detailed settings of the experiment and the analysis of the results.

Fitting

Metric	POD	AE
MSE of X	0.0077	0.0076
MSE of Y	0.0028	0.0038

Generalization

Metric	POD	AE
MSE of X	0.0121	1.9652
MSE of Y	0.0034	0.0549

Replacing AE with Linear AE

Reduction Dimension