Codes of paper 'Wenjian Hao, Bowen Huang, Wei Pan, Di Wu, and Shaoshuai Mou. "Deep Koopman learning of nonlinear time-varying systems." Automatica 159 (2024): 111372.'

Description

• Started on Sep/2021, last revision on Jan/2022.
• Author: Wenjian Hao, PhD, AAE, Purdue University.
• This code is about the first example in the paper, readers can refine the codes accordingly based on their research.
• The goal of this project is to learn the dynamics of various nonlinear time-varying systems (NTVS) for optimal control design purposes.
• If the paper or codes help your research or other projects please cite:
  

  @article{hao2024deep,
  title={Deep Koopman learning of nonlinear time-varying systems},
  author={Hao, Wenjian and Huang, Bowen and Pan, Wei and Wu, Di and Mou, Shaoshuai},
  journal={Automatica},
  volume={159},
  pages={111372},
  year={2024},
  publisher={Elsevier}
  }

Dependencies

• torch, numpy, os, scipy, matplotlib, joblib, odmd.

Methodologies

• Koopman operator and deep learning.
  

Usage

• Run main.py to learn and save the learned dynamics, then run the plot_comparison.py for results visualization and comparison.
  
• Parameters are defined in config.py.
  
• In folder '/SavedResults/', we include the plots data of the published paper, and '/SavedResults/SavedResults08/' contains the plots data with changing rate \gamma=0.8.

Possible extensions based on this codes

• Change the dynamics by replacing the codes in block 'data generation' of main.py based on your research or projects.
  
• Add the control inputs following the paper (changes need to be made in utils.py).
  
• Develop various model-based controllers using the learning dynamics matrices and neural network basis function, see the following paper for the application examples.
  

  @misc{hao2023deep,
    title={Deep Koopman Learning of Nonlinear Time-Varying Systems}, 
    author={Wenjian Hao and Bowen Huang and Wei Pan and Di Wu and Shaoshuai Mou},
    year={2023},
    eprint={2210.06272},
    archivePrefix={arXiv},
    primaryClass={eess.SY}
  }