Deep-Koopman-learning-of-nonlinear-time-varying-systems

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Deep-Koopman-learning-of-nonlinear-time-varying-systems

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# 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}
}
```

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