Note: this is a project developed from the course paper of MAE 6280.
PIDOC uses PINNs to simulate nonlinear dynamics control process, achieved by the encoded control trajectory in the losses. PIDOC has only been used for control the van der Pol systems (Zhai & Sands, 2022).
To play with our simple example cases, you need to first download and convert your tensorflow to version 1.x; (Google Colab is a great platform for it) or directly download it through
pip install tensorflow==1.15.0
If you already have tf v.2. preinstalled, you can considering uninstalling:
pip uninstall tensorflow==2.7.0
Then download our repo:
git clone https://github.com/hanfengzhai/PIDOC.git
Open the simple case of the van der Pol dynamics:
cd vanderPol
Run the basic example case with the benchmark case of 10% added noise:
python main.py
If the model start to train, you are ready to go! Try tunning the hyperparameters and change the training data (explore data) to play it around!
- Note that
main.pyis only a tutorial template code for playing around, you can also check the Notebook version. The uploading of the full version is incomplete and we will finish it soon.
Based on the general framework of PINNs, PIDOC can be used for control all based on the signal-encoded (physics-informed) loss
L = MSENN + MSEI + λ MSED
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where MSENN = MSE(xprediction, xtraining) is the neural network error given the training data.
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where MSEI = MSE(xprediction(0), xcontrol(0)) is the control error given the training data.
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where MSED = MSE(xprediction, xcontrol) is the neural network error given the training data.
and λ is the Lagrangian multiplier to enforce control (proved in our paper that enlarging which doesn't work for better control).
It is clearly stated in the paper: enlarging the systems nonlinearity will cause the reduced control quality. Also, this framework is not for actual experimental control implementation. It is simply a simulation-based idea for using deep learning to model control.
@Article{math10030453,
AUTHOR = {Zhai, Hanfeng and Sands, Timothy},
TITLE = {Controlling Chaos in Van Der Pol Dynamics Using Signal-Encoded Deep Learning},
JOURNAL = {Mathematics},
VOLUME = {10},
YEAR = {2022},
NUMBER = {3},
ARTICLE-NUMBER = {453},
URL = {https://doi.org/10.3390/math10030453},
ISSN = {2227-7390},
DOI = {10.3390/math10030453}
}