Koopman Operator

Dependency

• python

  • version 3.10 or higher is recommended.

• rye

  • seting up python environment easily and safely.
  • only numpy, matplotlib, notebook are needed to run all scripts in this repository.

Setup

git clone https://github.com/MizuhoAOKI/koopman_operator.git
cd koopman_operator
rye sync

Usage

[Ex. 1] Prediction of nonlinear affine system

cd kooopman_operator
rye run jupyter notebook notebooks/koopman_operator_ex1.ipynb

Single machine infinite bus system (ground truth)

Comparison between ground truth and approximated system by koopman operator

[Ex. 2] Prediction of nonlinear affine system

cd kooopman_operator
rye run jupyter notebook notebooks/koopman_operator_ex2.ipynb

Unicycle Model (ground truth)

Comparison between ground truth and approximated system by koopman operator

References

• Milan Korda, Igor Mezić, Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control, Automatica, 2018
• 薄良彦, クープマン作用素による非線形システムの制御, 計測と制御, 2022