“Physics Informed Fully Embedded Koopman Operator-based Optimal Control of Two-Link Robotic System”
Authors: Jeppe H. Andersen, Jokin L. Berakoetxea, Stas Kokotovic and Per Johansen,Affiliation: Aalborg University
Reference: 2025, Vol 46, No 4, pp. 163-170.
Keywords: Machine learning, Nonlinear systems, Koopman theory, Neural Networks, System Analysis
Abstract: This paper presents a data-driven framework utilising neural networks to approximate the Koopman operator for a discrete-time representation of an electrically actuated two-link mechanical system, enabling the application of linear control techniques. A validated dynamic model is used to generate training data. The Physics Informed Fully Embedded Koopman (PIFEK) framework embeds the original state space directly into the Koopman space, leading to sensible tuning of the controllers. The tuning was done using bandwidth analysis of the Koopman dynamics, yielding estimates of the true dynamics. This resulted in satisfactory control performance, including accurate tracking of a trajectory. Comparisons with a conventional PI controller show that while performance is similar, the data-driven PIFEK approach requires significantly less system-specific knowledge, underscoring its potential for efficient control design.
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DOI: 10.4173/mic.2025.4.3References:
[1] Anderson, B.H., Norkjaer, C.S., Mir, D., Andersen, J.H., Jensen, L.C., and Frohlich, M.A. (2022). Analysis of a 2-dof robot arm, Technical report, Aalborg University. Available at: https://github.com/headforest53/Robot5thSemhttps://github.com/headforest53/Robot5thSem.
[2] Brunton, S.L. (2019). Notes on koopman operator theory, Available at: https://fluids.ac.uk/files/meetings/KoopmanNotes.1575558616.pdfhttps://fluids.ac.uk/files/meetings/KoopmanNotes. 1575558616.pdf.
[3] Brunton, S.L. and Kutz, J.N. (2019). Data-driven science and engineering: Machine learning, dynamical systems, and control, Cambridge University Press.
[4] Lusch, B., Kutz, J.N., and Brunton, S.L. (2018). Deep learning for universal linear embeddings of nonlinear dynamics, Nature Communications. 9. doi:10.1038/s41467-018-07210-0
[5] Prosise, J. (2022). Applied machine learning and ai for engineers, O’Reilly Media.
[6] Shi, H. and Meng, M. Q.H. (2022). Deep koopman operator with control for nonlinear systems, IEEE Robotics and Automation Letters. 7(3):7700--7707. doi:10.1109/LRA.2022.3184036
[7] Slotine, J.-J.E. and Li, W. (1991). Applied nonlinear control, Prentice-Hall.
[8] X.Wang, Y.K. and Cao, Y. (2021). Deep koopman operator based model predictive control for nonlinear robotics systems, 6th IEEE Intl. Conf. on Advanced Robotics and Mechatronics (ICARM). pages 931--936. doi:10.1109/ICARM52023.2021.9536053
[9] Y.Han, W.H. and Vaidya, U. (2020). Deep learning of koopman representation for control, IEEE Conference on Decision and Control (CDC). 59:1890--1895. doi:10.1109/CDC42340.2020.9304238
BibTeX:
@article{MIC-2025-4-3,
title={{Physics Informed Fully Embedded Koopman Operator-based Optimal Control of Two-Link Robotic System}},
author={Andersen, Jeppe H. and Berakoetxea, Jokin L. and Kokotovic, Stas and Johansen, Per},
journal={Modeling, Identification and Control},
volume={46},
number={4},
pages={163--170},
year={2025},
doi={10.4173/mic.2025.4.3},
publisher={Norwegian Society of Automatic Control}
};