Data-Efficient Model Learning for Control with Jacobian-Regularized Dynamic-Mode Decomposition

Brian Edward Jackson, Jeong Hun Lee, Kevin Tracy, Zachary Manchester
Proceedings of The 6th Conference on Robot Learning, PMLR 205:2273-2283, 2023.

Abstract

We present a data-efficient algorithm for learning models for model-predictive control (MPC). Our approach, Jacobian-Regularized Dynamic-Mode Decomposition (JDMD), offers improved sample efficiency over traditional Koopman approaches based on Dynamic-Mode Decomposition (DMD) by leveraging Jacobian information from an approximate prior model of the system, and improved tracking performance over traditional model-based MPC. We demonstrate JDMD’s ability to quickly learn bilinear Koopman dynamics representations across several realistic examples in simulation, including a perching maneuver for a fixed-wing aircraft with an empirically derived high-fidelity physics model. In all cases, we show that the models learned by JDMD provide superior tracking and generalization performance within a model-predictive control framework, even in the presence of significant model mismatch, when compared to approximate prior models and models learned by standard Extended DMD (EDMD).

Cite this Paper

BibTeX
@InProceedings{pmlr-v205-jackson23a, title = {Data-Efficient Model Learning for Control with Jacobian-Regularized Dynamic-Mode Decomposition}, author = {Jackson, Brian Edward and Lee, Jeong Hun and Tracy, Kevin and Manchester, Zachary}, booktitle = {Proceedings of The 6th Conference on Robot Learning}, pages = {2273--2283}, year = {2023}, editor = {Liu, Karen and Kulic, Dana and Ichnowski, Jeff}, volume = {205}, series = {Proceedings of Machine Learning Research}, month = {14--18 Dec}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v205/jackson23a/jackson23a.pdf}, url = {https://proceedings.mlr.press/v205/jackson23a.html}, abstract = {We present a data-efficient algorithm for learning models for model-predictive control (MPC). Our approach, Jacobian-Regularized Dynamic-Mode Decomposition (JDMD), offers improved sample efficiency over traditional Koopman approaches based on Dynamic-Mode Decomposition (DMD) by leveraging Jacobian information from an approximate prior model of the system, and improved tracking performance over traditional model-based MPC. We demonstrate JDMD’s ability to quickly learn bilinear Koopman dynamics representations across several realistic examples in simulation, including a perching maneuver for a fixed-wing aircraft with an empirically derived high-fidelity physics model. In all cases, we show that the models learned by JDMD provide superior tracking and generalization performance within a model-predictive control framework, even in the presence of significant model mismatch, when compared to approximate prior models and models learned by standard Extended DMD (EDMD).} }
Endnote
%0 Conference Paper %T Data-Efficient Model Learning for Control with Jacobian-Regularized Dynamic-Mode Decomposition %A Brian Edward Jackson %A Jeong Hun Lee %A Kevin Tracy %A Zachary Manchester %B Proceedings of The 6th Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2023 %E Karen Liu %E Dana Kulic %E Jeff Ichnowski %F pmlr-v205-jackson23a %I PMLR %P 2273--2283 %U https://proceedings.mlr.press/v205/jackson23a.html %V 205 %X We present a data-efficient algorithm for learning models for model-predictive control (MPC). Our approach, Jacobian-Regularized Dynamic-Mode Decomposition (JDMD), offers improved sample efficiency over traditional Koopman approaches based on Dynamic-Mode Decomposition (DMD) by leveraging Jacobian information from an approximate prior model of the system, and improved tracking performance over traditional model-based MPC. We demonstrate JDMD’s ability to quickly learn bilinear Koopman dynamics representations across several realistic examples in simulation, including a perching maneuver for a fixed-wing aircraft with an empirically derived high-fidelity physics model. In all cases, we show that the models learned by JDMD provide superior tracking and generalization performance within a model-predictive control framework, even in the presence of significant model mismatch, when compared to approximate prior models and models learned by standard Extended DMD (EDMD).
APA
Jackson, B.E., Lee, J.H., Tracy, K. & Manchester, Z.. (2023). Data-Efficient Model Learning for Control with Jacobian-Regularized Dynamic-Mode Decomposition. Proceedings of The 6th Conference on Robot Learning, in Proceedings of Machine Learning Research 205:2273-2283 Available from https://proceedings.mlr.press/v205/jackson23a.html.

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