Physics-informed Gaussian Processes as Linear Model Predictive Controller

Jörn Tebbe, Andreas Besginow, Markus Lange-Hegermann
Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, PMLR 283:1434-1446, 2025.

Abstract

We introduce a novel algorithm for controlling linear time invariant systems in a tracking problem. The controller is based on a Gaussian Process (GP) whose realizations satisfy a system of linear ordinary differential equations with constant coefficients. Control inputs for tracking are determined by conditioning the prior GP on the setpoints, i.e. control as inference. The resulting Model Predictive Control scheme incorporates pointwise soft constraints by introducing virtual setpoints to the posterior Gaussian process. We show theoretically that our controller satisfies open-loop stability for the optimal control problem by leveraging general results from Bayesian inference and demonstrate this result in a numerical example.

Cite this Paper

BibTeX
@InProceedings{pmlr-v283-tebbe25a, title = {Physics-informed Gaussian Processes as Linear Model Predictive Controller}, author = {Tebbe, J{\"o}rn and Besginow, Andreas and Lange-Hegermann, Markus}, booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference}, pages = {1434--1446}, year = {2025}, editor = {Ozay, Necmiye and Balzano, Laura and Panagou, Dimitra and Abate, Alessandro}, volume = {283}, series = {Proceedings of Machine Learning Research}, month = {04--06 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v283/main/assets/tebbe25a/tebbe25a.pdf}, url = {https://proceedings.mlr.press/v283/tebbe25a.html}, abstract = {We introduce a novel algorithm for controlling linear time invariant systems in a tracking problem. The controller is based on a Gaussian Process (GP) whose realizations satisfy a system of linear ordinary differential equations with constant coefficients. Control inputs for tracking are determined by conditioning the prior GP on the setpoints, i.e. control as inference. The resulting Model Predictive Control scheme incorporates pointwise soft constraints by introducing virtual setpoints to the posterior Gaussian process. We show theoretically that our controller satisfies open-loop stability for the optimal control problem by leveraging general results from Bayesian inference and demonstrate this result in a numerical example.} }
Endnote
%0 Conference Paper %T Physics-informed Gaussian Processes as Linear Model Predictive Controller %A Jörn Tebbe %A Andreas Besginow %A Markus Lange-Hegermann %B Proceedings of the 7th Annual Learning for Dynamics \& Control Conference %C Proceedings of Machine Learning Research %D 2025 %E Necmiye Ozay %E Laura Balzano %E Dimitra Panagou %E Alessandro Abate %F pmlr-v283-tebbe25a %I PMLR %P 1434--1446 %U https://proceedings.mlr.press/v283/tebbe25a.html %V 283 %X We introduce a novel algorithm for controlling linear time invariant systems in a tracking problem. The controller is based on a Gaussian Process (GP) whose realizations satisfy a system of linear ordinary differential equations with constant coefficients. Control inputs for tracking are determined by conditioning the prior GP on the setpoints, i.e. control as inference. The resulting Model Predictive Control scheme incorporates pointwise soft constraints by introducing virtual setpoints to the posterior Gaussian process. We show theoretically that our controller satisfies open-loop stability for the optimal control problem by leveraging general results from Bayesian inference and demonstrate this result in a numerical example.
APA
Tebbe, J., Besginow, A. & Lange-Hegermann, M.. (2025). Physics-informed Gaussian Processes as Linear Model Predictive Controller. Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, in Proceedings of Machine Learning Research 283:1434-1446 Available from https://proceedings.mlr.press/v283/tebbe25a.html.

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