Flow matching for stochastic linear control systems

Yuhang Mei, Mohammad Al-Jarrah, Amirhossein Taghvaei, Yongxin Chen
Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, PMLR 283:484-496, 2025.

Abstract

This paper addresses the problem of steering an initial probability distribution to a target probability distribution through a deterministic or stochastic linear control system. Our proposed approach is inspired by the flow matching methodology, with the difference that we can only affect the flow through the given control channels. The motivation for the problem comes from applications such as robotic swarms and stochastic thermodynamics, where the state of the system, modeled as a probability distribution, should be steered to a desired target configuration. The feedback control law that achieves the task is characterized as the conditional expectation of the control inputs for the stochastic bridges that respect the given control system dynamics. Explicit forms are derived for Gaussian and mixture of Gaussian settings, and a numerical procedure is presented to approximate the control law in the general setting.

Cite this Paper

BibTeX
@InProceedings{pmlr-v283-mei25a, title = {Flow matching for stochastic linear control systems}, author = {Mei, Yuhang and Al-Jarrah, Mohammad and Taghvaei, Amirhossein and Chen, Yongxin}, booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference}, pages = {484--496}, 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/mei25a/mei25a.pdf}, url = {https://proceedings.mlr.press/v283/mei25a.html}, abstract = {This paper addresses the problem of steering an initial probability distribution to a target probability distribution through a deterministic or stochastic linear control system. Our proposed approach is inspired by the flow matching methodology, with the difference that we can only affect the flow through the given control channels. The motivation for the problem comes from applications such as robotic swarms and stochastic thermodynamics, where the state of the system, modeled as a probability distribution, should be steered to a desired target configuration. The feedback control law that achieves the task is characterized as the conditional expectation of the control inputs for the stochastic bridges that respect the given control system dynamics. Explicit forms are derived for Gaussian and mixture of Gaussian settings, and a numerical procedure is presented to approximate the control law in the general setting.} }
Endnote
%0 Conference Paper %T Flow matching for stochastic linear control systems %A Yuhang Mei %A Mohammad Al-Jarrah %A Amirhossein Taghvaei %A Yongxin Chen %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-mei25a %I PMLR %P 484--496 %U https://proceedings.mlr.press/v283/mei25a.html %V 283 %X This paper addresses the problem of steering an initial probability distribution to a target probability distribution through a deterministic or stochastic linear control system. Our proposed approach is inspired by the flow matching methodology, with the difference that we can only affect the flow through the given control channels. The motivation for the problem comes from applications such as robotic swarms and stochastic thermodynamics, where the state of the system, modeled as a probability distribution, should be steered to a desired target configuration. The feedback control law that achieves the task is characterized as the conditional expectation of the control inputs for the stochastic bridges that respect the given control system dynamics. Explicit forms are derived for Gaussian and mixture of Gaussian settings, and a numerical procedure is presented to approximate the control law in the general setting.
APA
Mei, Y., Al-Jarrah, M., Taghvaei, A. & Chen, Y.. (2025). Flow matching for stochastic linear control systems. Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, in Proceedings of Machine Learning Research 283:484-496 Available from https://proceedings.mlr.press/v283/mei25a.html.

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