Data-Enabled Gradient Flow as Feedback Controller: Regulation of Linear Dynamical Systems to Minimizers of Unknown Functions

Liliaokeawawa Cothren, Gianluca Bianchin, Emiliano Dall’Anese
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:234-247, 2022.

Abstract

This paper considers the problem of regulating a linear dynamical system to the solution of a convex optimization problem with an unknown or partially-known cost. We design a data-driven feedback controller – based on gradient flow dynamics – that (i) is augmented with learning methods to estimate the cost function based on infrequent (and possibly noisy) functional evaluations; and, concurrently, (ii) is designed to drive the inputs and outputs of the dynamical system to the optimizer of the problem. We derive sufficient conditions on the learning error and the controller gain to ensure that the error between the optimizer of the problem and the state of the closed-loop system is ultimately bounded; the error bound accounts for the functional estimation errors and the temporal variability of the unknown disturbance affecting the linear dynamical system. Our results directly lead to exponential input-to-state stability of the closed-loop system. The proposed method and the theoretical bounds are validated numerically.

Cite this Paper

BibTeX
@InProceedings{pmlr-v168-cothren22a, title = {Data-Enabled Gradient Flow as Feedback Controller: Regulation of Linear Dynamical Systems to Minimizers of Unknown Functions}, author = {Cothren, Liliaokeawawa and Bianchin, Gianluca and Dall'Anese, Emiliano}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {234--247}, year = {2022}, editor = {Firoozi, Roya and Mehr, Negar and Yel, Esen and Antonova, Rika and Bohg, Jeannette and Schwager, Mac and Kochenderfer, Mykel}, volume = {168}, series = {Proceedings of Machine Learning Research}, month = {23--24 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v168/cothren22a/cothren22a.pdf}, url = {https://proceedings.mlr.press/v168/cothren22a.html}, abstract = {This paper considers the problem of regulating a linear dynamical system to the solution of a convex optimization problem with an unknown or partially-known cost. We design a data-driven feedback controller – based on gradient flow dynamics – that (i) is augmented with learning methods to estimate the cost function based on infrequent (and possibly noisy) functional evaluations; and, concurrently, (ii) is designed to drive the inputs and outputs of the dynamical system to the optimizer of the problem. We derive sufficient conditions on the learning error and the controller gain to ensure that the error between the optimizer of the problem and the state of the closed-loop system is ultimately bounded; the error bound accounts for the functional estimation errors and the temporal variability of the unknown disturbance affecting the linear dynamical system. Our results directly lead to exponential input-to-state stability of the closed-loop system. The proposed method and the theoretical bounds are validated numerically.} }
Endnote
%0 Conference Paper %T Data-Enabled Gradient Flow as Feedback Controller: Regulation of Linear Dynamical Systems to Minimizers of Unknown Functions %A Liliaokeawawa Cothren %A Gianluca Bianchin %A Emiliano Dall’Anese %B Proceedings of The 4th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2022 %E Roya Firoozi %E Negar Mehr %E Esen Yel %E Rika Antonova %E Jeannette Bohg %E Mac Schwager %E Mykel Kochenderfer %F pmlr-v168-cothren22a %I PMLR %P 234--247 %U https://proceedings.mlr.press/v168/cothren22a.html %V 168 %X This paper considers the problem of regulating a linear dynamical system to the solution of a convex optimization problem with an unknown or partially-known cost. We design a data-driven feedback controller – based on gradient flow dynamics – that (i) is augmented with learning methods to estimate the cost function based on infrequent (and possibly noisy) functional evaluations; and, concurrently, (ii) is designed to drive the inputs and outputs of the dynamical system to the optimizer of the problem. We derive sufficient conditions on the learning error and the controller gain to ensure that the error between the optimizer of the problem and the state of the closed-loop system is ultimately bounded; the error bound accounts for the functional estimation errors and the temporal variability of the unknown disturbance affecting the linear dynamical system. Our results directly lead to exponential input-to-state stability of the closed-loop system. The proposed method and the theoretical bounds are validated numerically.
APA
Cothren, L., Bianchin, G. & Dall’Anese, E.. (2022). Data-Enabled Gradient Flow as Feedback Controller: Regulation of Linear Dynamical Systems to Minimizers of Unknown Functions. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:234-247 Available from https://proceedings.mlr.press/v168/cothren22a.html.

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