Sample Complexity of the Robust LQG Regulator with Coprime Factors Uncertainty

Yifei Zhang, Sourav Ukil, Ephraim Neimand, Serban Sabau, Myron Hohil
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:943-953, 2022.

Abstract

This paper addresses the end-to-end sample complexity bound for learning the H2 optimal controller (the Linear Quadratic Gaussian (LQG) problem) with unknown dynamics, for potentially unstable Linear Time Invariant (LTI) systems. The robust LQG synthesis procedure is performed by considering bounded additive model uncertainty on the coprime factors of the plant. The closed-loopidentification of the nominal model of the true plant is performed by constructing a Hankel-likematrix from a single time-series of noisy finite length input-output data, using the ordinary least squares algorithm from Sarkar and Rakhlin (2019). Next, an H$\infty$ bound on the estimated model error is provided and the robust controller is designed via convex optimization, much in the spirit of Mania et al. (2019) and Zheng et al. (2020b), while allowing for bounded additive uncertainty on the coprime factors of the model. Our conclusions are consistent with previous results on learning the LQG and LQR controllers.

Cite this Paper

BibTeX
@InProceedings{pmlr-v168-zhang22c, title = {Sample Complexity of the Robust LQG Regulator with Coprime Factors Uncertainty}, author = {Zhang, Yifei and Ukil, Sourav and Neimand, Ephraim and Sabau, Serban and Hohil, Myron}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {943--953}, 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/zhang22c/zhang22c.pdf}, url = {https://proceedings.mlr.press/v168/zhang22c.html}, abstract = {This paper addresses the end-to-end sample complexity bound for learning the H2 optimal controller (the Linear Quadratic Gaussian (LQG) problem) with unknown dynamics, for potentially unstable Linear Time Invariant (LTI) systems. The robust LQG synthesis procedure is performed by considering bounded additive model uncertainty on the coprime factors of the plant. The closed-loopidentification of the nominal model of the true plant is performed by constructing a Hankel-likematrix from a single time-series of noisy finite length input-output data, using the ordinary least squares algorithm from Sarkar and Rakhlin (2019). Next, an H$\infty$ bound on the estimated model error is provided and the robust controller is designed via convex optimization, much in the spirit of Mania et al. (2019) and Zheng et al. (2020b), while allowing for bounded additive uncertainty on the coprime factors of the model. Our conclusions are consistent with previous results on learning the LQG and LQR controllers.} }
Endnote
%0 Conference Paper %T Sample Complexity of the Robust LQG Regulator with Coprime Factors Uncertainty %A Yifei Zhang %A Sourav Ukil %A Ephraim Neimand %A Serban Sabau %A Myron Hohil %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-zhang22c %I PMLR %P 943--953 %U https://proceedings.mlr.press/v168/zhang22c.html %V 168 %X This paper addresses the end-to-end sample complexity bound for learning the H2 optimal controller (the Linear Quadratic Gaussian (LQG) problem) with unknown dynamics, for potentially unstable Linear Time Invariant (LTI) systems. The robust LQG synthesis procedure is performed by considering bounded additive model uncertainty on the coprime factors of the plant. The closed-loopidentification of the nominal model of the true plant is performed by constructing a Hankel-likematrix from a single time-series of noisy finite length input-output data, using the ordinary least squares algorithm from Sarkar and Rakhlin (2019). Next, an H$\infty$ bound on the estimated model error is provided and the robust controller is designed via convex optimization, much in the spirit of Mania et al. (2019) and Zheng et al. (2020b), while allowing for bounded additive uncertainty on the coprime factors of the model. Our conclusions are consistent with previous results on learning the LQG and LQR controllers.
APA
Zhang, Y., Ukil, S., Neimand, E., Sabau, S. & Hohil, M.. (2022). Sample Complexity of the Robust LQG Regulator with Coprime Factors Uncertainty. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:943-953 Available from https://proceedings.mlr.press/v168/zhang22c.html.

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