Sample Complexity of Linear Quadratic Gaussian (LQG) Control for Output Feedback Systems

Yang Zheng, Luca Furieri, Maryam Kamgarpour, Na Li
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:559-570, 2021.

Abstract

This paper studies a class of partially observed Linear Quadratic Gaussian (LQG) problems with unknown dynamics. We establish an end-to-end sample complexity bound on learning a robust LQG controller for open-loop stable plants. This is achieved using a robust synthesis procedure, where we first estimate a model from a single input-output trajectory of finite length, identify an H-infinity bound on the estimation error, and then design a robust controller using the estimated model and its quantified uncertainty. Our synthesis procedure leverages a recent control tool called Input-Output Parameterization (IOP) that enables robust controller design using convex optimization. For open-loop stable systems, we prove that the LQG performance degrades linearly with respect to the model estimation error using the proposed synthesis procedure. Despite the hidden states in the LQG problem, the achieved scaling matches previous results on learning Linear Quadratic Regulator (LQR) controllers with full state observations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-zheng21b, title = {Sample Complexity of Linear Quadratic Gaussian ({LQG}) Control for Output Feedback Systems}, author = {Zheng, Yang and Furieri, Luca and Kamgarpour, Maryam and Li, Na}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {559--570}, year = {2021}, editor = {Jadbabaie, Ali and Lygeros, John and Pappas, George J. and A. Parrilo, Pablo and Recht, Benjamin and Tomlin, Claire J. and Zeilinger, Melanie N.}, volume = {144}, series = {Proceedings of Machine Learning Research}, month = {07 -- 08 June}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v144/zheng21b/zheng21b.pdf}, url = {https://proceedings.mlr.press/v144/zheng21b.html}, abstract = {This paper studies a class of partially observed Linear Quadratic Gaussian (LQG) problems with unknown dynamics. We establish an end-to-end sample complexity bound on learning a robust LQG controller for open-loop stable plants. This is achieved using a robust synthesis procedure, where we first estimate a model from a single input-output trajectory of finite length, identify an H-infinity bound on the estimation error, and then design a robust controller using the estimated model and its quantified uncertainty. Our synthesis procedure leverages a recent control tool called Input-Output Parameterization (IOP) that enables robust controller design using convex optimization. For open-loop stable systems, we prove that the LQG performance degrades linearly with respect to the model estimation error using the proposed synthesis procedure. Despite the hidden states in the LQG problem, the achieved scaling matches previous results on learning Linear Quadratic Regulator (LQR) controllers with full state observations.} }
Endnote
%0 Conference Paper %T Sample Complexity of Linear Quadratic Gaussian (LQG) Control for Output Feedback Systems %A Yang Zheng %A Luca Furieri %A Maryam Kamgarpour %A Na Li %B Proceedings of the 3rd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2021 %E Ali Jadbabaie %E John Lygeros %E George J. Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire J. Tomlin %E Melanie N. Zeilinger %F pmlr-v144-zheng21b %I PMLR %P 559--570 %U https://proceedings.mlr.press/v144/zheng21b.html %V 144 %X This paper studies a class of partially observed Linear Quadratic Gaussian (LQG) problems with unknown dynamics. We establish an end-to-end sample complexity bound on learning a robust LQG controller for open-loop stable plants. This is achieved using a robust synthesis procedure, where we first estimate a model from a single input-output trajectory of finite length, identify an H-infinity bound on the estimation error, and then design a robust controller using the estimated model and its quantified uncertainty. Our synthesis procedure leverages a recent control tool called Input-Output Parameterization (IOP) that enables robust controller design using convex optimization. For open-loop stable systems, we prove that the LQG performance degrades linearly with respect to the model estimation error using the proposed synthesis procedure. Despite the hidden states in the LQG problem, the achieved scaling matches previous results on learning Linear Quadratic Regulator (LQR) controllers with full state observations.
APA
Zheng, Y., Furieri, L., Kamgarpour, M. & Li, N.. (2021). Sample Complexity of Linear Quadratic Gaussian (LQG) Control for Output Feedback Systems. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:559-570 Available from https://proceedings.mlr.press/v144/zheng21b.html.

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