Data-driven distributionally robust LQR with multiplicative noise

Peter Coppens, Mathijs Schuurmans, Panagiotis Patrinos
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:521-530, 2020.

Abstract

We present a data-driven method for solving the linear quadratic regulator problem for systems with multiplicative disturbances, the distribution of which is only known through sample estimates. We adopt a distributionally robust approach to cast the controller synthesis problem as semidefinite programs. Using results from high dimensional statistics, the proposed methodology ensures that their solution provides mean-square stabilizing controllers with high probability even for low sample sizes. As sample size increases the closed-loop cost approaches that of the optimal controller produced when the distribution is known. We demonstrate the practical applicability and performance of the method through a numerical experiment.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-coppens20a, title = {Data-driven distributionally robust LQR with multiplicative noise}, author = {Coppens, Peter and Schuurmans, Mathijs and Patrinos, Panagiotis}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {521--530}, year = {2020}, editor = {Bayen, Alexandre M. and Jadbabaie, Ali and Pappas, George and Parrilo, Pablo A. and Recht, Benjamin and Tomlin, Claire and Zeilinger, Melanie}, volume = {120}, series = {Proceedings of Machine Learning Research}, month = {10--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v120/coppens20a/coppens20a.pdf}, url = {https://proceedings.mlr.press/v120/coppens20a.html}, abstract = {We present a data-driven method for solving the linear quadratic regulator problem for systems with multiplicative disturbances, the distribution of which is only known through sample estimates. We adopt a distributionally robust approach to cast the controller synthesis problem as semidefinite programs. Using results from high dimensional statistics, the proposed methodology ensures that their solution provides mean-square stabilizing controllers with high probability even for low sample sizes. As sample size increases the closed-loop cost approaches that of the optimal controller produced when the distribution is known. We demonstrate the practical applicability and performance of the method through a numerical experiment.} }
Endnote
%0 Conference Paper %T Data-driven distributionally robust LQR with multiplicative noise %A Peter Coppens %A Mathijs Schuurmans %A Panagiotis Patrinos %B Proceedings of the 2nd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2020 %E Alexandre M. Bayen %E Ali Jadbabaie %E George Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire Tomlin %E Melanie Zeilinger %F pmlr-v120-coppens20a %I PMLR %P 521--530 %U https://proceedings.mlr.press/v120/coppens20a.html %V 120 %X We present a data-driven method for solving the linear quadratic regulator problem for systems with multiplicative disturbances, the distribution of which is only known through sample estimates. We adopt a distributionally robust approach to cast the controller synthesis problem as semidefinite programs. Using results from high dimensional statistics, the proposed methodology ensures that their solution provides mean-square stabilizing controllers with high probability even for low sample sizes. As sample size increases the closed-loop cost approaches that of the optimal controller produced when the distribution is known. We demonstrate the practical applicability and performance of the method through a numerical experiment.
APA
Coppens, P., Schuurmans, M. & Patrinos, P.. (2020). Data-driven distributionally robust LQR with multiplicative noise. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:521-530 Available from https://proceedings.mlr.press/v120/coppens20a.html.

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