Robust Data-Driven Output Feedback Control via Bootstrapped Multiplicative Noise

Benjamin Gravell, Iman Shames, Tyler Summers
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:650-662, 2022.

Abstract

We propose a robust data-driven output feedback control algorithm that explicitly incorporates inherent finite-sample model estimate uncertainties into the control design. The algorithm has three components: (1) a subspace identification nominal model estimator; (2) a bootstrap resampling method that quantifies non-asymptotic variance of the nominal model estimate; and (3) a non-conventional robust control design method comprising a coupled optimal dynamic output feedback filter and controller with multiplicative noise. A key advantage of the proposed approach is that the system identification and robust control design procedures both use stochastic uncertainty representations, so that the actual inherent statistical estimation uncertainty directly aligns with the uncertainty the robust controller is being designed against. Moreover, the control design method accommodates a highly structured uncertainty representation that can capture uncertainty shape more effectively than existing approaches. We show through numerical experiments that the proposed robust data-driven output feedback controller can significantly outperform a certainty equivalent controller on various measures of sample complexity and stability robustness.

Cite this Paper

BibTeX
@InProceedings{pmlr-v168-gravell22a, title = {Robust Data-Driven Output Feedback Control via Bootstrapped Multiplicative Noise}, author = {Gravell, Benjamin and Shames, Iman and Summers, Tyler}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {650--662}, 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/gravell22a/gravell22a.pdf}, url = {https://proceedings.mlr.press/v168/gravell22a.html}, abstract = {We propose a robust data-driven output feedback control algorithm that explicitly incorporates inherent finite-sample model estimate uncertainties into the control design. The algorithm has three components: (1) a subspace identification nominal model estimator; (2) a bootstrap resampling method that quantifies non-asymptotic variance of the nominal model estimate; and (3) a non-conventional robust control design method comprising a coupled optimal dynamic output feedback filter and controller with multiplicative noise. A key advantage of the proposed approach is that the system identification and robust control design procedures both use stochastic uncertainty representations, so that the actual inherent statistical estimation uncertainty directly aligns with the uncertainty the robust controller is being designed against. Moreover, the control design method accommodates a highly structured uncertainty representation that can capture uncertainty shape more effectively than existing approaches. We show through numerical experiments that the proposed robust data-driven output feedback controller can significantly outperform a certainty equivalent controller on various measures of sample complexity and stability robustness.} }
Endnote
%0 Conference Paper %T Robust Data-Driven Output Feedback Control via Bootstrapped Multiplicative Noise %A Benjamin Gravell %A Iman Shames %A Tyler Summers %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-gravell22a %I PMLR %P 650--662 %U https://proceedings.mlr.press/v168/gravell22a.html %V 168 %X We propose a robust data-driven output feedback control algorithm that explicitly incorporates inherent finite-sample model estimate uncertainties into the control design. The algorithm has three components: (1) a subspace identification nominal model estimator; (2) a bootstrap resampling method that quantifies non-asymptotic variance of the nominal model estimate; and (3) a non-conventional robust control design method comprising a coupled optimal dynamic output feedback filter and controller with multiplicative noise. A key advantage of the proposed approach is that the system identification and robust control design procedures both use stochastic uncertainty representations, so that the actual inherent statistical estimation uncertainty directly aligns with the uncertainty the robust controller is being designed against. Moreover, the control design method accommodates a highly structured uncertainty representation that can capture uncertainty shape more effectively than existing approaches. We show through numerical experiments that the proposed robust data-driven output feedback controller can significantly outperform a certainty equivalent controller on various measures of sample complexity and stability robustness.
APA
Gravell, B., Shames, I. & Summers, T.. (2022). Robust Data-Driven Output Feedback Control via Bootstrapped Multiplicative Noise. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:650-662 Available from https://proceedings.mlr.press/v168/gravell22a.html.

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