Optimistic robust linear quadratic dual control

Jack Umenberger, Thomas B. Schön
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:550-560, 2020.

Abstract

Recent work by Mania et al. has proved that certainty equivalent control achieves optimal regret for linear systems and quadratic costs. However, when parameter uncertainty is large, certainty equivalence cannot be relied upon to stabilize the true, unknown system. In this paper, we present a dual control strategy that attempts to combine the performance of certainty equivalence, with the practical utility of robustness. The formulation preserves structure in the representation of parametric uncertainty, which allows the controller to target reduction of uncertainty in the parameters that ‘matter most’ for the control task, while robustly stabilizing the uncertain system. Control synthesis proceeds via convex optimization, and the method is illustrated on a numerical example.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-umenberger20a, title = {Optimistic robust linear quadratic dual control}, author = {Umenberger, Jack and Sch\"on, Thomas B.}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {550--560}, 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/umenberger20a/umenberger20a.pdf}, url = {https://proceedings.mlr.press/v120/umenberger20a.html}, abstract = {Recent work by Mania et al. has proved that certainty equivalent control achieves optimal regret for linear systems and quadratic costs. However, when parameter uncertainty is large, certainty equivalence cannot be relied upon to stabilize the true, unknown system. In this paper, we present a dual control strategy that attempts to combine the performance of certainty equivalence, with the practical utility of robustness. The formulation preserves structure in the representation of parametric uncertainty, which allows the controller to target reduction of uncertainty in the parameters that ‘matter most’ for the control task, while robustly stabilizing the uncertain system. Control synthesis proceeds via convex optimization, and the method is illustrated on a numerical example.} }
Endnote
%0 Conference Paper %T Optimistic robust linear quadratic dual control %A Jack Umenberger %A Thomas B. Schön %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-umenberger20a %I PMLR %P 550--560 %U https://proceedings.mlr.press/v120/umenberger20a.html %V 120 %X Recent work by Mania et al. has proved that certainty equivalent control achieves optimal regret for linear systems and quadratic costs. However, when parameter uncertainty is large, certainty equivalence cannot be relied upon to stabilize the true, unknown system. In this paper, we present a dual control strategy that attempts to combine the performance of certainty equivalence, with the practical utility of robustness. The formulation preserves structure in the representation of parametric uncertainty, which allows the controller to target reduction of uncertainty in the parameters that ‘matter most’ for the control task, while robustly stabilizing the uncertain system. Control synthesis proceeds via convex optimization, and the method is illustrated on a numerical example.
APA
Umenberger, J. & Schön, T.B.. (2020). Optimistic robust linear quadratic dual control. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:550-560 Available from https://proceedings.mlr.press/v120/umenberger20a.html.

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