Robust Online Control with Model Misspecification

Udaya Ghai, Xinyi Chen, Elad Hazan, Alexandre Megretski
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:1163-1175, 2022.

Abstract

We study online control of an unknown nonlinear dynamical system that is approximated by a time-invariant linear system with model misspecification. Our study focuses on robustness, a measure of how much deviation from the assumed linear approximation can be tolerated by a controller while maintaining finite L2-gain. A basic methodology to analyze robustness is via the small gain theorem. However, as an implication of recent lower bounds on adaptive control, this method can only yield robustness that is exponentially small in the dimension of the system and its parametric uncertainty. The work of Cusumano and Poolla (1988) shows that much better robustness can be obtained, but the control algorithm is inefficient, taking exponential time in the worst case. In this paper we investigate whether there exists an efficient algorithm with provable robustness beyond the small gain theorem. We demonstrate that for a fully actuated system, this is indeed attainable. We give an efficient controller that can tolerate robustness that is polynomial in the dimension and independent of the parametric uncertainty; furthermore, the controller obtains an L2-gain whose dimension dependence is near optimal.

Cite this Paper

BibTeX
@InProceedings{pmlr-v168-ghai22a, title = {Robust Online Control with Model Misspecification}, author = {Ghai, Udaya and Chen, Xinyi and Hazan, Elad and Megretski, Alexandre}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {1163--1175}, 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/ghai22a/ghai22a.pdf}, url = {https://proceedings.mlr.press/v168/ghai22a.html}, abstract = {We study online control of an unknown nonlinear dynamical system that is approximated by a time-invariant linear system with model misspecification. Our study focuses on robustness, a measure of how much deviation from the assumed linear approximation can be tolerated by a controller while maintaining finite L2-gain. A basic methodology to analyze robustness is via the small gain theorem. However, as an implication of recent lower bounds on adaptive control, this method can only yield robustness that is exponentially small in the dimension of the system and its parametric uncertainty. The work of Cusumano and Poolla (1988) shows that much better robustness can be obtained, but the control algorithm is inefficient, taking exponential time in the worst case. In this paper we investigate whether there exists an efficient algorithm with provable robustness beyond the small gain theorem. We demonstrate that for a fully actuated system, this is indeed attainable. We give an efficient controller that can tolerate robustness that is polynomial in the dimension and independent of the parametric uncertainty; furthermore, the controller obtains an L2-gain whose dimension dependence is near optimal.} }
Endnote
%0 Conference Paper %T Robust Online Control with Model Misspecification %A Udaya Ghai %A Xinyi Chen %A Elad Hazan %A Alexandre Megretski %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-ghai22a %I PMLR %P 1163--1175 %U https://proceedings.mlr.press/v168/ghai22a.html %V 168 %X We study online control of an unknown nonlinear dynamical system that is approximated by a time-invariant linear system with model misspecification. Our study focuses on robustness, a measure of how much deviation from the assumed linear approximation can be tolerated by a controller while maintaining finite L2-gain. A basic methodology to analyze robustness is via the small gain theorem. However, as an implication of recent lower bounds on adaptive control, this method can only yield robustness that is exponentially small in the dimension of the system and its parametric uncertainty. The work of Cusumano and Poolla (1988) shows that much better robustness can be obtained, but the control algorithm is inefficient, taking exponential time in the worst case. In this paper we investigate whether there exists an efficient algorithm with provable robustness beyond the small gain theorem. We demonstrate that for a fully actuated system, this is indeed attainable. We give an efficient controller that can tolerate robustness that is polynomial in the dimension and independent of the parametric uncertainty; furthermore, the controller obtains an L2-gain whose dimension dependence is near optimal.
APA
Ghai, U., Chen, X., Hazan, E. & Megretski, A.. (2022). Robust Online Control with Model Misspecification. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:1163-1175 Available from https://proceedings.mlr.press/v168/ghai22a.html.

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