Contraction $\\mathcal{L}_1$-Adaptive Control using Gaussian Processes

Aditya Gahlawat, Arun Lakshmanan, Lin Song, Andrew Patterson, Zhuohuan Wu, Naira Hovakimyan, Evangelos A. Theodorou
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:1027-1040, 2021.

Abstract

We present a control framework that enables safe simultaneous learning and control for systems subject to uncertainties. The two main constituents are contraction theory-based $\mathcal{L}_1$-adaptive ($\mathcal{CL}_1$) control and Bayesian learning in the form of Gaussian process (GP) regression. The $\mathcal{CL}_1$ controller ensures that control objectives are met while providing safety certificates. Furthermore, the controller incorporates any available data into GP models of uncertainties, which improves performance and enables the motion planner to achieve optimality safely. This way, the safe operation of the system is always guaranteed, even during the learning transients.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-gahlawat21a, title = {Contraction $\mathcal{L}_1$-Adaptive Control using Gaussian Processes}, author = {Gahlawat, Aditya and Lakshmanan, Arun and Song, Lin and Patterson, Andrew and Wu, Zhuohuan and Hovakimyan, Naira and Theodorou, Evangelos A.}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {1027--1040}, 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/gahlawat21a/gahlawat21a.pdf}, url = {https://proceedings.mlr.press/v144/gahlawat21a.html}, abstract = { We present a control framework that enables safe simultaneous learning and control for systems subject to uncertainties. The two main constituents are contraction theory-based $\mathcal{L}_1$-adaptive ($\mathcal{CL}_1$) control and Bayesian learning in the form of Gaussian process (GP) regression. The $\mathcal{CL}_1$ controller ensures that control objectives are met while providing safety certificates. Furthermore, the controller incorporates any available data into GP models of uncertainties, which improves performance and enables the motion planner to achieve optimality safely. This way, the safe operation of the system is always guaranteed, even during the learning transients.} }
Endnote
%0 Conference Paper %T Contraction $\\mathcal{L}_1$-Adaptive Control using Gaussian Processes %A Aditya Gahlawat %A Arun Lakshmanan %A Lin Song %A Andrew Patterson %A Zhuohuan Wu %A Naira Hovakimyan %A Evangelos A. Theodorou %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-gahlawat21a %I PMLR %P 1027--1040 %U https://proceedings.mlr.press/v144/gahlawat21a.html %V 144 %X We present a control framework that enables safe simultaneous learning and control for systems subject to uncertainties. The two main constituents are contraction theory-based $\mathcal{L}_1$-adaptive ($\mathcal{CL}_1$) control and Bayesian learning in the form of Gaussian process (GP) regression. The $\mathcal{CL}_1$ controller ensures that control objectives are met while providing safety certificates. Furthermore, the controller incorporates any available data into GP models of uncertainties, which improves performance and enables the motion planner to achieve optimality safely. This way, the safe operation of the system is always guaranteed, even during the learning transients.
APA
Gahlawat, A., Lakshmanan, A., Song, L., Patterson, A., Wu, Z., Hovakimyan, N. & Theodorou, E.A.. (2021). Contraction $\\mathcal{L}_1$-Adaptive Control using Gaussian Processes. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:1027-1040 Available from https://proceedings.mlr.press/v144/gahlawat21a.html.

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