Parameter Optimization for Learning-based Control of Control-Affine Systems

Armin Lederer, Alexandre Capone, Sandra Hirche
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:465-475, 2020.

Abstract

Supervised machine learning is often applied to identify system dynamics where first principle methods fail. When combining learning with control methods, probabilistic regression is typically applied to increase robustness against learning errors and analyze the stability of the closed-loop system. Although this approach allows to formulate performance guarantees for many control techniques, the obtained bounds are usually conservative, and cannot be employed for efficient control parameter tuning. Therefore, we reformulate the parameter tuning problem using robust optimization with performance constraints based on Lyapunov theory. By relaxing the problem through scenario optimization we derive a provably optimal method for control parameter tuning. We demonstrate its flexibility and efficiency on parameter tuning problems for a feedback linearizing and a computed torque controller.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-lederer20a, title = {Parameter Optimization for Learning-based Control of Control-Affine Systems}, author = {Lederer, Armin and Capone, Alexandre and Hirche, Sandra}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {465--475}, 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/lederer20a/lederer20a.pdf}, url = {https://proceedings.mlr.press/v120/lederer20a.html}, abstract = {Supervised machine learning is often applied to identify system dynamics where first principle methods fail. When combining learning with control methods, probabilistic regression is typically applied to increase robustness against learning errors and analyze the stability of the closed-loop system. Although this approach allows to formulate performance guarantees for many control techniques, the obtained bounds are usually conservative, and cannot be employed for efficient control parameter tuning. Therefore, we reformulate the parameter tuning problem using robust optimization with performance constraints based on Lyapunov theory. By relaxing the problem through scenario optimization we derive a provably optimal method for control parameter tuning. We demonstrate its flexibility and efficiency on parameter tuning problems for a feedback linearizing and a computed torque controller.} }
Endnote
%0 Conference Paper %T Parameter Optimization for Learning-based Control of Control-Affine Systems %A Armin Lederer %A Alexandre Capone %A Sandra Hirche %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-lederer20a %I PMLR %P 465--475 %U https://proceedings.mlr.press/v120/lederer20a.html %V 120 %X Supervised machine learning is often applied to identify system dynamics where first principle methods fail. When combining learning with control methods, probabilistic regression is typically applied to increase robustness against learning errors and analyze the stability of the closed-loop system. Although this approach allows to formulate performance guarantees for many control techniques, the obtained bounds are usually conservative, and cannot be employed for efficient control parameter tuning. Therefore, we reformulate the parameter tuning problem using robust optimization with performance constraints based on Lyapunov theory. By relaxing the problem through scenario optimization we derive a provably optimal method for control parameter tuning. We demonstrate its flexibility and efficiency on parameter tuning problems for a feedback linearizing and a computed torque controller.
APA
Lederer, A., Capone, A. & Hirche, S.. (2020). Parameter Optimization for Learning-based Control of Control-Affine Systems. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:465-475 Available from https://proceedings.mlr.press/v120/lederer20a.html.

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