KPC: Learning-Based Model Predictive Control with Deterministic Guarantees

Emilio T. Maddalena, Paul Scharnhorst, Yuning Jiang, Colin N. Jones
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:1015-1026, 2021.

Abstract

We propose Kernel Predictive Control (KPC), a learning-based predictive control strategy that enjoys deterministic guarantees of safety. Noise-corrupted samples of the unknown system dynamics are used to learn several models through the formalism of non-parametric kernel regression. By treating each prediction step individually, we dispense with the need of propagating sets through highly non-linear maps, a procedure that often involves multiple conservative approximation steps. Finite-sample error bounds are then used to enforce state-feasibility by employing an efficient robust formulation. We then present a relaxation strategy that exploits on-line data to weaken the optimization problem constraints while preserving safety. Two numerical examples are provided to illustrate the applicability of the proposed control method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-maddalena21a, title = {{KPC}: Learning-Based Model Predictive Control with Deterministic Guarantees}, author = {Maddalena, Emilio T. and Scharnhorst, Paul and Jiang, Yuning and Jones, Colin N.}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {1015--1026}, 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/maddalena21a/maddalena21a.pdf}, url = {https://proceedings.mlr.press/v144/maddalena21a.html}, abstract = {We propose Kernel Predictive Control (KPC), a learning-based predictive control strategy that enjoys deterministic guarantees of safety. Noise-corrupted samples of the unknown system dynamics are used to learn several models through the formalism of non-parametric kernel regression. By treating each prediction step individually, we dispense with the need of propagating sets through highly non-linear maps, a procedure that often involves multiple conservative approximation steps. Finite-sample error bounds are then used to enforce state-feasibility by employing an efficient robust formulation. We then present a relaxation strategy that exploits on-line data to weaken the optimization problem constraints while preserving safety. Two numerical examples are provided to illustrate the applicability of the proposed control method.} }
Endnote
%0 Conference Paper %T KPC: Learning-Based Model Predictive Control with Deterministic Guarantees %A Emilio T. Maddalena %A Paul Scharnhorst %A Yuning Jiang %A Colin N. Jones %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-maddalena21a %I PMLR %P 1015--1026 %U https://proceedings.mlr.press/v144/maddalena21a.html %V 144 %X We propose Kernel Predictive Control (KPC), a learning-based predictive control strategy that enjoys deterministic guarantees of safety. Noise-corrupted samples of the unknown system dynamics are used to learn several models through the formalism of non-parametric kernel regression. By treating each prediction step individually, we dispense with the need of propagating sets through highly non-linear maps, a procedure that often involves multiple conservative approximation steps. Finite-sample error bounds are then used to enforce state-feasibility by employing an efficient robust formulation. We then present a relaxation strategy that exploits on-line data to weaken the optimization problem constraints while preserving safety. Two numerical examples are provided to illustrate the applicability of the proposed control method.
APA
Maddalena, E.T., Scharnhorst, P., Jiang, Y. & Jones, C.N.. (2021). KPC: Learning-Based Model Predictive Control with Deterministic Guarantees. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:1015-1026 Available from https://proceedings.mlr.press/v144/maddalena21a.html.

Related Material