Probabilistic robust linear quadratic regulators with Gaussian processes

Alexander von Rohr, Matthias Neumann-Brosig, Sebastian Trimpe
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:324-335, 2021.

Abstract

Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. While learning-based control has the potential to yield superior performance in demanding applications, robustness to uncertainty remains an important challenge. Since Bayesian methods quantify uncertainty of the learning results, it is natural to incorporate these uncertainties in a robust design. In contrast to most state-of-the-art approaches that consider worst-case estimates, we leverage the learning methods’ posterior distribution in the controller synthesis. The result is a more informed and thus efficient trade-off between performance and robustness. We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin. The formulation is based on a recently proposed algorithm for linear quadratic control synthesis, which we extend by giving probabilistic robustness guarantees in the form of credibility bounds for the system’s stability. Comparisons to existing methods based on worst-case and certainty-equivalence designs reveal superior performance and robustness properties of the proposed method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-rohr21a, title = {Probabilistic robust linear quadratic regulators with Gaussian processes}, author = {von Rohr, Alexander and Neumann-Brosig, Matthias and Trimpe, Sebastian}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {324--335}, 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/rohr21a/rohr21a.pdf}, url = {https://proceedings.mlr.press/v144/rohr21a.html}, abstract = {Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. While learning-based control has the potential to yield superior performance in demanding applications, robustness to uncertainty remains an important challenge. Since Bayesian methods quantify uncertainty of the learning results, it is natural to incorporate these uncertainties in a robust design. In contrast to most state-of-the-art approaches that consider worst-case estimates, we leverage the learning methods’ posterior distribution in the controller synthesis. The result is a more informed and thus efficient trade-off between performance and robustness. We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin. The formulation is based on a recently proposed algorithm for linear quadratic control synthesis, which we extend by giving probabilistic robustness guarantees in the form of credibility bounds for the system’s stability. Comparisons to existing methods based on worst-case and certainty-equivalence designs reveal superior performance and robustness properties of the proposed method.} }
Endnote
%0 Conference Paper %T Probabilistic robust linear quadratic regulators with Gaussian processes %A Alexander von Rohr %A Matthias Neumann-Brosig %A Sebastian Trimpe %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-rohr21a %I PMLR %P 324--335 %U https://proceedings.mlr.press/v144/rohr21a.html %V 144 %X Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. While learning-based control has the potential to yield superior performance in demanding applications, robustness to uncertainty remains an important challenge. Since Bayesian methods quantify uncertainty of the learning results, it is natural to incorporate these uncertainties in a robust design. In contrast to most state-of-the-art approaches that consider worst-case estimates, we leverage the learning methods’ posterior distribution in the controller synthesis. The result is a more informed and thus efficient trade-off between performance and robustness. We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin. The formulation is based on a recently proposed algorithm for linear quadratic control synthesis, which we extend by giving probabilistic robustness guarantees in the form of credibility bounds for the system’s stability. Comparisons to existing methods based on worst-case and certainty-equivalence designs reveal superior performance and robustness properties of the proposed method.
APA
von Rohr, A., Neumann-Brosig, M. & Trimpe, S.. (2021). Probabilistic robust linear quadratic regulators with Gaussian processes. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:324-335 Available from https://proceedings.mlr.press/v144/rohr21a.html.

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