Frequency Domain Gaussian Process Models for $H^∞$ Uncertainties

Alex Devonport, Peter Seiler, Murat Arcak
Proceedings of The 5th Annual Learning for Dynamics and Control Conference, PMLR 211:1046-1057, 2023.

Abstract

Complex-valued Gaussian processes are used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same model could be used for probabilistic robust control, allowing for robustly safe learning. We investigate sufficient conditions for a general complex-domain Gaussian process to have this property. For the special case of processes whose Hermitian covariance is stationary, we provide an explicit parameterization of the covariance structure in terms of a summable sequence of nonnegative numbers.

Cite this Paper

BibTeX
@InProceedings{pmlr-v211-devonport23a, title = {Frequency Domain Gaussian Process Models for $H^∞$ Uncertainties}, author = {Devonport, Alex and Seiler, Peter and Arcak, Murat}, booktitle = {Proceedings of The 5th Annual Learning for Dynamics and Control Conference}, pages = {1046--1057}, year = {2023}, editor = {Matni, Nikolai and Morari, Manfred and Pappas, George J.}, volume = {211}, series = {Proceedings of Machine Learning Research}, month = {15--16 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v211/devonport23a/devonport23a.pdf}, url = {https://proceedings.mlr.press/v211/devonport23a.html}, abstract = {Complex-valued Gaussian processes are used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same model could be used for probabilistic robust control, allowing for robustly safe learning. We investigate sufficient conditions for a general complex-domain Gaussian process to have this property. For the special case of processes whose Hermitian covariance is stationary, we provide an explicit parameterization of the covariance structure in terms of a summable sequence of nonnegative numbers. } }
Endnote
%0 Conference Paper %T Frequency Domain Gaussian Process Models for $H^∞$ Uncertainties %A Alex Devonport %A Peter Seiler %A Murat Arcak %B Proceedings of The 5th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2023 %E Nikolai Matni %E Manfred Morari %E George J. Pappas %F pmlr-v211-devonport23a %I PMLR %P 1046--1057 %U https://proceedings.mlr.press/v211/devonport23a.html %V 211 %X Complex-valued Gaussian processes are used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same model could be used for probabilistic robust control, allowing for robustly safe learning. We investigate sufficient conditions for a general complex-domain Gaussian process to have this property. For the special case of processes whose Hermitian covariance is stationary, we provide an explicit parameterization of the covariance structure in terms of a summable sequence of nonnegative numbers.
APA
Devonport, A., Seiler, P. & Arcak, M.. (2023). Frequency Domain Gaussian Process Models for $H^∞$ Uncertainties. Proceedings of The 5th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 211:1046-1057 Available from https://proceedings.mlr.press/v211/devonport23a.html.

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