Frequency Domain Gaussian Process Models for $h^∞$ Uncertainties
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
Text
Devonport et al. "Frequency Domain Gaussian Process Models for $h^∞$ Uncertainties." Proceedings of The 5th Annual Learning for Dynamics and Control Conference, 2023.Markdown
[Devonport et al. "Frequency Domain Gaussian Process Models for $h^∞$ Uncertainties." Proceedings of The 5th Annual Learning for Dynamics and Control Conference, 2023.](https://mlanthology.org/l4dc/2023/devonport2023l4dc-frequency/)BibTeX
@inproceedings{devonport2023l4dc-frequency,
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},
year = {2023},
pages = {1046-1057},
volume = {211},
url = {https://mlanthology.org/l4dc/2023/devonport2023l4dc-frequency/}
}