Probabilistic Invariance for Gaussian Process State Space Models
Abstract
Gaussian process state space models are becoming common tools for the analysis and design of nonlinear systems with uncertain dynamics. When designing control policies for these systems, safety is an important property to consider. In this paper, we provide safety guarantees for Gaussian process state space models in the form of probabilistic invariant sets, where the state trajectory is guaranteed to lie within an invariant set for all time with a particular probability. We provide a sufficient condition in the form of a linear matrix inequality to evaluate the probabilistic invariance of the system, and we demonstrate our contributions with an illustrative example.
Cite
Text
Griffioen et al. "Probabilistic Invariance for Gaussian Process State Space Models." Proceedings of The 5th Annual Learning for Dynamics and Control Conference, 2023.Markdown
[Griffioen et al. "Probabilistic Invariance for Gaussian Process State Space Models." Proceedings of The 5th Annual Learning for Dynamics and Control Conference, 2023.](https://mlanthology.org/l4dc/2023/griffioen2023l4dc-probabilistic/)BibTeX
@inproceedings{griffioen2023l4dc-probabilistic,
title = {{Probabilistic Invariance for Gaussian Process State Space Models}},
author = {Griffioen, Paul and Devonport, Alex and Arcak, Murat},
booktitle = {Proceedings of The 5th Annual Learning for Dynamics and Control Conference},
year = {2023},
pages = {458-468},
volume = {211},
url = {https://mlanthology.org/l4dc/2023/griffioen2023l4dc-probabilistic/}
}