Probabilistic Invariance for Gaussian Process State Space Models

Paul Griffioen, Alex Devonport, Murat Arcak
Proceedings of The 5th Annual Learning for Dynamics and Control Conference, PMLR 211:458-468, 2023.

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 this Paper

BibTeX
@InProceedings{pmlr-v211-griffioen23a, 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}, pages = {458--468}, 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/griffioen23a/griffioen23a.pdf}, url = {https://proceedings.mlr.press/v211/griffioen23a.html}, 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.} }
Endnote
%0 Conference Paper %T Probabilistic Invariance for Gaussian Process State Space Models %A Paul Griffioen %A Alex Devonport %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-griffioen23a %I PMLR %P 458--468 %U https://proceedings.mlr.press/v211/griffioen23a.html %V 211 %X 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.
APA
Griffioen, P., Devonport, A. & Arcak, M.. (2023). Probabilistic Invariance for Gaussian Process State Space Models. Proceedings of The 5th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 211:458-468 Available from https://proceedings.mlr.press/v211/griffioen23a.html.

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