Finite-sample-based reachability for safe control with Gaussian process dynamics
File(s)
Published version
Author(s)
Prajapat, Manish
Kohler, Johannes
Lahr, Amon
Krause, Andreas
Zeilinger, Melanie N
Type
Journal Article
Abstract
Gaussian Process (GP) regression has been shown to be effective for learning unknown dynamics, enabling efficient and safety-aware control strategies across diverse applications. However, existing GP-based model predictive control (GP-MPC) methods either rely on approximations, thus lacking guarantees, or are overly conservative, which limits their practical utility. To address this gap, we present a sampling-based framework that efficiently propagates the model’s epistemic uncertainty. We establish a novel sample complexity result that enables the construction of a reachable set using a finite number of dynamics functions sampled from the GP posterior. Building on this, we design a sampling-based GP-MPC scheme that is recursively feasible and guarantees closed-loop safety and stability with high probability. Finally, we showcase the effectiveness of our method on two numerical examples, highlighting accurate reachable set over-approximation and safe closed-loop operation.
Date Issued
2026-11-01
Date Acceptance
2026-05-31
Citation
Automatica, 2026, 193
ISSN
0005-1098
Publisher
Elsevier
Journal / Book Title
Automatica
Volume
193
Copyright Statement
© 2026 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Identifier
10.1016/j.automatica.2026.113204
Publication Status
Published
Article Number
113204
Date Publish Online
2026-07-30