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.

@article{prajapat26finite,
	author = {Manish Prajapat and Johannes K{\"o}hler and Amon Lahr and Andreas Krause and Melanie N. Zeilinger},
	doi = {https://doi.org/10.1016/j.automatica.2026.113204},
	issn = {0005-1098},
	journal = {Automatica},
	pages = {113204},
	title = {Finite-sample-based reachability for safe control with Gaussian Process dynamics},
	volume = {193},
	year = {2026}}