Gaussian Process (GP) regression is 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 close this gap, we present a sampling-based framework that efficiently propagates the model's epistemic uncertainty while avoiding conservatism. 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 performance.
View on arXiv@article{prajapat2025_2505.07594,
title={ Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamics },
author={ Manish Prajapat and Johannes Köhler and Amon Lahr and Andreas Krause and Melanie N. Zeilinger },
journal={arXiv preprint arXiv:2505.07594},
year={ 2025 }
}