Finite-sample-based reachability for safe control with Gaussian Process dynamics
Manish Kumar Prajapat, Johannes Köhler, Amon Lahr, Andreas Krause, Melanie N. Zeilinger · Automatica · 2026
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. (c) 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/).