Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamics

• URL: http://arxiv.org/abs/2505.07594v1
• Date: Mon, 12 May 2025 14:20:20 GMT
• Title: Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamics
• Authors: Manish Prajapat, Johannes Köhler, Amon Lahr, Andreas Krause, Melanie N. Zeilinger,
• Abstract summary: We present a sampling-based framework that efficiently propagates the model's uncertainty while avoiding conservatism.<n>We show that our method highlights accurate reachable set over-approximation and safe closed-loop performance.
• Score: 35.79393879150088
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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