Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamics
This work addresses the challenge of balancing safety guarantees and practicality in GP-based model predictive control for applications like robotics and autonomous systems, offering a novel approach to reduce conservatism while maintaining theoretical assurances.
The paper tackles the problem of ensuring safety and stability in control systems with unknown dynamics using Gaussian Process regression, by developing a sampling-based framework that provides finite-sample reachability guarantees and demonstrates safe closed-loop performance in numerical examples.
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.