R-DDH enables provably safe control under noise and disturbances

Safe set computation is critical for safety-critical control systems like autonomous driving and aircraft taxiing. Traditional methods require an accurate system model, but direct data-driven approaches bypass modeling by working directly from measurements. The Data-Driven Hamiltonian (DDH) method previously enabled reachability analysis from data, but it assumed noise-free measurements. In a new arXiv paper, Mohammad Bajelani, Christopher Strong, Claire Tomlin, Jason Choi, and Klaske van Heusden propose Robust Data-Driven Hamiltonian (R-DDH) to handle real-world imperfections: measurement noise, exogenous disturbances, and state-velocity estimation errors from sampling. R-DDH derives a certified lower bound on the true Hamiltonian, providing a provable inner approximation of the safe set—meaning the controller can guarantee safety even under uncertainty.

The method is shown to converge to the exact safe set as more data becomes available in noise-free conditions with additive disturbances. The gap between data-driven and exact Hamiltonians is quantified and shrinks with data volume. Case studies include a constrained double integrator and an aircraft taxiing system with a nonlinear closed-loop controller operating under perceptual uncertainty (e.g., camera noise). This work extends DDH to practical, noisy environments, making data-driven safety analysis viable for real-world autonomous systems.