Robust Direct Data-Driven Hamiltonian for Safe Set Computation under Measurement Noise and Disturbances
For safety-critical control systems, this work provides a robust data-driven method for safe set computation that accounts for real-world imperfections like noise and disturbances, offering theoretical guarantees.
This paper extends the Data-Driven Hamiltonian (DDH) framework to handle measurement noise, disturbances, and sampling errors, deriving a Robust DDH that provides a certified lower bound on the exact Hamiltonian, leading to provable under-approximations of safe sets. The gap between data-driven and exact Hamiltonians is shown to converge to zero with more data in noise-free settings, with effectiveness demonstrated on a double integrator and an aircraft taxiing system.
Safe set computation is a fundamental challenge in safety-critical control systems, especially in direct data-driven settings where safety analysis is performed directly from noise-affected measurements, without explicit modeling. A recently proposed method, Data-Driven Hamiltonian (DDH), enables reachability analysis directly from measurements, without relying on prior knowledge of the underlying system dynamics. This paper extends the DDH framework to a robust setting that accounts for measurement noise, exogenous disturbances, and sampling-induced state-velocity estimation error. A Robust Data-Driven Hamiltonian (R-DDH) is derived from noisy measurements and shown to yield a certified lower bound on the exact Hamiltonian. This results in a provable under-approximation of the value function and an inner approximation of the associated safe set. The gap between the data-driven and exact Hamiltonians is quantified, and it is shown to converge to zero with more data in a noise-free setting with additive disturbances. The effectiveness of the approach is shown through two case studies: a constrained double integrator and an aircraft taxiing system with a nonlinear closed-loop controller operating under perceptual uncertainty.