Gradient-Free Neural Hamilton-Jacobi Reachability for Scalable Safety-Critical Control

The paper proposes a discrete-time neural reachability framework for control-disturbance-affine systems that learns backward reachable tubes (BRTs) and backward reach-avoid tubes (BRATs) through Bellman-Isaacs value propagation. It combines equation-driven self-supervision with structured policy learning to avoid explicit PDE-gradients, using gradient-free value probes to construct approximate teacher actions. The method demonstrates scalability up to 80 dimensions and generalizes to real-world applications like F1-tenth racing with over 16,000-dimensional inputs, achieving real-time robust collision avoidance.