Neural Barriers: An Online Certifiable Learning-enhanced Adaptive High Order Safety Critical Control

As the number of autonomous robots continues to grow, safety becomes increasingly important. Control barrier functions (CBFs) provide a theoretically grounded framework for ensuring safety, but existing design methods often face limitations in effectiveness, scalability, or interpretability, and may result in overly conservative safe sets. In this paper, we propose \emph{VertexCBF}, a framework for learning neural CBFs in a scalable, systematic, and explainable way. We approximate the stationary Hamilton--Jacobi value function using a neural network trained via a combination of physics-informed and sparsely supervised learning. By exploiting control-affine dynamics and a convex polytope control set, under which the Hamiltonian is maximized at the control vertices, we efficiently generate supervision points via GPU-parallel vertex-restricted tree search, while a residual architecture guarantees that the learned CBF is never larger than the specified constraint function. We evaluate the method on 15 systems and compare it against relevant baselines, showing that it reliably recovers large safe sets where the baselines are conservative or fail completely. In addition, we perform a hardware experiment in which a mobile robot safely avoids pedestrians using a neural CBF trained with our method.

Merely pursuing performance may adversely affect safety, while a conservative policy for safe exploration will degrade the performance. How to guarantee both safety and performance in learning-based control problems is an interesting yet challenging issue. This paper aims to enhance system performance with a safety guarantee by solving reinforcement learning (RL)-based optimal control problems for nonlinear systems subject to high-relative-degree state constraints and unknown time-varying disturbance/actuator faults. A new type of control barrier functions (CBFs), termed high-order reciprocal-based control barrier function, is proposed to handle high-relative-degree constraints, which extends the design of CBFs to enforce robust safety without knowing the disturbance bound. The concept of gradient similarity is proposed to quantify the relationship between safety and performance. Finally, gradient manipulation and adaptive mechanisms are introduced in the model-based safe RL framework to enhance the performance with a safety guarantee. Two simulation examples illustrate the efficacy of the proposed algorithms.

We augment the Slotine--Li adaptive controller for Euler--Lagrange systems with three learned components: a structured-quadratic Lyapunov function $V_ψ$ whose positive-definiteness follows from a Cholesky parameterization, a residual Soft Actor--Critic policy that adds bounded torque corrections to the analytic baseline, and a physics-informed neural network that estimates unmodeled dynamics. A closed-form safety filter, derived from the single affine constraint $\dot V_ψ+ αV_ψ\le 0$, projects every policy output onto the safe set without requiring an online QP solver. We prove: global feasibility of the filter under a drift-decay condition on the control-degeneracy set; exponential stability under exact shielding, with a robust extension whose margin depends on the PINN approximation error; almost-sure convergence of the three-timescale policy--certificate--multiplier updates to a KKT point; and a PAC generalization bound for the certificate over compacts. On a 2-DOF manipulator with nonlinear friction and variable payload, the learned certificate accounts for most of the empirical gain: tracking error drops by 41% on nominal friction and 24% on aggressive friction at the centroid of the training distribution. A 7-DOF scalability study on a Franka Emika Panda confirms clean convergence of the full pipeline at industrial scale, identifies the conditions under which gains over exact model-based baselines should and should not be expected, and documents a warm-start pathology of the learned certificate that has practical implications for deployment.