46 research outputs found
Approximate Predictive Control Barrier Functions using Neural Networks: A Computationally Cheap and Permissive Safety Filter
A predictive control barrier function (PCBF) based safety filter allows for
verifying arbitrary control inputs with respect to future constraint
satisfaction. The approach relies on the solution of two optimization problems
computing the minimal constraint relaxations given the current state, and then
computing the minimal deviation from a proposed input such that the relaxed
constraints are satisfied. This paper presents an approximation procedure that
uses a neural network to approximate the optimal value function of the first
optimization problem from samples, such that the computation becomes
independent of the prediction horizon. It is shown that this approximation
guarantees that states converge to a neighborhood of the implicitly defined
safe set of the original problem, where system constraints can be satisfied for
all times forward. The convergence result relies on a novel class
lower bound on the PCBF decrease and depends on the approximation error of the
neural network. Lastly, we demonstrate our approach in simulation for an
autonomous driving example and show that the proposed approximation leads to a
significant decrease in computation time compared to the original approach.Comment: Submitted to ECC2