Learning Control Barrier Functions with Deterministic Safety Guarantees

TL;DR

This paper introduces a data-driven method for designing Control Barrier Functions using neural networks, providing deterministic safety guarantees for nonlinear dynamical systems through convex optimization.

Contribution

It proposes a novel approach to construct continuous piecewise affine barrier functions with safety guarantees using sampled data and iterative convex overbounding.

Findings

Successfully applied to autonomous and non-autonomous systems

Provides deterministic safety guarantees

Uses neural networks for flexible barrier function design

Abstract

Barrier functions (BFs) characterize safe sets of dynamical systems, where hard constraints are never violated as the system evolves over time. Computing a valid safe set and BF for a nonlinear (and potentially unmodeled), non-autonomous dynamical system is a difficult task. This work explores the design of BFs using data to obtain safe sets with deterministic assurances of control invariance. We leverage ReLU neural networks (NNs) to create continuous piecewise affine (CPA) BFs with deterministic safety guarantees for Lipschitz continuous, discrete-time dynamical system using sampled one-step trajectories. The CPA structure admits a novel classifier term to create a relaxed \ac{bf} condition and construction via a data driven constrained optimization. We use iterative convex overbounding (ICO) to solve this nonconvex optimization problem through a series of convex optimization steps. We then demonstrate our method's efficacy on two-dimensional autonomous and non-autonomous dynamical systems.