Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation

Abstract

Control Barrier Functions (CBFs) offer an elegant framework for constraining nonlinear control system dynamics to an invariant subset of a pre-specified safe set. However, finding a CBF that simultaneously promotes performance by maximizing the resulting control invariant set while accommodating complex safety constraints, especially in high relative degree systems with actuation constraints, remains a significant challenge. In this work, we propose a novel self-supervised learning framework that holistically addresses these hurdles. Given a Boolean composition of multiple state constraints defining the safe set, our approach begins by constructing a smooth function whose zero superlevel set provides an inner approximation of the safe set. This function is then used with a smooth neural network to parameterize the CBF candidate. Finally, we design a physics-informed training loss function based on a Hamilton-Jacobi Partial Differential Equation (PDE) to train the PINN-CBF and enlarge the volume of the induced control invariant set. We demonstrate the effectiveness of our approach on a 2D double integrator (DI) system and a 7D fixed-wing aircraft system (F16).