Designing Control Barrier Functions Using a Dynamic Backup Policy
arXiv:2510.09810
Abstract
This paper presents a systematic approach to construct control barrier functions for nonlinear control affine systems subject to arbitrary state and input constraints. Taking inspiration from the reference governor literature, the proposed method defines a family of backup policies, parametrized by the equilibrium manifold of the system. The control barrier function is defined on the augmented state-and-reference space: given a state-reference pair, the approach quantifies the distance to constraint violation at any time in the future. The proposed method is applied to an inverted pendulum on cart.
6 pages, 1 figure