{"ID":2860138,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.05436","arxiv_id":"2510.05436","title":"Safety-Critical Control with Bounded Inputs: A Closed-Form Solution for Backup Control Barrier Functions","abstract":"Verifying the safety of controllers is critical for many applications, but is especially challenging for systems with bounded inputs. Backup control barrier functions (bCBFs) offer a structured approach to synthesizing safe controllers that are guaranteed to satisfy input bounds by leveraging the knowledge of a backup controller. While powerful, bCBFs require solving a high-dimensional quadratic program at run-time, which may be too costly for computationally-constrained systems such as aerospace vehicles. We propose an approach that optimally interpolates between a nominal controller and the backup controller, and we derive the solution to this optimization problem in closed form. We prove that this closed-form controller is guaranteed to be safe while obeying input bounds. We demonstrate the effectiveness of the approach on a double integrator and a nonlinear fixed-wing aircraft example.","short_abstract":"Verifying the safety of controllers is critical for many applications, but is especially challenging for systems with bounded inputs. Backup control barrier functions (bCBFs) offer a structured approach to synthesizing safe controllers that are guaranteed to satisfy input bounds by leveraging the knowledge of a backup...","url_abs":"https://arxiv.org/abs/2510.05436","url_pdf":"https://arxiv.org/pdf/2510.05436v1","authors":"[\"David E. J. van Wijk\",\"Ersin Das\",\"Tamas G. Molnar\",\"Aaron D. Ames\",\"Joel W. Burdick\"]","published":"2025-10-06T23:02:18Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"cs.RO\"]","methods":"[]","has_code":false}