Output Feedback Backup Control Barrier Functions: Safety Guarantees Under Input Bounds and State Estimation Error

Abstract: Guaranteeing the safety of controllers is vital for real-world applications, but is markedly difficult when the states are not perfectly known and when the control inputs are bounded. Backup control barrier functions (bCBFs) use predictions of the flow under a prescribed controller to achieve safety in the presence of bounded inputs and perfect state information. However, when only an estimate of the true state is known, this flow may not be precisely computed, as the initial condition is unknown. Furthermore, the true flow evolves using feedback from the estimated state, thus introducing coupling between known and unknown flows. To address these challenges, we propose a technique that leverages an uncertainty envelope centered around the estimated flow and show that ensuring the safety of this envelope guarantees that the true state satisfies the safety constraints. Additionally, we show that in the presence of state uncertainty, using the resulting Output Feedback Backup Control Barrier Functions (O-bCBFs), there always exists a feasible control input that can guarantee the safety of the true state, even in the presence of input constraints.

David E. J. van Wijk, Tamas G. Molnar, Samuel Coogan, Manoranjan Majji, Aaron D. Ames and Joel W. Burdick, "Output Feedback Backup Control Barrier Functions: Safety Guarantees Under Input Bounds and State Estimation Error," Submitted to Systems & Control Letters, 2026. Preprint: [link]

Supplemental Video: Double Integrator

The objective is to keep the system inside the green region. Our approach obeys the constraint on position in the presence of state estimation error by using predictions of an open-loop trajectory. Click the thumbnail below to watch!

BibTeX Citation

@article{van2026outputCBF,
  title={Output Feedback Backup Control Barrier Functions: Safety Guarantees Under Input Bounds and State Estimation Error},
  author={van Wijk, David EJ and Molnar, Tamas G and Coogan, Samuel and Majji, Manoranjan and Ames, Aaron D and Burdick, Joel W},
  journal={arXiv preprint arXiv:2604.19893},
  year={2026}
}