Disturbance Observers for Robust Backup Control Barrier Functions

Abstract: Designing safe controllers is crucial and notoriously challenging for input-constrained safety-critical control systems. Backup control barrier functions offer an approach for the construction of safe controllers online by considering the flow of the system under a backup controller. However, in the presence of model uncertainties, the flow cannot be accurately computed, making this method insufficient for safety assurance. To tackle this shortcoming, we integrate backup control barrier functions with a disturbance observer and estimate the flow under a reconstruction of the disturbance while refining this estimate over time. We prove that the controllers resulting from the proposed Disturbance Observer Backup Control Barrier Function (DO-bCBF) approach guarantee safety, are robust to unknown disturbances, and satisfy input constraints.