Tube-Based Control Barrier Function With Integral Quadratic Constraints for Unknown Input Delay

This letter proposes a Control Barrier Function (CBF)-based controller design to achieve safety for systems subjecting to unknown input delay and additive disturbance. Integral quadratic constraints characterizing the input-output behavior of the unmodeled dynamics caused by the unknown input delay are used to generate a bound of the error between the nominal model and the true uncertain system. The bound is incorporated into a tube-based CBF formulation to ensure robust system safety. The proposed method guarantees that the constraints are input affine, so the safe controller can be implemented by solving a quadratic programming problem in real-time. A simple example demonstrates the effectiveness of the tube-based CBF approach.