Control Barrier Functions With Unmodeled Dynamics Using Integral Quadratic Constraints

This paper presents a control design method that achieves safety for systems with unmodeled dynamics at the plant input. The proposed method combines control barrier functions (CBFs) and integral quadratic constraints (IQCs). Simplified, low-order models are often used in the design of the controller. Parasitic, unmodeled dynamics (e.g. actuator dynamics, time delays, etc) can lead to safety violations. The proposed method bounds the input-output behavior of these unmodeled dynamics in the time-domain using an alpha-IQC. The alpha-IQC is then incorporated into the CBF constraint to ensure safety. The approach is demonstrated with a simple example.