Control Barrier Functions With Unmodeled Dynamics Using Integral Quadratic Constraints

TL;DR

This paper introduces a control design approach that ensures safety in systems with unmodeled dynamics by integrating integral quadratic constraints into control barrier functions, effectively handling parasitic effects like actuator dynamics and delays.

Contribution

It combines control barrier functions with alpha-IQCs to explicitly account for unmodeled dynamics in safety-critical control design.

Findings

Successfully bounded unmodeled dynamics using alpha-IQCs.

Ensured safety constraints are maintained despite unmodeled effects.

Demonstrated effectiveness with a simple example.

Abstract

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.