Online Adaptive Compensation for Model Uncertainty Using Extreme Learning Machine-based Control Barrier Functions

A control barrier functions-based quadratic programming (CBF-QP) method has emerged as a controller synthesis tool to assure safety of autonomous systems owing to the appealing safe forward invariant set. However, the provable safety relies on a precisely described dynamic model, which is not always available in practice. Recent works leverage learning to compensate model uncertainty for a CBF controller. However, these approaches based on reinforcement learning or episodic learning are limited to dealing with time-invariant uncertainty. Also, the reinforcement learning approach learns the uncertainty offline, while episodic learning only updates the controller after a batch of data is available by the end of an episode. Instead, we propose a novel tuning extreme learning machine (tELM)-based CBF controller that can compensate time-variant and time-invariant model uncertainty adaptively in an online manner. We validate our approach's effectiveness in a simulation of an Adaptive Cruise Control (ACC) system.