Discrete Implementations Modify the Intuition of Final Set Adjustment in Barrier Function Based Control

ABSTRACT This paper establishes an implementation‐aware framework for Barrier Function Adaptation (BFA) and shows that discrete‐time realizations fundamentally alter the logic of final‐set adjustment. In particular, sufficient conditions are derived to preserve the key benefits of BFA (predefined performance, gain adaptation with uncertain perturbation bounds, and chattering avoidance when implemented via sample‐and‐hold). These conditions depend on the sampling time, actuator capacity, and the barrier function width (BFW). Additionally, a normalized BFASPC controller is proposed, which exploits actuator limitations to reduce the size of the final set (FS) without prior knowledge of the perturbation and permits longer sampling intervals. All controllers are validated experimentally on a physical ball‐and‐plate system, confirming the theoretical findings and exposing trade‐offs between the size of the FS, robustness, and implementability.