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Paper Title: Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functions
Authors: Fernando Castañeda, Jason J. Choi, Wonsuhk Jung, Bike Zhang, Claire J. Tomlin, Koushil Sreenath
The authors propose a novel safe online learning framework that combines Gaussian process uncertainty modeling with control barrier function (CBF)-based safety filters. Their event-triggered data collection strategy maintains recursive feasibility of the safety filter while guaranteeing probabilistic set invariance with high confidence under model uncertainty.
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State-space illustration of the adaptive cruise control (ACC) scenario demonstrating the core idea of the authors' method. The black curve shows the system trajectory up to the current state (marked by a star). The colored background visualizes the feasibility certificate λ†(x) of the probabilistic CBF constraint, computed from the Gaussian Process posterior over the CBF dynamics. Regions where λ†(x) < 0 denote certified safe states (shown in green and yellow) given the dataset of measurements collected up until that point. In the top plot, as the vehicle approaches a boundary where uncertainty threatens this condition, the algorithm triggers an active measurement along an exploratory, safety-informed control direction, expanding the certified safe region with new states (in blue). As new data accumulate, this safe region continues to expand, enabling progression into states that were previously too uncertain. This adaptive interplay ensures the controller never leaves itself without a guaranteed safe backup direction, thereby maintaining recursive feasibility of the probabilistic CBF constraint. The bottom plot shows the final snapshot after completing the trajectory, highlighting the enlarged certified safe region resulting from the collected measurements.