  As the use of autonomous robotic systems expands in tasks that are complex
and challenging to model, the demand for robust data-driven control methods
that can certify safety and stability in uncertain conditions is increasing.
However, the practical implementation of these methods often faces scalability
issues due to the growing amount of data points with system complexity, and a
significant reliance on high-quality training data. In response to these
challenges, this study presents a scalable data-driven controller that
efficiently identifies and infers from the most informative data points for
implementing data-driven safety filters. Our approach is grounded in the
integration of a model-based certificate function-based method and Gaussian
Process (GP) regression, reinforced by a novel online data selection algorithm
that reduces time complexity from quadratic to linear relative to dataset size.
Empirical evidence, gathered from successful real-world cart-pole swing-up
experiments and simulated locomotion of a five-link bipedal robot, demonstrates
the efficacy of our approach. Our findings reveal that our efficient online
data selection algorithm, which strategically selects key data points, enhances
the practicality and efficiency of data-driven certifying filters in complex
robotic systems, significantly mitigating scalability concerns inherent in
nonparametric learning-based control methods.
