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Recent advances in safety-critical risk-aware control are predicated onapriori knowledge of the disturbances a system might face. This paper proposesa method to efficiently learn these disturbances online, in a risk-awarecontext. First, we introduce the concept of a Surface-at-Risk, a risk measurefor stochastic processes that extends Value-at-Risk -- a commonly utilized riskmeasure in the risk-aware controls community. Second, we model the norm of thestate discrepancy between the model and the true system evolution as ascalar-valued stochastic process and determine an upper bound to itsSurface-at-Risk via Gaussian Process Regression. Third, we provide theoreticalresults on the accuracy of our fitted surface subject to mild assumptions thatare verifiable with respect to the data sets collected during system operation.Finally, we experimentally verify our procedure by augmenting a drone'scontroller and highlight performance increases achieved via our risk-awareapproach after collecting less than a minute of operating data.

Learning Disturbances Online for Risk-Aware Control: Risk-Aware Flight with Less Than One Minute of Data