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Safe control of constrained linear systems under both epistemic and aleatoryuncertainties is considered. The aleatory uncertainty characterizes randomnoises and is modeled by a probability distribution function (PDF) and theepistemic uncertainty characterizes the lack of knowledge on the systemdynamics. Data-based probabilistic safe controllers are designed for the caseswhere the noise PDF is 1) zero-mean Gaussian with a known covariance, 2)zero-mean Gaussian with an uncertain covariance, and 3) zero-mean non-Gaussianwith an unknown distribution. Easy-to-check model-based conditions forguaranteeing probabilistic safety are provided for the first case byintroducing probabilistic contractive sets. These results are then extended tothe second and third cases by leveraging distributionally-robust probabilisticsafe control and conditional value-at-risk (CVaR) based probabilistic safecontrol, respectively. Data-based implementations of these probabilistic safecontrollers are then considered. It is shown that data-richness requirementsfor directly learning a safe controller is considerably weaker thandata-richness requirements for model-based safe control approaches thatundertake a model identification. Moreover, an upper bound on the minimal risklevel, under which the existence of a safe controller is guaranteed, is learnedusing collected data. A simulation example is provided to show theeffectiveness of the proposed approach.

Data-driven Safe Control of Linear Systems Under Epistemic and Aleatory Uncertainties