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In this work, we investigate the data-driven safe control synthesis problemfor unknown dynamic systems. We first formulate the safety synthesis problem asa robust convex program (RCP) based on notion of control barrier function. Toresolve the issue of unknown system dynamic, we follow the existing approach byconverting the RCP to a scenario convex program (SCP) by randomly collectingfinite samples of system trajectory. However, to improve the sample efficiencyto achieve a desired confidence bound, we provide a new posteriori method withvalidation tests. Specifically, after collecting a set of data for the SCP, wefurther collect another set of independent \emph{validate data} as posteriorinformation to test the obtained solution. We derive a new overall confidencebound for the safety of the controller that connects the original sample data,the support constraints, and the validation data. The efficiency of theproposed approach is illustrated by a case study of room temperature control.We show that, compared with existing methods, the proposed approach cansignificantly reduce the required number of sample data to achieve a desiredconfidence bound.

Data-Driven Safe Controller Synthesis for Deterministic Systems: A Posteriori Method With Validation Tests