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We develop a control algorithm that ensures the safety, in terms ofconfinement in a set, of a system with unknown, 2nd-order nonlinear dynamics.The algorithm establishes novel connections between data-driven and robust,nonlinear control. It is based on data obtained online from the currenttrajectory and the concept of reciprocal barriers. More specifically, it firstuses the obtained data to calculate set-valued functions that over-approximatethe unknown dynamic terms. For the second step of the algorithm, we design arobust control scheme that uses these functions as well as reciprocal barriersto render the system forward invariant with respect to the safe set. Inaddition, we provide an extension of the algorithm that tackles issues ofcontrollability loss incurred by the nullspace of the control-direction matrix.The algorithm removes a series of standard, limiting assumptions considered inthe related literature since it does not require global boundedness, growthconditions, or a priori approximations of the unknown dynamics' terms.

Safety-Constrained Learning and Control using Scarce Data and Reciprocal Barriers