Learning-Based, Safety-Constrained Control from Scarce Data via Reciprocal Barriers

We develop a control algorithm for the safety of a control-affine system with unknown nonlinear dynamics in the sense of confinement in a given safe set. The algorithm leverages robust nonlinear feedback control laws integrated with on-the-fly, data-driven approximations to output a control signal that guarantees the boundedness of the closed-loop system in the given set. More specifically, it first computes estimates of the dynamics based on differential inclusions constructed from data obtained online from a single finite-horizon trajectory. It then computes a novel feedback safety control law that renders the system forward invariant with respect to the safe set, given an accurate enough estimate, using reciprocal barriers. An extension of the algorithm is capable of coping with the controllability loss incurred by the control matrix along the safe set. The algorithm removes a series of common and limiting assumptions considered in the related literature since it does not require global boundedness, growth conditions, or a priori approximations of the unknown dynamics’ terms.