Current control in a tilted washboard potential via time-delayed feedback

We consider motion of an overdamped Brownian particle in a washboard potential exerted to a static tilting force. The bias yields directed net particle motion, i.e. a current. It is demonstrated that with an additional time-delayed feedback term the particle current can be reversed against the direction of the bias. The control function induces a ratchet-like effect that hinders further current reversals and thus the particle moves against the direction of the static bias. Furthermore, varying the delay time allows also to continuously depreciate and even stop the transport in the washboard potential. We identify and characterize the underlying mechanism which applies to current control in a wide temperature range.