  We report on experiments probing the evolution of a vortex state in response
to a driving current in 2H-NbSe$_2$ crystals. By following the vortex motion
with fast transport measurements we find that the current enables the system to
reorganize and access new configurations. During this process the system
exhibits a long-term memory: if the current is turned off the vortices freeze
in place remembering their prior motion. When the current is restored the
motion resumes where it stopped. The experiments provide evidence for a
dynamically driven structural change of the vortex lattice and a corresponding
dynamic phase diagram that contains a previously unknown regime where the
critical current can be either $increased$ or $decreased$ by applying an
appropriate driving current.
