We study experimentally and theoretically, the reorganization of superconducting vortices driven by oscillatory forces near the plastic depinning transition. We show that the system can be taken to configurations that are tagged by the shaking parameters but keep no trace of the initial conditions. In experiments performed in $NbSe_2$ crystals, the periodic drive is induced by ac magnetic shaking fields and the overall order of the resulting configuration is determined by non invasive ac susceptibility measurements. With a model of interacting particles driven over random landscapes, we perform molecular dynamics simulations that reveal the nature of the shaking dynamics as fluctuating states similar to those predicted for other interacting particle systems.
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