  There are two fundamental paradigms for non-equilibrium dynamics: on the one
hand, aging towards an equilibrium state that cannot be reached on reasonable
timescales; on the other, external driving that can lead to non-equilibrium
steady states. We explore how these two mechanisms interact, by studying the
behaviour of trap models, which are paradigmatic descriptions of slow glassy
dynamics, when driven by trajectory bias towards high or low activity. To
diagnose whether the driven systems continue to age, we establish a framework
for mapping the biased dynamics to a Markovian time evolution with
time-dependent transition rates. We find that the original aging dynamics
reacts in two qualitatively distinct ways to the driving: it can be destroyed
by driving of any nonzero strength (fragile aging), whereby the dynamics either
reaches an active steady state or effectively freezes; or it can persist within
a finite range of driving strengths around the undriven case (robust aging).
This classification into fragile and robust aging could form the basis for
distinguishing different universality classes of aging dynamics.
