  We present a general protocol to control closed quantum systems that is based
on minimising the adiabatic action. Using tools based on the geometry of
quantum evolutions through the quantum adiabatic brachistochrone, we show that
high fidelity control of the ground state of critical quantum systems can be
achieved and requires only a reasonable approximation for the ground state
spectral gap. We demonstrate our results for three widely applicable systems:
the Landau-Zener, Ising, and fully connected spin models.
