The vertical position of elongated tokamak plasmas is unstable on the time scale of the eddy currents in the axisymmetric conducting structures. In the absence of feedback control, the plasma would drift vertically and quench on the wall, a situation known as Vertical Displacement Event (VDE), with serious consequences for machine integrity. As tokamaks approach reactor regimes, VDEs cannot be tolerated: vertical feedback control must be robust against system uncertainty and the occurrence of noise and disturbances. At the same time, adaptive routines should be in place to handle unexpected...