A robust control procedure for precision pointing and tracking of fast moving elastic structures is proposed. Based on a combination of the sliding manifold approach with the theory of optimal interpolation, this design procedure generates a control effort capable of insuring high pointing and tracking performance in the presence of induced disturbances and modelling uncertainties. The uncertainties are handled by sliding control and estimation of the nonlinearly excited elastic elastic dynamics by an interpolator of the structure dynamic response. Chattering behaviour of the controller is avoided at the expense of tolerating a known tracking error. It is shown through analysis that a trade-off has to be set, by taking into account the main requirements of a given mission and the system hardware capabilities. For illustration purposes, a set of numerical simulations is then run to assess the system dynamical performance.