A nonlinear modeling strategy is introduced to drive online optimization-based controllers for trajectory tracking and stabilization of very flexible aircraft. This is achieved thanks to a compact residualized modal projection of the aeroelastic equations of motion, including large (geometrically nonlinear) wing deflections, that is used to describe the vehicle dynamics. This study shows that a model-predictive control system can then be built with an internal model based on successive linearization of the equations of motion around the instantaneous vehicle geometry. Significant improvements in stability against large disturbances and maneuverability are demonstrated on numerical simulations of a very flexible flying wing when geometrically nonlinear effects are included in the internal model of the controller.