Wave-based control of under-actuated, flexible systems has many advantages over other methods. It considers actuator motion as launching a mechanical wave into the flexible system which it absorbs on its return to the actuator. The launching and absorbing proceed simultaneously. This simple, intuitive idea leads to robust, generic, highly efficient, precise, adaptable controllers, allowing rapid and almost vibrationless re-positioning of the system, using only sensors collocated at the actuator-system interface. It has been very successfully applied to simple systems such as mass-spring strings, systems of Euler-Bernoulli beams, planar mass-spring arrays, and flexible three-dimensional space structures undergoing slewing motion. In common with most other approaches, this work also assumed that, during a change of position, the forces from the environment were negligible in comparison with internal forces and torques. This assumption is not always valid. Strong external forces considerably complicate the flexible control problem, especially when unknown, unexpected or unmodelled. The current work extends the wave-based strategy to systems experiencing significant external disturbing forces, whether enduring or transient. The work also provides further robustness to sensor errors. The strategy has the controller learn about the disturbances and compensate for them, yet without needing new sensors, measurements or models beyond those of standard wave-based control.