In this paper, explicit model predictive control is applied in conjunction with nonlinear optimisation to a magnetically actuated flexible endoscope for the first time. The approach is aimed at computing the motion of the external permanent magnet, given the desired forces and torques. The strategy described here takes advantage of the nonlinear nature of the magnetic actuation and explicitly considers the workspace boundaries, as well as the actuation constraints. Initially, a simplified dynamic model of the tethered capsule, based on the Euler-Lagrange equations is developed. Subsequently, the explicit model predictive control is described and a novel approach for the external magnet positioning, based on a single step, nonlinear optimisation routine, is proposed. Finally, the strategy is implemented on the experimental platform, where bench-top trials are performed on a realistic colon phantom, showing the effectiveness of the technique. The work presented here constitutes an initial exploration for model-based control techniques applied to magnetically manipulated payloads, the techniques described here may be applied to a wide range of devices, including flexible endoscopes and wireless capsules. To our knowledge, this is the first example of advanced closed loop control of magnetic capsules.