We design, implement and test two control algorithms for autonomously landing a drone on an autonomous boat. The first algorithm uses distributed model predictive control (DMPC), while the second combines a cascade controller with DMPC. The algorithms are implemented on a real drone, while the boat's motion is simulated, and their performance is compared to a centralized model predictive controller. Field experiments are performed, where all algorithms show an ability to land while avoiding violation of the safety constraints. The two distributed algorithms further show the ability to use longer prediction horizons than the centralized model predictive controller, especially in the cascade case, and also demonstrate improved robustness towards breaks in communication.