Wave energy is a promising source of clean and renewable energy. In order to tap this energy various designs for wave-energy converters are currently under development. One of these devices is the Archimedes Wave Swing. It is basically a submerged air vessel consisting of a floater and a stator. The floater is free to move vertically under varying wave pressure, while the stator is anchored to the sea bed. Energy is extracted from the relative motion of the two parts. The control objective is to optimize the power produced while ensuring that the motion of the floater remains within certain prescribed limits. The main difficulty is due to the high degree of irregularity of ocean waves. Two consecutive waves can have significantly different heights and periods, and the controller should be able to deal with that. The controllers are designed based on two different principles. The first method controls the trajectory so that the velocity of the floater remains in phase with the excitation force. Model predictive control is used in order to be able to eact to the constraints ahead of time. The second method makes use of a prediction of the excitation force in order to calculate the control force which maximizes the energy produced.