Wave-energy point absorbers can be defined as oscillators excited by ocean waves. Devices of this kind are meant to be deployed offshore for the production of renewable energy. As wave conditions at a given site can vary widely over time, advanced control strategies for point absorbers are required to guarantee good performance. This article presents a state-space control scheme for a point absorber, which builds on an approach outlined in an earlier article by the same authors. Strongly based on model predictive control (MPC), the control scheme makes use of an unusual form of the objective function, and aims at maximising the production of energy by the point absorber. The control scheme remedies some of the shortcomings of existing approaches to the control of a point absorber, such as reactive control and latching control, and is meant to be extendable to any point absorber that can be well described by a linear model. Results of numerical simulations of a heaving point absorber controlled with this scheme are presented and confirm the potential of this approach.