Terminal weight and constraint design for wave energy converter economic model predictive control problems

The wave energy converter (WEC) control problem aims to make the best use of wave excitation to maximize energy capture and ensure safe operation across a broad range of sea states. This falls into the recently developed economic model predictive control (EMPC) framework, subject to wave excitation being treated as a predictable additive disturbance in the control problem. However, there are few theoretical developments on EMPC theory that can be directly used, as the persistent disturbances bring nontrivial problems to optimal operation, safety etc. Whilst the disturbance is beneficial for the energy production objective, it may cause safe operation problems. This article develops a systematic WEC EMPC design approach for WECs with essential linear hydrodynamical characteristics. By introducing terminal weight and terminal state constraint design into the WEC EMPC structure, important features such as convexity, satisfaction of safety constraints, and recursive feasibility can be guaranteed. Contrary to our intuition, we show that (1) the proposed EMPC with a terminal weight provides an unbiased estimate of the ideal conceptual infinite horizon solution, and (2) the WEC operational range, in terms of the operational sea states, is extended by imposing a terminal constraint. Finally, numerical simulations are provided to verify the efficacy of the proposed approach.