Frequency-domain-based regularisation of energy-maximising control for wave energy conversion

Maximising energy through optimal control strategies is crucial in developing ocean wave energy harvesting technologies. Among these strategies, direct optimal control techniques, including model predictive control, are widely employed for energy maximisation. The specific energy-based objective function might result in non-convex formulations according to the discretisation procedure used, directly affecting real-time feasibility. To address this, modifications are commonly made to the overall objective function to ensure convexity. These modifications are virtually always based on numerical computation of a set of eigenvalues, and depend on the designer's ability to balance numerical accuracy with the objective of energy maximisation. In this study, leveraging the duality between time-domain and frequency-domain control formulations, a condition based on the spectral properties of the model, characterising the energy harvester, is proposed, to determine an accurate regularisation condition for the problem. The developed methodology is demonstrated with numerical examples.