Optimal control of a wave energy converter

The optimal control strategy for a wave energy converter (WEC) with constraints on the control torque is investigated. The goal is to optimize the total energy delivered to the electricity grid. Using Pontryagin's maximum principle, the solution is found to be singular-bang. Using higher order conditions, the optimal control on the singular arc is found as a function of the state and costate trajectories. Furthermore, it is shown that the transitions between bang and singular subarcs are discontinuous. Based on these findings the results of a numerical direct method are validated. Finally, the optimal control is used to benchmark an existing MPC strategy. It is found that for active control torque constraints the MPC strategy does not result in the discontinuous singular-bang transitions. However, the difference in harvested power is small.