Optimal Control of Variable-Shape Wave Energy Converters

This letter solves the optimal control problem for variable-shape wave energy converters analytically, where Pontryagin's minimum principle is applied to get the optimal control laws. The optimal control solution for the conventional fixed-shape wave energy converters requires power take-off units with bidirectional power flow capability; this means that it can harvest energy from the waves at certain times and act as an actuator at other instants to keep the system in resonance with the ocean waves. This bidirectional capability requires designing complex and expensive power take-off units. The variable shape wave energy converters were recently introduced to reduce the need for this bidirectional power capability. The main contribution of this letter is to derive the optimal control laws for variable-shape wave energy converters for the flexible passive shell and flexible controlled shell. The optimal control that maximizes the harvested energy is found to include both bang-bang and singular arc phases.