We consider predictive control of a wave energy converter
(WEC) that can switch between three modes: 1) power
generation; 2) declutched with no power generation; or 3) latched
with zero velocity. We propose a formulation that turns the optimal
control problem into a small dimensional discrete optimization
problem, where the only decision variables are bounds on
the latching time and power take-off (PTO) time, whereas the
objective function is computed from the trajectory of a hybrid
system with linear dynamics in each sample interval. The optimization
problem is solved using a novel derivative-free algorithm
that exploits the quantization of the decision variables in order
to reduce the number of function evaluations. Two closed-loop
formulations are also studied within a receding horizon implementation:
the first one uses past wave information and can double the
energy generation compared to the uncontrolled case, while the
second formulation uses predictions of future waves and is able to
result in a further increase in energy generation. The benefits of
codesigning the physical system and controller is compared to the
sequential approach of first optimizing the physical system without
control, followed by controller design.