  We implement a causal model predictive control (MPC) strategy to maximize
power generation from a wave energy converter (WEC) system, for which the power
take-off (PTO) systems have both hard stroke (i.e., displacement) limits and
force ratings. The approach models the WEC dynamics in discrete-time, in a
manner that exactly preserves energy-flow quantities, and assumes a stationary
stochastic disturbance model for the incident wave force. The control objective
is to maximize the expected power generation in stationarity, while accounting
for parasitic losses in the power train. PTO stroke measurements are assumed to
be available for real-time feedback, as well as the free-surface elevation of
the waves at a designated location relative to the WEC, and the open-loop
dynamics of the WEC are assumed to be linear and time-invariant. Mean-square
stability of the MPC algorithm is proven. The methodology is illustrated in a
simulation example pertaining to a heaving cylindrical buoy.
