  In this paper, we systematically investigate the feasibility of different
extremum-seeking (ES) control schemes to improve the conversion efficiency of
wave energy converters (WECs). Continuous-time and model-free ES schemes based
on the sliding mode, relay, least-squares gradient, self-driving, and
perturbation-based methods are used to improve the mean extracted power of a
heaving point absorber subject to regular and irregular waves. This objective
is achieved by optimizing the resistive and reactive coefficients of the power
take-off (PTO) mechanism using the ES approach. The optimization results are
verified against analytical solutions and the extremum of reference-to-output
maps. The numerical results demonstrate that except for the self-driving ES
algorithm, the other four ES schemes reliably converge for the two-parameter
optimization problem, whereas the former is more suitable for optimizing a
single-parameter. The results also show that for an irregular sea state, the
sliding mode and perturbation-based ES schemes have better convergence to the
optimum, in comparison to other ES schemes considered here. The convergence of
PTO coefficients towards the performance-optimal values are tested for widely
different initial values, in order to avoid bias towards the extremum. We also
demonstrate the adaptive capability of ES control by considering a case in
which the ES controller adapts to the new extremum automatically amidst changes
in the simulated wave conditions.
