Energy maximising controllers (EMCs), for wave energy converters (WECs), based on linear models, are attractive in terms of simplicity and computation. However, such (Cummins equation) models are normally built around the still water level as an equilibrium point and assume small movement, leading to poor model validity for realistic WEC motions, especially for the large amplitude motions obtained by a well controlled WEC. The method proposed here is to use an adaptive algorithm to estimate the control model online, whereby system identification techniques are employed to identify a linear model that is most representative of the actual controlled WEC behaviour. Using exponential forgetting, the linear model can be regularly adapted to remain representative in changing operational conditions. To that end, this paper presents a novel adaptive controller based on a receding horizon pseudospectral formulation. A case study is presented, providing an preliminary evaluation of the adaptive receding horizon pseudospectral control (ARHPC), using simulations based on both linear hydrodynamic modelling and computational fluid dynamics (CFD). The parameter adaptation is shown to behave as expected in both different simulation environments. The ARHPC is observed to perform well in irregular sea states, absorbing more power than its nonadaptive counterpart. The optimal trajectory calculated by the adaptive model is seen to have a smaller motion and power take-off (PTO) forces, compared to those calculated by the nonadaptive linear control model, due to the increased amount of hydrodynamic resistance estimated by the adaptive model, as identified from the nonlinear viscous CFD simulation.