## 1 Introduction  
Sea waves are an attractive source of energy due to their relatively large energy density as compared to solar and wind resources [1]. This same high-energy sea environment conspires against the widespread use of wave energy converters (WECs) due to engineering challenges, including extreme event survivability and maintenance [2; 3; 4; 5]. Extracting energy and transferring it to a load efficiently is a WEC's typical objective. Harmonizing its mechanical, power take-off (PTO), and control strategy designs may lead to the practical application of WECs for terrestrial and at-sea energy grids. A point absorber WEC's PTO extracts energy from the relative velocity between its floating buoy and fixed base. By definition, maximum energy extraction is achieved by controlling its PTO force such that the integrated product of the force and relative velocity is maximized subject to the PTO's force and stroke limits. At times the PTO will do work on the buoy, momentarily sacrificing energy extraction to produce a buoy response leading to greater energy extraction later. Energy optimal control has been studied extensively for assumed buoy geometries, including quantifying upper bounds [1; 6; 7], impedance matching [7; 8; 9; 10; 11], and both closed-form [12] and numerical optimal control solutions [13] such as with model predictive control [14; 15; 16]. Early efforts focused on buoy response regimes that can be modeled using linear differential equations considering a buoy's nonlinear response a more recent focus [17; 18; 19]. While this paper investigates a particular buoy geometry, the hourglass shape of [PERSON] et al. [17; 20; 21], it is important to note that understanding mechanical energy extraction is only part of the more complex problem of energy production. Addressing this system-level objective requires simultaneous consideration of the entire process, including the design of the WEC, its PTO, and electrical energy transmission power electronics [22]. Since a point absorber's buoy shape and mass affects its dynamics response, the shape is a crucial design consideration and should be exploited. [PERSON] et al. [23; 24] quantified the benefit of the simultaneous design of a point absorber's buoy geometry and control law. Adaptive shape modification is another method for expanding the performance of a WEC operating in off-nominal sea conditions [25]. The review article by [PERSON] and [PERSON] provides a comprehensive accounting of past and current efforts in shape optimization, clearly illustrating the importance of geometry for a broad range of WEC types. While buoy shape affects a WEC's model form when operating in a linear regime, it can profoundly affect its nonlinear model and response. Computational fluid dynamics (CFD) models can capture these effects but are impractical for real-time, model-based control laws [26]. Closed-form nonlinear Froude-Krylov (FK) force models have been developed in [27; 28; 29] to incorporate buoy shape effects into model-based control laws for large-motion, nonlinear operating regimes. [PERSON] et al. [27] present an analytical approach with 2% error to derive the nonlinear FK forces using [PERSON]'s wave theory for deep water waves to represent the static and dynamic pressure forces acting on the buoy. Researchers have proposed various control strategies that incorporate the analytical nonlinear FK forces. The authors in [30; 31] developed a sliding mode controller for a heaving point absorber that demonstrated the robustness and energy maximization of the WEC. In [32], an optimal model-based control was developed for a data-based modeled heaving point absorber. The latching control is a well-established technique that has also been used in WECs, including those that utilize the computationally efficient closed-form nonlinear FK forces [26; 33; 34]. All of these papers have used conventional buoy shapes such as spheres and cylinders, which have well-studied hydrodynamics.