# Real-Time Sea State Estimation for Wave Energy Converter Control via Machine Learning
## 1 Introduction  
Harnessing ocean wave energy offers a promising renewable energy resource by exploiting the vast and consistent energy of the ocean. Wave energy converters (WECs) face significant challenges in achieving efficient energy conversion due to the dynamic and unpredictable nature of ocean waves [1]. Effective control strategies are crucial to ensure that WECs operate optimally and safely under these varying conditions, although developing such strategies is a challenging task. Several types of WEC control strategies have been widely explored in the literature. These strategies mainly utilize predefined incoming ocean wave characteristics to optimize control actions and maximize energy extraction. Model predictive control (MPC) is a popular approach for WECs when wave profiles are known, and it can be used in diverse sea state conditions while obeying system constraints. [PERSON] and [PERSON] [2] introduced an MPC framework that used wave profile information to optimize Power Take-Off (PTO) forces for enhanced energy absorption. Similarly, [PERSON] et al. [3] demonstrated simplified wave models for MPC, improving real-time performance. Complex conjugate control (CCC) maximizes power transfer by matching the impedance of the WEC to the incoming wave. Foundational work by [PERSON] [4] showed that known wave excitation forces allow impedance matching for optimal energy transfer. However, CCC is non-causal,as it requires future knowledge of wave forces. [PERSON] and [PERSON] [5] developed predictive approximations to make CCC viable in real-time applications. Feedback resonating control (FBR) tested by [PERSON] et al. [6] shows promising results by leveraging known sea states to adjust resonance frequencies. Proportional-integral-derivative (PID) controllers, often adapted with wave prediction, have also been studied in the WEC context. [PERSON] and [PERSON] [7] demonstrated that PID control tuned to anticipated wave periods and amplitudes allowed WECs to track wave oscillations effectively. Adaptive PID gains, as seen in the work of [PERSON] et al. [8], further improved performance over short intervals as wave conditions varied. In parallel, classical state-estimation algorithms such as Kalman filtering [9], the Extended Kalman Filter (EKF) [10], and the Unscented Kalman Filter (UKF) [11] have long been used to infer unmeasured dynamic states under linear or mildly nonlinear models and Gaussian noise assumptions. Particle filters [12] generalize this to highly nonlinear, non-Gaussian settings via sequential Monte Carlo sampling. In the WEC domain, [PERSON] et al. [6] demonstrated a Kalman-based wave-prediction scheme to infer excitation forces from onboard measurements, though its accuracy degrades under model mismatch and non-Gaussian disturbances. Linear quadratic regulator (LQR) controllers [13] optimize a quadratic cost around a fixed linearization, requiring re-linearization or gain scheduling as sea conditions change. A central assumption for these approaches is to have a well-defined model representation of the WEC device, which is often computationally expensive given diverse sea conditions. Machine learning techniques, particularly deep learning, have recently emerged as promising tools for WEC control due to their adaptability and ability to generalize across diverse conditions [14; 15]. In wave energy research, deep neural networks (DNNs) have been explored for predicting wave characteristics based on historical data and WEC operational parameters [16]. These studies suggest that DNNs can be effective in identifying patterns in highly variable data, enabling WECs to respond more flexibly to changing ocean states without direct wave measurements. More recently, reinforcement learning has been applied to optimize control based on known sea states. [PERSON] and [PERSON] [17] developed a reinforcement learning-based controller trained on wave data, predicting control actions across various sea states.