Non-causal model predictive control for rigid-body wave energy converters based on physics-informed neural networks

• Introduced a novel Model Predictive Control (MPC) based on Physics Informed Neural Networks (PINNs) framework to optimise energy generation in rigid-body Wave Energy Converters (WECs). • Demonstrated comparable energy generation performance of the proposed PINNs-MPC scheme compared to traditional MPC with perfect model information. • Incorporating physical model knowledge and constraints to reduce sampling complexity compared to traditional neural networks (NNs). • Demonstrating PINNs-MPC capability to generate energy in different irregular wave conditions. The energy maximisation for Wave Energy Converters (WECs) is a non-causal problem where the current power take-off (PTO) force incorporates knowledge of future wave prediction to significantly boost energy harnessing. Since WECs are constrained by PTO limitation and other limitation regarding safe operations, model predictive control (MPC), as a well-known non-causal control algorithm, is considered as a proper algorithm to optimise the energy output subject to multiple constraints. However, MPC controller relies on an accurate model to generate maximum energy. Obtaining and utilising such fully known models is challenging due to the highly nonlinear dynamics and stochastic sea wave environment of WECs in various wave conditions. Traditional machine learning method can be a solution since they are able to model complex dynamical systems. However, they suffer from the requirement of a large amount of training data, which introduces significantly increased computational burden. To tackle these challenges, this paper introduces a control framework that can utilise prior partial model information and have better sampling efficiency by integrating Physics-Informed Neural Networks (PINNs) with MPC to optimise the energy generation of WECs. As the benchmark of WECs control, the point absorber is chosen to evaluate the effectiveness of the proposed PINNs-MPC, in which 35 sea wave scenarios ranging from H s = 1.25 m, T p = 1 s to H s = 2.50 m, T p = 12 s are tested. The proposed method can be applied to other types of WECs by retaining the PINNs.