<p>Due to the stochastic, fluctuating, and unstable nature of the output power from offshore floating wind–solar–wave hybrid generation systems under varying weather conditions, a hybrid energy storage system (HESS) is required to smooth power imbalances and stabilize the DC bus voltage of the generation system. To address this, a finite control set model predictive control (FCS-MPC) strategy based on a bidirectional DC–DC converter is proposed. In this approach, the reference power of the energy storage devices, which is essential for the FCS-MPC cost function, is determined by a power decomposition algorithm. Traditional real-time power decomposition methods, such as low-pass filters, exhibit poor adaptability to frequency variations of wave-induced signals. Therefore, an adaptive filtering algorithm combining a convolutional neural network–long short-term memory (CNN-LSTM) hybrid neural network with the multivariate variational mode decomposition (MVMD) preprocessing method was proposed. Simulation results demonstrate that the proposed method effectively maintains the SOC of the hybrid storage systems within a safe operating range under complex power fluctuation conditions, while ensuring that the DC bus voltage remains within permissible voltage fluctuation limits.</p>