In recent years, increasing attention has been given to reducing energy consumption in hydraulic excavators, resulting in extensive research in this field. One promising solution has been the integration of hydrostatic transmission (HST) and hydraulic pump/motor (HPM) configurations in parallel systems. However, these systems face challenges such as noise, throttling losses, and leakage, which can negatively impact both tracking accuracy and energy efficiency. To address these issues, this paper introduces an intelligent real-time prediction framework for system positioning, incorporating particle swarm optimization (PSO), long short-term memory (LSTM), a gated recurrent unit (GRU), and proportional–integral–derivative (PID) control. The process begins by analyzing real-time system data using Pearson correlation to identify hyperparameters with medium to strong correlations to the positioning parameters. These selected hyperparameters are then used as inputs for forecasting models. Independent LSTM and GRU models are subsequently developed to predict the system’s position, with PSO optimizing four key hyperparameters of these models. In the final stage, the PSO-optimized LSTM-GRU models are employed to perform real-time intelligent predictions of motion trajectories within the system. Simulation and experimental results show that the model achieves a prediction deviation of less than 3 mm, ensuring precise real-time predictions and providing reliable data for system operators. Compared to traditional PID and LSTM-GRU-PID controllers, the proposed controller demonstrated superior tracking accuracy while also reducing energy consumption, achieving energy savings of up to 10.89% and 2.82% in experimental tests, respectively.