## 1 Introduction
The article evaluates performance in terms of control acceleration and fuel cost, employing Jordan decomposition to simplify relative dynamics. The trajectory optimization method, based on a functional integral and polynomial series, is analytically proven to be valid. The numerical results demonstrate successful and efficient formation reconfiguration. [PERSON] [8] introduces ESVR-MFS, a multi-fidelity surrogate model based on extreme support vector regression (ESVR) for engineering system optimization. ESVR-MFS efficiently utilizes both higher-fidelity and lower-fidelity samples, demonstrating competitive performance in terms of prediction accuracy and computational cost. The proposed approach is valuable for practical multi-fidelity engineering design problems. [PERSON] [9] has proposed an ammonia-diesel stratified injection technology for the application of low-carbon ammonia fuel in marine engines, aiming to meet future low-carbon emission regulations. The results indicate that this strategy achieves a power output comparable to those of traditional diesel engines, without the need for additional matching pilot fuel injectors, and while significantly reducing CO2 and NOx emissions. This innovative approach holds promising prospects for future applications in marine engines. [PERSON] [10] investigated the potential threat posed by subsurface mesoscale cracks in the outer ring of full ceramic ball bearings (FCBBs) to the stable operation of related devices. Using a dynamic model based on the strain energy theory, the study analyzed the impact of different crack lengths on the operational state. [PERSON] [11] presents a digital-twin-driven model for predicting early degradation in ceramic bearings. Using an LSTM neural network and vibration signals, it maps stiffness weakening factors to degradation indices. The model, combining digital-twin technology with real-time data, effectively predicts early degradation trends, offering insights for life-prediction and maintenance strategies for ceramic components in key aviation and military equipment. [PERSON] [12] proposes a low-pass virtual filter (VF) for wind energy conversion systems (WECSs) to smooth power output without the need for a physical energy storage system. The VF, integrated into the active power control loop, effectively reduces high-frequency wind power fluctuations. A stability-constrained coefficient ensures wind turbine (WT) stability. Simulations and experiments validate the VF's efficacy in minimizing wind power fluctuations and the stability-constrained coefficient's role in maintaining WT stability. [PERSON] [13] used objective function optimization theory with the maximum level bucket capacity as the objective function. They optimized the parameters for a high-performance bucket for a 3-ton EWL. Through comprehensive performance experiments, they verified the advantages of the high-performance bucket in terms of operating efficiency, fuel economy, and other aspects. [PERSON] [14] places greater emphasis on detecting the impact caused by uneven terrain during vehicle travel, particularly concerning speed control, and extracts roughness coefficients by monitoring actual vertical acceleration caused by uneven terrain. This tactic utilizes a self-supervised learning approach to predict these coefficients from laser data, aiming to facilitate the safe deceleration of vehicles. The key distinction of the present work lies in the fact that this paper focuses on the prediction of shovel force and power-matching optimization for large-tonnage EWLs, emphasizing the optimization of vehicle power matching and control. This paper employs the discrete element method (DEM) and a backpropagation neural network learning algorithm (BP NNLA), combining theoretical analysis and simulation to predict shovel force and optimize power matching. The design of the bucket and engine matching is guided by the research on shovel force. Many scholars have conducted extensive research on the loading section of the device [15; 16].