## 1 Introduction
### State of the Art  
Significant efforts have been made to understand and mitigate the nonlinear characteristics of hydraulic systems. Many applications require dynamic control compensation to ensure performance, which is crucial for maintaining the robustness of hydraulic systems. Hydraulic presses, among the most important hydraulic drive systems, are often used in manufacturing processes such as forging, stamping, extrusion, molding, and bending. For instance, [PERSON] et al. [6] investigated the effects of forming processes on hydraulic press performance, demonstrating how advanced control techniques improve product quality by minimizing positioning errors caused by nonlinearities. Model-driven approaches have been widely employed to replicate the physical behavior of hydraulic systems under varying conditions. However, researchers report that these methods face limitations and show deviations from the real environment of up to 60% in pressure, flow, and displacement conditions [12; 13]. Physical models often inadequately capture the complex interactions in hydraulic systems under variable operational conditions, such as dynamic loads or environmental changes. Highly accurate position tracking for hydraulic systems is challenging and requires complicated control algorithms, where data-driven approaches are introduced, achieving an accuracy of over 92% [14]. As a drawback, the relationships among variables in hydraulic systems are complex and require data acquisition from the actual system. Therefore, the data-driven models are more complementary in the operational domain of the system under defined conditions and can be integrated as soft sensors [15]. Data-driven approaches have emerged as complementary solutions, leveraging machine learning (ML) and artificial intelligence techniques to improve predictive accuracy and real-time monitoring. For instance, [PERSON] and [PERSON] [16] developed an online fuzzy PID controller using a robust extended Kalman filter, significantly enhancing the performance of an electrohydraulic actuator. [PERSON] et al. [17] improved steering system performance by 19.7% with an adaptive controller combining the evolutionary bat algorithm, a fuzzy neural network, the Lyapunov theory, and the backstepping method. [PERSON] et al. [18] proposed hydraulic cylinder piston position detection using a data-driven complex-valued convolutional neural network (CNN) with frequency encoding, outperforming conventional ML models such as support vector machines (SVM), k-nearest neighbor (k-NN), and decision trees (DT) with an accuracy that has an error reduction of 1/12 compared to the physical model. Similarly, [PERSON] et al. [19] used Bayesian network models for fault diagnosis, leveraging Gaussian process (GP) distributions to understand relationships between monitored variables. The verification results of the engineering examples show that the most accurate ML models are based on neural network (NN) or Gaussian process regression (GPR) with Bayesian optimization following GP distribution [20; 21; 22]. However, it should be noted that there is no single machine learning model used in hydraulic press applications that enables intelligent and adaptive control to reconfigure and adapt to the conditional changes of external disturbances. Despite these advances, the integration of adaptive control systems into hydraulic presses remains an open area for research [23]. Adaptive control, which dynamically reconfigures the system in response to external disturbances, holds promise for addressing the limitations of both model-driven and data-driven methods [24; 25; 26]. Efficient ML strategies can further enhance hydraulic system performance. Researchers have shown that simpler ML models integrated within expert systems, when carefully designed, can achieve similar levels of accuracy as complex models (more than 95%) while requiring less computational power [27; 28].