## 1 Introduction  
Underwater exploration is critical in understanding our oceans, impacting fields such as climate science, environmental monitoring, and resource management [1, 2]. Recent technological advancements have enabled the development of sophisticated autonomous underwater vehicles (AUVs), equipped with high-resolution sensors, advanced navigation systems, and powerful propulsion capabilities, allowing them to operate in complex and deep-sea environments. Among these AUVs, underwater gliders (UGs) represent a unique subclass, first conceptualized by [PERSON] in 1989. UGs utilize buoyancy adjustments to glide through the water, collecting data on essential parameters like temperature, salinity, and currents [3, 4]. Their energy-efficient design enables long-term autonomous operation, making them particularly valuable for monitoring complex oceanic phenomena such as mesoscale eddies, internal waves, and hurricane activity [5]. Despite their inherent advantages, during operation, UGs confront considerable challenges arising from complex and time-varying currents, which can significantly compromise their control precision and operational efficiency [6, 7, 8]. The accurate prediction of their operational parameters is crucial for optimizing mission planning and ensuring data quality [9, 10]. The current control methods for UGs in practical applications can generally be categorized into onboard control methods and remote control algorithms [11, 12]. The former operate within the UG control unit, focusing extensively on constructing the dynamic model and selecting parameters specifically for the glider's body. This tends to result in highly specific control approaches, lack universality, and struggle with the complexity and dynamic nature of underwater environments [7; 13]. Remote control algorithms, operated from shore-based control centers, not only allow the application of complex control algorithms but also enable human intervention and real-time adjustments to the control precision of underwater gliders, thereby avoiding mishaps in this regard [14; 15]. However, this undoubtedly increases human and time costs. Currently, UG control parameter tuning primarily relies on manual experience, which significantly lowers the accuracy and efficiency of control in practical missions [16]. In the research on the control and navigation of underwater gliders, scholars have proposed various methods to improve control accuracy, address environmental disturbances, and optimize energy efficiency. [PERSON] et al. [17] employed an anti-system approach to decouple the original multi-input, multi-output (MIMO) system into two independent single-input, single-output (SISO) linear subsystems, then used sliding mode control (SMC) to control each subsystem individually, followed by simulation verification. [PERSON] and [PERSON] [18] applied the LQR method to control the depth of a zigzag gliding path, and also conducted simulation validation. [PERSON] et al. [19] designed a layered PID controller that adjusted the heading via the rudder, achieving enhanced energy efficiency. [PERSON] et al. [20] investigated how the initial heading error in underwater gliders affects trajectory accuracy and explore sensitivity analysis of navigation commands to enhance path precision. In the context of interdisciplinary integration across various fields, researchers have introduced deep neural network models into UG control studies, aiming to reduce reliance on physics-based modeling. [PERSON] et al. [21] proposed a model predictive control method based on recurrent neural networks to regulate the pitch angle, and its effectiveness was verified through simulation. [PERSON] et al. [22] utilized neural networks to fit dynamic models and designed a neural network predictive controller for UG motion control, comparing its performance with model predictive controllers (MPCs) and linear quadratic regulators (LQRs) through simulation. [PERSON] et al.