## 1 Introduction  
The accelerated growth of the global aging population has led to a surge in various associated challenges. Advancing age is associated with a progressive decline in physical function, including heightened risks of hemiplegia, stroke, and cardiovascular/cerebrovascular diseases among the elderly [1]. Simultaneously, complications such as lower limb hypokinesia, dyskinesia, and neurological damage--common in elderly patients--severely impair motor function and activities of daily living (ADLs). Furthermore, prolonged unhealthy lifestyles, high-intensity occupational postures, and traffic accidents elevate the risk of lower limb musculoskeletal injuries and neurological disorders [2], imposing additional psychological and lifestyle burdens. Rehabilitation robots are integrated mechanical systems capable of human-machine interaction. Compared to traditional therapist-assisted rehabilitation, lower limb rehabilitation tion robots enable consistent, timely therapy, reduce labor and material costs, and enhance the recovery of independent ambulation [3,4]. To overcome the limitations of conventional rehabilitation, researchers have developed diverse exoskeleton systems aimed at alleviating the physical burden on therapists during training [5]. Gait rehabilitation robots primarily facilitate lower limb training in an upright posture, mitigating muscle atrophy via repetitive gait exercises, and are particularly effective for mid-to-late-stage recovery in patients with motor impairments [6]. Notably, three commercially advanced gait rehabilitation robots--the FREE Walk [7], Indego [8], and HALML05 [9] exoskeletons--are tailored for patients with spinal cord injuries (SCIs) or other neurological/musculoskeletal impairments but preserved upper limb function. These systems aid rehabilitation by supporting gait training and sit-to-stand transitions. In clinical trials, gait rehabilitation robotics employs clinical gait analysis (CGA) curves [10] to plan corrective exoskeleton motion trajectories, thereby accelerating anticipated patient recovery [10]. However, environmental factors may introduce deviations between the exoskeleton's planned motion and the patient's actual joint kinematics during training. For effective lower limb rehabilitation, precise alignment with the patient's ideal gait trajectory is critical for optimal outcomes. Advances in artificial intelligence (AI) and computing have enabled the integration of AI with conventional control methods for non-linear system regulation. Notably, control strategies like sliding mode control (SMC), fuzzy logic control, and zero-moment-point (ZMP) control have been successfully implemented in rehabilitation exoskeletons [11]. For instance, [PERSON] et al. developed an adaptive RBF neural sliding mode (ARNNSM) controller for a mobile lower-limb rehabilitation robot. The controller leverages asynchronous bias and functional assessments to evaluate patient capability, computing adaptive assistive torques with a challenge factor to optimize motor function. Simulations confirm its robustness against perturbations and accurate trajectory tracking [12]. Similarly, [PERSON] devised a finite-time fractional-order non-singular fast terminal sliding-mode controller, employing a fuzzy neural network to estimate external disturbances, guaranteeing finite-time convergence and robust exoskeleton performance. Nevertheless, in real-world rehabilitation systems, control instability primarily stems from system uncertainties and external disturbances. Sliding mode control (SMC) remains prevalent owing to its robustness, rapid convergence, and implementation simplicity [13]. However, conventional SMC cannot guarantee finite-time convergence to equilibrium and suffers from singular perturbation issues [14,15]. Thus, enhancing traditional control methods is essential for reliable rehabilitation system deployment and improved patient outcomes.