Abstract: This study addressed the trajectory tracking control problem for upper-limb rehabilitation exoskeletons under unknown model information. A model-free prescribed-time control strategy based on control barrier functions was proposed. Acquiring an accurate dynamic model of the human-robot system is difficult. To solve this problem, a second-order ultra-local model was established to characterize the system's dynamic behavior. RBF neural networks were introduced to estimate the lumped disturbances in the model online. A prescribed-time sliding mode control strategy based on state transformation was designed. This strategy ensured that the system states rapidly and stably tracked the desired motion trajectory. The convergence time of the tracking error has a predefined upper bound. To further enhance rehabilitation training safety, a high-order prescribed-performance control barrier function was constructed. The optimal control law satisfying safety constraints was solved by incorporating the KKT conditions. This law ensures that the system states converge to and remain within the safe set within a prescribed time. The global stability of the closed-loop system and the forward invariance of the safety set were rigorously proved using Lyapunov stability theory. Numerical simulation results verify the proposed strategy. The control strategy drives the system states to zero within the prescribed time. It also continues to satisfy the safety constraints even under sudden disturbances.