Wearable exoskeletons can augment human phys ical capabilities during complex activities. However, ensuring adaptation across diverse tasks while guaranteeing interaction safety remains a critical challenge. To address this, a simulation trained variable impedance control approach with stability guarantees is proposed. First, a simulation-based human exoskeleton motion data generation pipeline is established, utilizing Proximal Policy Optimization (PPO) to synthesize human muscle activations while the exoskeleton provides direct compensation for human biological joint torques. Subsequently, the generated dataset is used to train a dual modality policy that fuses semantic instructions with proprioceptive history, enabling the prediction of reference trajectories and variable impedance gains for nine different motion tasks. To guarantee safety, the network outputs are constrained by a stability criterion derived from Lyapunov stability theory, which bounds stiffness variations to ensure the asymptotic stability of the coupled system. Experimental results indicate that the proposed framework reduces metabolic cost in real-world scenarios com pared with standard baseline methods. These findings suggest the feasibility of the proposed framework for safe, multitask exoskeleton control.