This study presents a control design of an angular position for the exoskeleton knee assistance system based on a model reference adaptive control (MRAC) strategy. Three schemes of the MRAC design have been proposed: the classical MRAC, MRAC with an adaptive disturbance observer, and MRAC with a nonlinear observer. The stability analysis for each scheme has been conducted and developed based on the Lyapunov theorem to prove the uniform ultimate bound of tracking and estimation errors. In addition, the adaptive laws have been developed for the proposed schemes according to the stability analysis. The effectiveness of the proposed state and output feedback controllers has been verified via computer simulation. The results based on numerical simulation have shown that the MRAC with a nonlinear observer could give better robustness characteristics and better performance in terms of tracking and estimation errors as compared to the other controllers.