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A novel nonlinear adaptive control method is presented for a near-space hypersonic vehicle（NHV) in the presence of strong uncertainties and disturbances. The control law consists of the optimal generalized predictive control （OGPC) method and functional link network（FLN) adaptive adjustment law. The output prediction defined on finite horizon is carried out via Taylor series expansion. The FLN adaptive law is used to cancel the unmodeled dynamics and unknown disturbances in flight through online learning. The stability analyses of the close-loop system are provided also. The simulation results show satisfactory performance of the controller for the tracking of reference attitude angles and angular accelerations，and the robustness to parameters variations and the disturbance rejection are successfully accomplished.