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Since the air-breathing hypersonic vehicle model is uncertain, multivariable and coupled, an adaptive generalized backstepping control strategy is proposed to realize the tracking of velocity and altitude in this paper. As the additional control input, the canard deflection is introduced into the standard adaptive backstepping procedure to counteract the coupling between the lift force and the elevator deflection. An integral filter is used to replace the complicated derivation operation during designing the controller. For attack angle and flight-path angle being immeasurable, the sliding mode observer is designed under the measurement of the other states. The simulation results show the good performance of the controller and observer.