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In this study, the adaptive Kriging controller is investigated for the longitudinal dynamics of a generic hypersonic flight vehicle. For the altitude subsystem, the dynamics are transformed into the strict-feedback form where the back-stepping scheme is used. The velocity subsystem is transformed into the output-feedback form. Considering the non-linearity of the dynamics, the nominal feedback is included in the controller while Kriging system is used to estimate the uncertainty, which is described as the realisations of Gaussian random functions. To eliminate the infinite increase of the data size, the recursive Kriging algorithm is adopted in this study. Under the proposed controller, the almost surely bounded stability analysis is presented. The simulation study compared with neural back-stepping control is presented to show the effectiveness of the proposed control approach.