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The emphasis of this article lies in the development of a gain scheduling algorithm for the constant dynamic pressure ascent trajectory. Due to the broad flight envelope and nonlinear characteristics of hypersonic vehicles, a design method of adaptive control based on guardian maps is proposed. Two types of ascent trajectory are considered: acceleration within Scram mode and acceleration across the Ram–Scram mode transition. A velocity-based linear parameter varying model of an air-breathing hypersonic vehicle is established. The gain vector of controller is determined via optimal control theory based on linear quadratic regulator technology with the specified flying qualities. With the iteration of proposed guardian maps approach, the set of controller gain vector within the flight envelope is obtained. The results of nonlinear simulation show that the proposed approach of control system design has the ability to ensure the global stability through the flight envelope and to maintain the flying qualities.