Periodic cruise has the potential to improve the fuel-saving efficiency of hypersonic cruise vehicle but is difficult to optimize. In this paper, a two-level optimization method for the trajectory of periodic cruise is proposed. Due to that the periodic cruise trajectory can be divided into an acceleration phase where engine works and a glide phase where engine is off, the two-level optimization method is proposed to optimize the trajectory in each phase by the corresponding level. In the first level, Downhill Simplex Method (DSM) is employed to find an optimal angle of attack in the acceleration phase. Subsequently, the optimal trajectory in glide phase is obtained by the Pseudo-Spectral Method (PSM) in the second optimization level. Numerical results demonstrate the effectiveness of the proposed method. Finally, through comparing with steady-state cruise, it is concluded that periodic cruise makes full use of the change of atmospheric density and lift-drag ratio; thus, fuel saving is achieved.

中文翻译：

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一种高超声速周期巡航轨迹的两级优化方法

周期性巡航具有提高高超音速巡航飞行器节油效率的潜力，但难以优化。本文提出了一种周期性巡航轨迹的两级优化方法。由于周期性巡航轨迹可分为发动机工作的加速阶段和发动机关闭的滑行阶段，提出了两级优化方法，将每个阶段的轨迹按相应级别进行优化。在第一级，下坡单纯形法 (DSM) 用于在加速阶段找到最佳攻角。随后，通过伪谱方法（PSM）在第二优化级别中获得滑行阶段的最佳轨迹。数值结果证明了所提出方法的有效性。最后，通过与稳态巡航的对比，得出周期性巡航充分利用了大气密度和升阻比的变化；从而达到节省燃料的目的。