利用高斯伪谱法求解升力航天器最优再入轨迹

Using Gauss Pseudospectral Method to Solve Optimal Reentry Trajectory for Lifting Vehicle

为了获得升力式航天器再入大气后的飞行轨迹,利用高斯伪谱法求解了同时满足路径约束和终端约束条件下的总吸热量最小再入轨迹。其中,路径约束包括驻点热流峰值约束和最大动压约束;终端约束为高度和位置。选取优化控制变量为迎角和倾斜角。仿真结果表明,高斯伪谱法能够快速优化出满足以上优化性能指标和约束条件的再入轨迹。最后,通过对哈密尔顿函数的分析给出了最优性验证。

To obtain the flight trajectory for lifting vehicle after reentry atmosphere, the gauss pseudospectral method（GPM） is used to solve the reentry trajectory with minimum total heat absorption, satisfying both path constraints and terminal constraints. The path constraints include the heat flux peak on stagnation point and maximum dynamic pressure and the terminal constraints include the vehicle＇s height and position. The attack angle and bank angle are chosen as optimal control variables. The simulation results indicate that GPM can solve the reentry trajectory to satisfy the above optimization index and constraint conditions. The optimization performance is tested by Hamiltonian analysis.