高超声速飞行器滑行航迹优化

Optimization of glide trajectory for a hypersonic vehicle

针对高超声速飞行器滑行的密度模型、动力学模型、空气动力模型和作为输入的攻角,将弹道问题转化为最优控制问题,采用极大值原理求得航程最大的一阶必要条件,采用多次变区间的遗传算法、非线性单纯形法和邻近极值法的组合优化策略来求解此两点边值问题,首先用多次变区间的遗传算法和单纯形方法求得全局航程最大,然后用邻近极值法得到合适的初值满足所有终端约束,通过对一高超声速飞行器的算例进行了优化计算,得到了最优弹道和优化算法的收敛曲线,并与升阻比最大飞行方案进行比较可知,最优控制方案求得的航程大于升阻比最大飞行方案的航程.

According to hypersonic vehicle＇s density model, dynamic model, areodynamic force models and the angle of attack considered as the input, the trajectory problem was cast as the optimal control problem and pontriaghin maximum principle was used to obtain first order necessary condition. A combined optimal approach including changing-region gene algorithm and nelder-mead simplex method and neighboring extrem method were proposed to explore two point boundary value problem. Firstly the gene algorithm and simplex method was used to get the goal optimal solution and then gained the fit initial value which is satisfied with strictly terminal constraints by neighboring extrem method. By optimizing a hypersonic vehicle case, optimal trajectory and the curve convergent was gained, and the result was compared with the flight scheme of maximizing the rate of lift and drag, the range obtaining by optimal control is longer than that by the flight scheme of maximizing the rate of lift and drag.