基于hp自适应Radau伪谱法的再入飞行器轨迹优化

Track Optimizing for Reentry Vehicle Based on hp-adaptive Radau Pseudospectral Method

全局伪谱方法在解决平滑最优控制问题时具有指数级收敛速度,但对于状态变量震荡的最优控制问题往往难以在短时间内取得满意解。飞行器机动再入轨迹通常为震荡形式,因此设计了hp自适应Radau伪谱算法(hp-RPM)求解再入最优轨迹。hp-RPM以相对曲率作为判据,将震荡轨迹划分为多个平滑子区间,在每个子区间内采用低阶插值多项式逼近最优轨迹,以提高算法效率、估计精度和解的最优性。仿真结果表明,hp-RPM方法在算法效率、估计精度、解的最优性上,较全局Radau伪谱方法均有较大程度的提高。

Global pseudospectral method converges exponentially in smooth optimum control problems, but it is hard to gain a satisfactory solution of the problem whose status variables are fluctuating. The maneuvering track of reentry vehicle is always fluctuating, so an hp-adaptive Radau pseudospectral algorithm（hp-RPM） was designed to optimize reentry track. In hp-RPM, the fluctuating track was divided into several sub intervals according to the rel- ative curve ratio; low order polynomial was used to approach the optimal track in each sub interval. Simulation re- sults showed that, hp-RPM performed better than global Radau method in efficiency, estimation precision and solu- tion optimality to a variable extent.