基于hp自适应伪谱法的固体运载火箭轨迹优化

多级固体运载火箭轨迹优化是一个多阶段多约束的最优控制问题。hp自适应伪谱法融合了有限元法和全局伪谱法的思想,采用双层优化策略对细化单元数和插值基函数的阶次进行自适应调节以满足精度和快速性要求。对基于hp自适应伪谱法的多级固体运载火箭主动段轨迹优化问题进行了数值计算,结果表明该优化方法能够很好的满足过程约束和终端入轨条件,具有收敛速度快、对初值不敏感等优点,有一定的工程应用价值。

Trajectory Optimization of Solid Launch Vehicle Based on Hp-Adaptive Pseudospectral Method

The active phase trajectory optimization of multistage solid launch vehicle is the problem of multi-phases and multi-constraints optimal control.The global pseudospectral method is combined with the finite element method in the hp-adaptive pseudospectral method which adopts double layer optimization strategy to adjust adaptively the segment breaks and the polynomial degree in each segment to meet the precision and speed requirements.The simulation based on hp-adaptive pseudospectral method is implemented,and the results show that the process constraints and terminal conditions are fulfilled and the algorithm has fast convergence and is not sensitive to the initial values.Thus,this optimization method has a great value in the practical applications.