基于参数优化的再入制导律设计

Design of Reentry Guidance Law Based on Parametric Optimization

本文介绍了一种基于参数优化解决再入制导的方法。由于再入飞行过程中存在各种约束,再入制导问题可以看做是一个对给定的目标函数进行优化的最优控制问题。但是直接采用经典最优控制理论的变分法运算量巨大且难以得到解析解。本文把再入制导问题的所有约束都转化成一个目标函数,然后将动力学方程中的控制量进行有限维数的参数化,使再入制导变成了一个有限维的参数优化问题。采用Powell非梯度式优化算法对此问题进行求解。仿真结果表明,在经过26次迭代,301次目标函数计算,目标函数收敛到精度范围,实现了制导的目的。

This paper presents a parametric optimization approach to solve reentry guidance. Due to the various constraints imposed on the trajectory, original guidance problem can be converted into an optimal control problem with a merit function to be minimized. Direct implementation is too complex to get a reasonable result, while a numerical parametric optimization approach is feasible and efficient if we choose appropriate control variables as the optimization parameters and effective optimization algorithm. This paper converts all the constraints into a penalty function, and parameterizes the control variable in infinite-dimension to transform the reentry guidance to an infinite-dimension parametric optimization problem. Simulation result reveals that, the penalty function divergence to the pre-set threshold after 26 iterations and 301 calculation of penalty function.