基于改进梯度法的助推段快速弹道优化

Improved Gradient Algorithm for Ascent Trajectory Optimization

针对固体火箭大气层内助推段弹道优化问题,对梯度法进行了改进。在动力学方程的线性化模型中加入控制的二阶项,从而使得在应用梯度法时不需要在目标函数中引入控制相关附加项。对上述线性时变最优控制问题进行解析求解,获得了控制曲线的最优修正。通过多次迭代修正标准控制曲线,最终获得了固体火箭大气层内助推段弹道的最优解。仿真校验表明,该方法具有计算量小、收敛速度快、对初值不敏感等优点,可运用于助推段迭代制导。

The gradient method has been improved and applied to endoatmospheric trajectory optimization of solid rocket. The second order term of the control is added to the linearized dynamic equations,and thus no additional control item is needed by the objective function to implement the gradient algorithm.Then the optimal control modifications are obtained by resolving the above linear time-varying optimal control problem. Finally,the optimal ascent trajectory of the solid rocket is obtained by updating the standard control. The results show that the method is characterized by light computational load,fast convergence speed and insensitivity of the initial value,and can be applied to the iterative guidance of the boost phase.