为提高运载火箭在大气层外当推力出现故障条件下制导算法的最优性、鲁棒性和适应性，提出了一种改进的迭代制导方法。该方法以基于最优控制理论推导的解析形式作为最优控制解，并推导出以5个轨道根数作为终端约束的横截条件，增强了算法的最优性；迭代过程中采用高斯-勒让德方法计算推力积分，并采用球极坐标系下泰勒多项式逼近方法计算引力积分，提高了故障模式下算法的积分精度；该算法采用降维迭代求解模式，并结合对控制变量的合理限幅，保障了推力故障条件下算法的实时性和收敛性。分别基于蒙特卡洛打靶和推力故障条件下进行仿真验证，结果验证了所提方法具有较强的最优性、鲁棒性和故障适应能力。
To improve the optimality, robustness and adaptability of the guidance method for the launch vehicle in case of thrust fault outside the atmosphere, this paper proposes an improved iterative guidance method which derives the transversality condition with five orbital elements as the terminal constraint using the analytical expression based on the optimal control theory as the optimal control solution, thereby enhancing the optimization of the algorithm. In the iterative process, a Gauss Legendre integral method is adopted to calculate the thrust integral, and a Taylor polynomial approximation method is used to calculate the gravity integral, improving the integration accuracy in the fault mode. The proposed method adopts the dimension reduction iteration mode and the reasonable limiting of the control variables to ensure the real-timeness and convergence of the algorithm under the condition of thrust fault. The simulation results based on the Monte Carlo method and thrust fault conditions show the strong optimality, robustness and fault adaptability of the proposed method.
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