基于间接Radau伪谱法的滑翔段轨迹跟踪制导律

针对高超声速飞行器滑翔段制导问题，提出一种利用间接Radau伪谱法求解最优反馈控制律的全状态标称轨迹跟踪制导律。将标称轨迹跟踪问题转化为线性时变系统状态调节器问题，基于Pontryagin极大值原理进一步将状态调节器问题转化为线性两点边值问题；利用间接Radau伪谱法求解所得的线性两点边值问题，获得最优反馈控制律，并在此基础上设计了易于在线执行的闭环轨迹跟踪制导律。数值仿真结果表明，该制导律对飞行器初始状态量的较大范围偏差和飞行环境参数的有限扰动不敏感，具有良好的鲁棒性，并且能够满足实时性的需求。

Gliding Trajectory Tracking Guidance Law Based on Indirect Radau Pseudospectral Method

A full-state nominal trajectory tracking guidance scheme, in which the optimal feedback control law is solved by indirect Radau pseudospectral method, for hypersonic vehicle gliding guidance is proposed. Based on the Pontryagin maximum principle, the state regulator problem for a linear time-varying system converted from the original trajectory tracking problem is transformed into the linear two point boundary value problem. The indirect Radau pseudospectral method is applied to solve the obtained linear two point boundary value problem, and the closed-loop trajectory tracking guidance law easily implemented online is designed on the basis of the resulting optimal feedback control law. Simulation results indicate that the proposed guidance scheme is robust to the presence of large initial state deviations and limited flight environment parameter disturbances, and satisfies real-time requirement.