高超声速再入轨迹跟踪控制的微分变换方法

针对多约束条件下高超声速飞行器再入制导问题，提出一种基于微分变换法求解最优反馈控制的全状态标准轨迹跟踪制导律。利用滚动时域控制方法设计易于在线执行的闭环跟踪制导策略，在每个制导周期内将标准轨迹跟踪问题转化为线性时变系统状态调节器问题，并通过最优控制理论进一步转化为两点边值问题，采用微分变换法进行求解获得最优反馈控制律。数值仿真表明微分变换法的引入有效解决了传统两点边值问题求解的数值不稳定性与耗时问题，所设计的闭环制导律对状态偏差与模型不确定性具有较强的鲁棒性，可为工程设计提供有益参考。
Concentrating on the hypersonic reentry guidance under multiple constraints, a full-state nominal trajectory tracking guidance scheme was proposed by applying the differential transformation approach to the optimal feedback control. In the period of the online closed-loop guidance scheme based on the receding horizon control, the nominal trajectory tracking problem was transformed into a state regulator problem of the associated linear time-varying system, and then into a two-point boundary value problem by utilizing the optimal control theory. The differential transformation approach was suggested for the optimal feedback control, avoiding the time-consuming and numerical instabilities of conventional methods. Numerical simulation results validate that the proposed guidance scheme is robust to state dispersions and model uncertainties, providing a reference for engineering design. 