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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。
Aiming at the problem of reentry guidance for hypersonic vehicles under multiple constraints, a state-of-the-art standard trajectory tracking guidance law based on differential transformation to solve the optimal feedback control is proposed. The closed-loop tracking guidance strategy which is easy to carry out on-line is designed by rolling time domain control method, and the problem of standard trajectory tracking is transformed into the linear time-varying system state regulator problem in each guidance period and further transformed into two-point edge by optimal control theory Value problem, using the differential transform method to obtain the optimal feedback control law. The numerical simulation shows that the introduction of the differential transformation method effectively solves the numerical instability and time-consuming problem of the traditional two-point boundary value problem. The closed-loop guidance law is robust to the state deviation and model uncertainty, Can provide a useful reference for engineering design.