基于邻域最优控制的跟踪制导律设计

针对拦截临近空间高超声速飞行器的中制导过程，设计了一种基于邻域最优控制（NOC）的跟踪制导律.首先，采用高斯伪谱法离线设计得到满足终端约束与过程约束的标称最优弹道；其次，为了对标称弹道进行精确跟踪，将弹道满足的一阶最优性必要条件进行二阶变分，在标称弹道邻域内得到一条满足二阶最优的修正弹道；最后，应用间接高斯伪谱法，在离散的勒让德-高斯（LG）点上将转化后的两点边值问题离散为代数方程进行矩阵求逆运算，利用标称弹道数据求得反馈控制律.仿真结果表明，该方法能有效地消除跟踪误差，并且能够满足在线实施的要求. 

Design of Tracking Guidance Law Based on Neighboring Optimal Control

To improve the midcourse guidance process of the interception against hypersonic targets in near space, a novel trajectory tracking guidance law based on neighboring optimal control (NOC) was designed. Firstly, the nominal trajectory satisfying terminal and path constraints were generated by Gauss pseudospectral method. Secondly, in order to track nominal trajectory accurately, the first order necessary conditions were further differentiated to second order to obtain the second-order optimal updating trajectory in the neighborhood of nominal trajectory. Finally, based on indirect Gauss pseudospectral method, the transformed two-point boundary value problem was discretized to algebraic equation for matrix inverse operation at Legendre-Gauss (LG) point and then feedback control law was obtained using nominal trajectory. Simulation results show that this method can eliminate tracking error effectively and satisfy the requirements of on-line implementation.