临近空间拦截弹最优弹道跟踪制导律

摘要

In allusion to the trajectory tracking process of interception against hypersonic targets in near space,a novel tracking guidance law based on linear quadratic regulator theory and Gauss pseudospectral method was designed.In order to track the nominal trajectory accurately, the linear quadratic tracking problem was considered, while the sufficient and necessary conditions for optimal solutions were deduced with the optimal control theory to acquire the expression of linear state feedback control variables.Based on Gauss pseudospectral method,the time-varying difference matrixes and coefficient matrixes were calculated by using the information of the nominal trajectory on the Legendre-Gauss points to obtain the state disturbances feedback control law.Simulation results show that,compared with the method by solving Riccati equation, this method can obtain the feedback control variables with high accuracy and computation efficiency by less nodes and satisfy the requirement of on-line implementation.%针对拦截临近空间高超声速飞行器的弹道跟踪过程,基于线性二次型调节器理论和高斯伪谱法设计一种跟踪制导律.为了对标称弹道进行精确跟踪,考虑线性二次型跟踪问题,应用最优控制理论推导最优解的充要条件,得到带时变增益的线性状态反馈控制量的表达式;基于高斯伪谱法,在离散的勒让德-高斯点上利用标称弹道数据计算差分矩阵和系数矩阵,求得状态扰动反馈控制律.仿真结果表明,与基于求解矩阵黎卡提方程的方法相比,该方法选取较少的节点即可获得高精度的反馈控制量,且运算效率大幅提高,满足在线实施要求.