考虑导弹速度时变的角度约束最优中制导律
Impact angle constrained optimal midcourse guidance law for missiles of time-varying speed

以导弹逆轨拦截高速运动目标为背景，本文运用间接高斯伪谱法设计带攻击角度约束的最优中制导律.通 过零化弹目相对法向速度，将攻击角度约束转化为视线角约束.考虑导弹速度时变的情况，建立带角度约束的制 导方程.根据极小值原理推导最优中制导律的解析表达式，运用高斯伪谱法对最优中制导律进行离散化，把微分 方程转化为代数方程，避免了求解Riccati方程.该方法不需要预先知道导弹未来的速度信息，计算量小，具有较 好的实时性.仿真结果表明该中制导律可以满足逆轨拦截对弹目交会角的约束，且中制导末端的过载较小.
In the background of counter parallel intercepting high-speed moving target, the indirect Gauss pseudospectral method is employed to design an impact angle constrained optimal midcourse guidance law in this paper. Through vanishing the relative normal velocity between missile and target, the impact angle constraint is converted into the line of sight angle constraint. Considering the time-varying velocity of missile, the guidance equation with impact angle constraint is established. An analytical expression of optimal midcourse guidance law is derived based on the Minimum Principle. The Gauss pseudospectral method is used to discretize the optimal midcourse guidance law, then differential equations are turned into algebraic equations, and solving the Riccati equations is avoided. It does not need to know in advance the future velocity information of missiles and the computation load is small, which in-dicates that the proposed method has good real time property. The simulation results show that the proposed mid-course guidance law can satisfy the intersection angle constraint of counter parallel intercepting, and the acceleration command at the end of the midcourse guidance is small.