逆轨拦截机动目标的三维最优制导律

以大气层内导弹逆轨拦截高速机动目标为背景，本文运用最优控制和双曲正切函数设计带角度约束的三维最优制导律。分别假设导弹弹道倾角和弹道偏角保持瞬时恒定，将三维制导分解为两个相互垂直平面内的二维制导。考虑导弹速度时变的情况，建立带角度约束的制导方程。设计一种双曲正切函数的变种，并将其设为脱靶量和角度约束的权重系数，根据极小值原理推导了最优制导律的解析表达式。双曲正切函数变种的引入，使得制导律对脱靶量和角度约束的要求是逐渐增强的，可以解决传统最优制导律初始段过载指令过大的问题。仿真结果表明了该制导律的有效性。

Three Dimensional Optimal Guidance Law Against Maneuvering Targets for Head on Engagement

In the background of counter parallel intercepting high-speed maneuvering targets in the atmosphere, the optimal control and hyperbolic tangent function are employed to design a three dimensional optimal guidance law with impact angle constraints in this paper. Assuming that the flight path angle and heading angle keep instantaneous constant, the three-dimensional guidance design is decomposed into two two-dimensional guidance designs in two planes perpendicular to each other. Considering the time-varying speed of missile, a guidance equation with angle constraint is established. A variant of the hyperbolic tangent function is designed and set as the weighting coefficients of miss distance and intercept angle constraints. An analytic expression of the optimal guidance law is derived according to the minimum principle. The introduction of a variant of the hyperbolic tangent function makes that guidance law’s requirement on miss distance and intercept angle constraint gradually increase, and can solve the problem of overloading in initial stage of the traditional optimal guidance law. The simulation results show the effectiveness of the proposed guidance law.