Abstract: 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.

Key words: Optimal control, Three dimensional guidance law, Head on interception, Hyperbolic tangent function, Impact angle constraint, Time-varying velocity of missile