关键词: 飞行器控制、导航技术, 扩展弹道成型, 剩余飞行时间, 最优控制, 施瓦茨不等式, 脱靶量

Abstract: The extended weighted and object functions are proposed based on the time-to-go exponential function. The optimal control theory is used to deduce a family of extended optimal trajectory shaping guidance laws for the constant maneuvering target. According to Schwartz inequality, the analytical solution of the guidance law acceleration command is derived by introducing the initial displacement, initial heading error, target maneuver and final impact angle into the lag-free guidance system. The analysis shows that the final acceleration command approaches to zero when the exponent of the time-to-go exponential function is greater than zero. The non-dimensional position and angle miss distance of guidance system with first order lag are studied using the non-dimensional method and the adjoint method. The results show that the position and angle miss distance induced by the heading error and final impact angle approach to zero when the missile terminal guidance time is about 15 times of the system lag time constant. And also, the position and angle miss-distance are smaller when the signs of initial heading error angle and final impact angle are opposite.

Key words: control and navigation technology of aerocraft, extended trajectory shaping, time-to-go, optimal control, Schwartz inequality, miss distance