无动力学滞后的广义最优制导律解析研究

Analytical study of generalized optimal guidance law for lag-free system

通过建立相对于终端弹目连线的导弹运动方程,将time-to-go的负n次幂函数引入到目标函数中,推导得到不考虑制导动力学的扩展比例导引和扩展的带落角约束的最优制导律。提出了广义最优制导律的概念,阐述了其在两种不同坐标系下的表现形式和意义。针对终端弹目连线坐标系下的广义最优制导律,利用幂级数解法对闭环弹道微分方程进行了解析求解,得到了导弹相对终端弹目连线的位置、速度和加速度指令的解析表达式,并利用仿真的方法对解析结果进行了验证。

Based on the equations of missile motion with respect to the desired terminal line of sight （DTLOS）, the extended proportional navigation and extended optimal guidance law with impact angle constraint was deduced for lag-free system when - n power of time-to-go was introduced into the object function. The concept of the generalized optimal guidance law （GOPL） was proposed and the expressions and meaning of which in two different frames of reference were demonstrated. For the GOPL in the DTLOS frame, the analytical solutions of the closed-form trajectory were derived according to the method of power series and the analytical position, velocity and acceleration command were obtained. Finally, the analytical solutions were validated by the simulation results.