基于最优控制的高超螺旋俯冲轨迹设计

针对高超声速飞行器在俯冲阶段的突防与制导问题，提出了一种基于最优控制的螺旋俯冲轨迹设计方法。首先，根据二阶视线角加速度相对运动方程强耦合、非线性的特点，引入了反馈线性化技术，将非线性系统转化成了线性系统；其次，为了让飞行器实现对目标的期望角度打击，在状态方程中引入了终端落角约束项。然后，以零化视线角速率和使消耗能量最小为目标，采用最优控制得到了加速度形式的控制输入。接着，为了让飞行器在空间内进行螺旋机动，设计了螺旋加速度控制飞行器速度矢量可绕瞬时视线轴进行旋转；最后，考虑到机动与制导的冲突，设计了高度函数使得最优与螺旋两种信号进行匹配。仿真结果显示，在面对相同的防空威胁时，与基于比例螺旋的轨迹相比，本文设计的俯冲轨迹具有更好的突防效果。

Supersonic Vehicle Spiral Dive Trajectory Design Based on Optimal Control

In this paper, aiming at the penetration and guidance of hypersonic vehicles in the dive phase, a method of spiral dive trajectory design based on optimal control is proposed. First, according to strong coupling and nonlinear characteristics of the second-order line-of-sight angular acceleration relative to the equation of motion, the feedback linearization technology is introduced to transform the nonlinear system into a linear system. On this basis, the terminal angle constraint was added. And, the optimal control is adopted to obtain control input in the form of acceleration for zeroing the line-of-sight angular rate and minimizing energy. Then, in order to make the speed of the aircraft rotate around the instantaneous line of sight, a spiral signal was designed. Finally, considering the conflict between maneuvering and guidance, the optimal and spiral signals are weighted combined. The simulation results show that when facing the same air defense threat, the dive trajectory designed in this paper has better penetration than the spiral trajectory via proportional guidance.