针对考虑终端脱靶量、碰撞角和加速度多约束的精确制导问题,提出了一种可解析求解的多项式最优制导律。将视场角正切值设定为弹目距离的多项式函数形式,将终端多约束条件转化为多项式系数的代数关系式,并引入优化思想,得到弹目距离加权的能量最优指标下的多项式系数最优解,依据弹目运动关系将视场角正切值变化改写为相应满足终端碰撞角约束与加速度约束的制导指令解析式。针对不同加权系数、不同终端打击角度等条件对制导律制导效果进行了仿真验证,并与弹道成型制导律进行了对比。仿真结果表明,所提出的制导律可以使导弹以任意期望碰撞角准确命中目标,终端过载指令平稳收敛至0,避免了末端指令饱和现象。相较此前多项式制导相关研究,文中制导方法避免了在制导模型中引入小角度线性近似条件,提高了对轨迹与制导指令的设计精度,并能约束视场角大小从而规避系统可能出现的奇异性问题和自变量单调性问题,在终端可实现全向攻击。

An analytically solvable polynomial optimal guidance law is proposed for the precision guidance problem considering multiple constraints on terminal miss distance, impact angle and acceleration. By setting the tangent value of look angle as a polynomial function of the relative distance between target and missile, the terminal multiple constraints are transformed into algebraic relations of polynomial coefficients. The optimization theory is introduced to obtain the optimal solution of polynomial coefficients under the energy optimal index weighted by the distance between target and missile. According to the motion relationship of missile and target, the tangent value of look angle is rewritten as the analytic expression of guidance instruction which satisfies the terminal impact angle and acceleration constraint. The guidance effect of guidance law is verified by simulation according to different weighted coefficients and different terminal impact angles, and the results are compared with the trajectory shaping guidance law. The simulation results show that the proposed guidance law is able to lead the missiles attack the target accurately at any desired impact angle, and the terminal acceleration instruction converges to 0 smoothly, which avoids the phenomenon of terminal instruction saturation. Compared with previous research on polynomial guidance, the guidance method avoids introducing linear approximation condition for small angles into the guidance model, which improves the accuracy of trajectory and guidance instruction design. At the same time it can constrain the look angle to avoid the singularity problem and the monotonicity problem of the independent variable that may occur in the system, and can attack in all directions at the terminal time.