加速度峰值最小的落角约束导引律设计

Minimax Acceleration Guidance Law Design with Impact Angle Constraint

针对静稳定度较高的导弹在实现大落角攻击时存在操纵能力不足的问题,提出了一种带落角约束的加速度峰值最小的导引律,以降低末制导需用过载、避免控制饱和。通过引入辅助状态将峰值最小化问题转化为常规最优控制问题,采用假设-验证的思路推导出无惯性环节系统的解析解,并借助高斯伪谱法求解无惯性环节系统和一阶惯性系统的数值解。仿真结果检验了两种方法的有效性,并表明无惯性环节系统和一阶惯性系统下,加速度峰值最小的弹道分别为精确和近似的圆弧与线段的拼接。

With regard to the maneuverability insufficiency encountered by missiles with large static margin when achieving large impact angle constraint,the minimax acceleration guidance law with impact angle constraint is proposed to reduce the missile ＇s required acceleration and avoid control saturation.First,the minimax problem is transformed to a conventional optimal control problem by introducing an auxiliary state into the dynamic equations. Then the analytic solution for lag-free system is deduced through trial and error,while the numerical solutions for lag-free and first-order lag systems are obtained by Gauss pseudospectral method. The effectiveness of these two approaches is validated through numerical simulations. It is shown that the optimal trajectories for lag-free and first-order lag systems are respectively accurate and approximate combinations of circular arc and line segment.