H_∞制导律的统计性能分析

A Theoretical Exploration of H_∞ Guidance Law with Strong Robustness for Tactical Homing Missile

为了验证 H∞ 制导律对于目标机动和外界干扰的鲁棒性 ,针对战术寻的导弹在追踪平面内的非线性运动学问题 ,全面分析了 H∞ 制导律的制导性能。采用蒙特卡洛数字仿真方法 ,统计了导弹攻击过程的相对距离、法向 /径向速度和鲁棒性能指标。统计仿真结果表明 ,对于目标随机机动 ,H∞ 制导律具有良好的鲁棒性。

Starting from the paper by the first author and Chen [2] , we explore theoretically a H ∞ guidance law with strong robustness for tactical homing missile. Our theoretical exploration is not limited by the capability of existing rocket motor. For example, existing rocket motor, to our best knowledge, can not control its tangential velocity, but our theoretical exploration assumes that future rocket motor can control its tangential velocity. Section 1 reviews relevant information in Ref.2 by the first author and Chen. Section 2 uses Monte Carlo method to simulate the process of nonlinear kinematics of pursuit evasion motion. Specifically, section 2 performs statistical analysis of two items concerning homing missile: (1) relative distance, relative normal velocity and relative tangential velocity; (2) robustness performance. Figs.1 through 6 and Table 1 present results of statistical analysis. These results compare the robustnesses obtainable with H ∞ guidance law and PN (proportional navigation) guidance law respectively. Based on this comparison, we draw the following preliminary conclusions: (1) the missile guided by H ∞ guidance law with attenuation level γ<1 can turn sharply (Fig.3); this affluent maneuverability is very helpful to the missile for tackling a maneuvering target; (2) H ∞ guidance law with γ<1 can guarantee strong robustness except for small terminal relative velocity and long interceptive time (Fig.4);(3) miss number of H ∞ guidance law is less than that of PN guidance law (Tab.1) when parameters such as v and k are selected appropriately; in other words, robustness of the H ∞ guidance laws is stronger than that of PN guidance law.