非线性H_∞导引律设计与分析

Design and Analysis of Nonlinear H_∞ Guidance Law

针对导弹拦截目标制导过程中的测量噪声和干扰以及未知目标机动,本文提出了具有严格解析形式的三维非线性H∞导引律的设计方法。通过构建基于改进极坐标系下的三维弹目相对运动方程和存在多种测量噪声和干扰下的弹目相对运动方程,归纳推导出简洁的导弹拦截目标的系统方程;利用非线性H∞控制理论构造相应的HJI偏微分方程不等式,并且提出了HJI偏微分方程不等式的一种解法,得到了一组解析解,同时得到了拦截系统的一个正定储能函数,进而构造了非线性H∞导引律;通过分析非线性H∞导引律的设计方法和几项关键的制导拦截影响因素,定性指出了如何调整设计参数能够有效对抗各种不利因素,提高制导性能;最后,仿真研究验证了非线性H∞导引律的有效性和定性分析的有效性。

An analytical three-dimensional nonlinear H∞ guidance law is designed for coping with measurement noise and disturbance and unknown target maneuvering in the process of a missile intercepting an attacking target. By building a three-dimensional relative motion equation between the missile and the target in the modified polar coordinate and a relative motion equation between the missile and the target involving many types of measurement noise and disturbance, a simplified system equation of the missile intercepting the target is deduced. Then the corresponding HJI partial differential inequality is constructed by using nonlinear control theory. And then a solution method of HJI partial differential inequality is offered. Thus a set of analytical solutions and a positive definite storage function are obtained, and then the analytical three-dimensional nonlinear H∞ guidance law is designed successfully. By analyzing the relationship of the design parameters of nonlinear H∞ guidance law and several key interception factors of guidance, the analysis qualitatively points out that how to adjust design parameters can deal with a variety of adverse factors and improve guidance performance further more. Finally, simulation results verify the effectiveness of the proposed guidance law and the effectiveness of the qualitative analysis.