非线性系统的高阶线性化方法及其在二阶摄动制导中的应用

HIGHER ORDER LINEARIZATION METHOD OF NONLINEAR SYSTEMS AND ITS APPLICATION FOR SECOND ORDER PERTURBATION GUIDANCE

本文讨论了非线性系统相对于标称轨道的高阶线性化方法。文中在一阶线性展开的基础上,提出了高阶误差项的补偿方法,导出了计算二阶补偿项系数的线性方程组,并给出了补偿项的计算公式。然后,采用所得方法研究了飞行器的二阶摄动制导方法。

This paper has derived a higher order linear approximation of nonlinear systems related to the nominal state and nominal control. The method for a nonlinear system to be approximated to higher order by the transformation of a linear system is obtained by using ideals of nonlinear coordinate change and nonlinear state feedback. The formulas for calculating the coefficients of higher order terms are given. Then, the use of this technique in design second order perturbation guidance equations has been suggested.