High-order Lie derivatives are essential in nonlinear systems analysis. If done symbolically, their evaluation becomes increasingly expensive as the order increases. We present a compact and efficient numerical approach for computing Lie derivatives of scalar, vector, and covector fields using the MATLAB ADTAYL package. The method exploits a fact noted by Röbenack: that these derivatives coincide, up to factorial scaling, with the Taylor coefficients of expressions built from a Taylor expansion about a trajectory point and, when required, the associated variational matrix. Computational results for a gantry crane model demonstrate orders of magnitude speedups over symbolic evaluation using the MATLAB Symbolic Math Toolbox.

翻译：高阶李导数在非线性系统分析中至关重要。若采用符号计算方法，其计算成本会随着阶数的增加而急剧上升。本文提出了一种基于MATLAB ADTAYL包的紧凑且高效的数值方法，用于计算标量场、向量场和余向量场的李导数。该方法利用了Röbenack指出的一个事实：这些导数（除阶乘缩放因子外）与在轨迹点处进行泰勒展开所构建表达式的泰勒系数相一致，并且在需要时，也与相关的变分矩阵相一致。以一个龙门起重机模型的计算结果为例，相较于使用MATLAB符号数学工具箱的符号求值方法，本方法实现了数量级级别的加速。