对称非线性控制系统的串级解耦标准形

A NORMAL FORM WITH CASCADE DECOMPOSITION OF SYMMETRIC NONLINEAR CONTROL SYSTEMS

证明了具有对称性的非线性控制系统存在局部的串级解耦标准形．这种标准形由一个维数等于系统维数与对称性Ｌｉｅ群维数之差的独立子系统和一个不含控制量的子系统串联而成．

It is shown that a nonlinear control system possessing symmetries has locally a normal form with cascade decomposition. This normal form consists of two subsystems. One is a independent subsystem of the dimension equal to the difference of the dimensions between the total system and the symmetry Lie group. The other is a subsystem without controls. Using differential geometric method and choosing properly a few symmetric functions of coordinate transformation whose Lie derivatives with respect to input vector fields all vanish, we can construct the normal form.