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
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摘要: 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.利用对称性和微分几何方法可将这种标准形构造出来.Abstract: 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.
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Key words:
- Symmetries /
- normal form /
- nonlinear systems
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