对称非线性控制系统的能控分解

Controllability Decomposition for Nonlinear Control Systems with Symmetries

本文利用群作用来定义非线性系统的对称性,在此基础上讨论对称系统的能控分解,并证明:若对称非线性控制系统在某点可能控分解,那么该系统在此点所属的轨道上的所有点均可能控分解;特别是若状态流形是齐次流形的话,则由系统在某一点可能控分解就能推出系统可全局能控分解。这表明,对称结构能使系统可能控分解的区域扩大。

This paper defines the symmetry for nonlinear control systems using the concept of group action, and further discusses the controllability decomposition problems for systems with symmetries. It is proven that if the systems with symmetries can be decomposed at a point, then it can be decomposed at all the points in the orbit of this point. The results show that the symmetric structure can make the region in which the systems can be decomposed larger.