关于非线性系统的对称性、可达性与可控性

On Symmetries, Reachability and Controllability of Nonlinear Systems

本文讨论对称及广义对称非线性系统的可达性与可控性。文中证明了如果广义对称系统在一点的邻域可控,那么系统在包含该点群作用轨道的一个开集上是可控的。利用广义对称性还给出了控制律的原则算法。对于对称系统,给出了可控性的充要条件。

This paper discusses the reachability and the controllability of symmetric and generalized symmetric systems.It is shown that if a generalized symmetric system is controllable on a neighborhood of a point,then the system is controllable on some open set which includes the group action-orbit at the point.With generalized symmetries an approach to calculate control laws is given in principle.A sufficient and necessary condition of controllability for symmetric systems is also presented in this paper.