非线性控制系统的奇异降阶
Singular reduction for nonlinear control systems
摘要：
讨论了具有对称性的光滑非线性控制系统。对于对称群的自由和适当的作用，对称性的约化产生约化的光滑非线性控制系统。如果对称群的作用是适当的，则简化的非线性控制系统不必是光滑的。利用Sikorski的微分空间理论提供的非光滑空间上的光滑微积分，我们证明了Sussmann关于光滑向量场族轨道的定理的一个推广.
英文摘要：
We discuss smooth nonlinear control systems with symmetry. For a free and proper action of the symmetry group, the reduction of symmetry gives rise to a reduced smooth nonlinear control system. If the action of the symmetry group is only proper, the reduced nonlinear control system need not be smooth. Using the smooth calculus on nonsmooth spaces, provided by the theory of differential spaces of Sikorski, we prove a generalization of Sussmann's theorem on orbits of families of smooth vector fields.
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