Singular reduction for nonlinear control systems

Details Singular reduction for nonlinear control systems Singular reduction for nonlinear control systems

2003-05-06

arxiv.org/abs/math/0305098v1

Mathematics

Differential Geometry

13 pages

Scientific paper

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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