Controlled Invariant Manifolds: a Normally-Hyperbolic Viewpoint

In the dynamical systems community the concept of normal hyperbolicity has been used to devise efficient numerical algorithms for the computation of invariant manifolds. These numerical algorithms have been designed based on the proof of the invariant manifold theorem. In this paper we extend this theorem to the controlled-invariant manifold case. We also briefly discuss the conditions under which a given invariant manifold can be determined to be normally-hyperbolic. We present a few prototypical control problems, and discuss the relevance of normal hyperbolicity for these, an important issue here is the concept of structurally stable manifolds