Reverse-engineering invariant manifolds with asymptotic phase

Matthew Kvalheim, Shai Revzen

arXiv preprint, 2016

Abstract

We present a recipe for rendering a submanifold normally hyperbolic and invariant within a stability basin. The construction includes the ability to choose the asymptotic phase map. We are motivated by the notion of "templates and anchors" – the biomechanical observation that animal motions are often governed by low dimensional dynamics – and the growing applications in robotics which desire means for making such biologically derived templates govern the dynamics of robots. Our approach is fairly universal, in the sense that a broad range of model reduction constructions must be normally hyperbolic if they are robust, and a broad range of such normally hyperbolic systems can be produces from our construction.

BibTeX

@unpublished{kvalheim-2016-reverse,
  author = {Kvalheim, Matthew and Revzen, Shai},
  title = {Reverse-engineering invariant manifolds with asymptotic phase},
  year = {2016},
  cvtopic = {dsctrl},
  eprint = {1608.08442},
  doi = {10.48550/arXiv.1608.08442},
  eprinttype = {arxiv},
  journal = {arXiv preprint},
}