Dimension reduction near periodic orbits of hybrid systems

S Burden, Shai Revzen, S S Sastry

IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), pp. 6116 – 6121, 2011

Abstract

When the Poincare map associated with a periodic orbit of a hybrid dynamical system has constant-rank iterates, there exists a constant-dimensional invariant subsystem near the orbit which attracts all nearby trajectories in finite time. This result shows that the long-term behavior of a hybrid model with a large number of degrees-of-freedom may be governed by a low-dimensional smooth dynamical system. The appearance of such simplified models enables the translation of analytical tools from smooth systems to the hybrid setting and provides a bridge between the efforts of biologists and engineers studying legged locomotion.

BibTeX

@article{burden-2011-drn,
  author = {Burden, S and Revzen, Shai and Sastry, S S},
  title = {Dimension reduction near periodic orbits of hybrid systems},
  journal = {IEEE Conference on Decision and Control and European Control Conference (CDC-ECC)},
  year = {2011},
  pages = {6116 -- 6121},
  doi = {10.1109/CDC.2011.6160405},
  entrysubtype = {ReviewedPaper},
  cvtopic = {dsctrl}
}