Dimension Reduction Near Periodic Orbits of Hybrid Systems: Appendix
Abstract
When the Poincare map associated with a periodic orbit of a hybrid dynamical system has constant-rank iterates, we demonstrate the existence of 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-such as Floquet theory-to the hybrid setting and provides a bridge between the efforts of biologists and engineers studying legged locomotion.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 07, 2011
- Accession Number
- ADA559003
Entities
People
- S. Shankar Sastry
- Samuel A. Burden
- Shai Revzen
Organizations
- University of California, Berkeley