Dimension Reduction Near Periodic Orbits of Hybrid Systems
arXiv:1109.1780 · doi:10.1109/CDC.2011.6160405
Abstract
When the Poincaré 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.
arXiv commentFull version of conference paper appearing in IEEE CDC/ECC 2011