1 research outputs found
Dimension Reduction Near Periodic Orbits of Hybrid Systems
When the Poincar\'{e} 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.Comment: Full version of conference paper appearing in IEEE CDC/ECC 201