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 longterm 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.
Recently, REF provided an analytical technique to extract a reduced-order smooth dynamical system near a periodic orbit of a hybrid dynamical system.
Dimension Reduction Near Periodic Orbits of Hybrid Systems
IEEE Conference on Decision and Control and European Control Conference
IEEE Conference on Decision and Control and European Control Conference
Mathematics Physics Computer Science