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arXiv · 1109.1780

Dimension Reduction Near Periodic Orbits of Hybrid Systems

Samuel Burden·Shai Revzen·S. Shankar Sastry
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Abstract

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.

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Samuel Burden, Shai Revzen, S. Shankar Sastry. 2011-09-08. Dimension Reduction Near Periodic Orbits of Hybrid Systems. https://doi.org/10.1109/cdc.2011.6160405

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