Sam Burden and Shai Revzen and S. Shankar Sastry

EECS Department, University of California, Berkeley

Technical Report No. UCB/EECS-2011-100

September 7, 2011

http://www2.eecs.berkeley.edu/Pubs/TechRpts/2011/EECS-2011-100.pdf

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.

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BibTeX citation:

@techreport{Burden:EECS-2011-100,
    Author= {Burden, Sam and Revzen, Shai and Sastry, S. Shankar},
    Title= {Dimension Reduction Near Periodic Orbits of Hybrid Systems: Appendix},
    Year= {2011},
    Month= {Sep},
    Url= {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2011/EECS-2011-100.html},
    Number= {UCB/EECS-2011-100},
    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.},
}

EndNote citation:

%0 Report
%A Burden, Sam 
%A Revzen, Shai 
%A Sastry, S. Shankar 
%T Dimension Reduction Near Periodic Orbits of Hybrid Systems: Appendix
%I EECS Department, University of California, Berkeley
%D 2011
%8 September 7
%@ UCB/EECS-2011-100
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2011/EECS-2011-100.html
%F Burden:EECS-2011-100