Citation
Aaron Ames, Shankar Sastry. "Hybrid Geometric Reduction of Hybrid Systems". 2006 45th IEEE Conference on Decision and Control, 923-929, December, 2006.

Abstract
This paper presents a unifying framework in which to carry out the hybrid geometric reduction of hybrid systems, generalizing classical reduction to a hybrid setting. Utilizing hybrid category theory, all of the major ingredients necessary for classical reduction can be hybridized through the notion of a hybrid object and a hybrid morphism over a general category. By leveraging the results of Marsden and Weinstein, we are able to show that when there is a hybrid symplectic manifold (the hybrid phase space) on which a hybrid Lie group acts symplectically, we can reduce the hybrid phase space to another hybrid symplectic manifold in which the hybrid symmetries are "divided out." In addition, hybrid trajectories of a hybrid Hamiltonian on the hybrid phase space determine corresponding hybrid trajectories on the reduced hybrid space.

Electronic downloads

• http://dx.doi.org/10.1109/CDC.2006.377245

• HTML

  Aaron Ames, Shankar Sastry. <a
  href="http://chess.eecs.berkeley.edu/pubs/122.html"
  >Hybrid Geometric Reduction of Hybrid Systems</a>,
  2006 45th IEEE Conference on Decision and Control, 923-929,
  December, 2006.

• Plain text

  Aaron Ames, Shankar Sastry. "Hybrid Geometric Reduction
  of Hybrid Systems". 2006 45th IEEE Conference on
  Decision and Control, 923-929, December, 2006.

• BibTeX

  @inproceedings{AmesSastry06_HybridGeometricReductionOfHybridSystems,
      author = {Aaron Ames and Shankar Sastry},
      title = {Hybrid Geometric Reduction of Hybrid Systems},
      booktitle = {2006 45th IEEE Conference on Decision and Control},
      pages = {923-929},
      month = {December},
      year = {2006},
      abstract = {This paper presents a unifying framework in which
                to carry out the hybrid geometric reduction of
                hybrid systems, generalizing classical reduction
                to a hybrid setting. Utilizing hybrid category
                theory, all of the major ingredients necessary for
                classical reduction can be hybridized through the
                notion of a hybrid object and a hybrid morphism
                over a general category. By leveraging the results
                of Marsden and Weinstein, we are able to show that
                when there is a hybrid symplectic manifold (the
                hybrid phase space) on which a hybrid Lie group
                acts symplectically, we can reduce the hybrid
                phase space to another hybrid symplectic manifold
                in which the hybrid symmetries are "divided out."
                In addition, hybrid trajectories of a hybrid
                Hamiltonian on the hybrid phase space determine
                corresponding hybrid trajectories on the reduced
                hybrid space.},
      URL = {http://chess.eecs.berkeley.edu/pubs/122.html}
  }
  

Posted by Aaron Ames on 15 May 2006.
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