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Epsilon-Tubes and Generalized Skorokhod Metrics for Hybrid Paths Spaces

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Hybrid Systems: Computation and Control (HSCC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5469))

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Abstract

We develop several generalized Skorokhod pseudo-metrics for hybrid path spaces, cast in a quite general setting, where the basic open sets are epsilon-tubes around paths that, intuitively, allow for some “wiggle room” in both time and space via set-valued retiming maps between the time domains of paths. We then determine necessary and sufficient conditions under which these topologies are Hausdorff and their distance functions are metrics. On spaces of paths with closed time domains, our metric topology of generalized Skorokhod uniform convergence on finite prefixes is equivalent to the implicit topology of graphical convergence of hybrid paths, currently used extensively by Teel and co-workers.

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Author information

Authors and Affiliations

  1. Department of Electrical & Electronic Engineering, The University of Melbourne, VIC 3010, Australia

    J. M. Davoren

Authors
  1. J. M. Davoren
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of California, 4531E Boelter Hall, CA 90095, Los Angeles, USA

    Rupak Majumdar

  2. Department of Electrical Engineering, University of California, 66-147F Engineering, IV Building, CA 90095-1594, Los Angeles, USA

    Paulo Tabuada

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Davoren, J.M. (2009). Epsilon-Tubes and Generalized Skorokhod Metrics for Hybrid Paths Spaces. In: Majumdar, R., Tabuada, P. (eds) Hybrid Systems: Computation and Control. HSCC 2009. Lecture Notes in Computer Science, vol 5469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00602-9_10

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  • DOI: https://doi.org/10.1007/978-3-642-00602-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00601-2

  • Online ISBN: 978-3-642-00602-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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