Citation
Alessandro Abate, Alessandro D'Innocenzo, Maria D Di Benedetto, Shankar Sastry. "Markov Set-Chains as Abstractions of Stochastic Hybrid Systems". M. Egerstedt and B. Misra (eds.), 1, Springer Verlag, 2008.

Abstract
The objective of this study is to introduce an abstraction procedure that applies to a general class of dynamical systems, that is to discrete-time stochastic hybrid systems (dt-SHS). The procedure abstracts the original dt-SHS into a Markov set-chain (MSC) in two steps. First, a Markov chain (MC) is obtained by partitioning the hybrid state space, according to a controllable parameter, into non-overlapping domains and computing transition probabilities for these domains according to the dynamics of the dt-SHS. Second, explicit error bounds for the abstraction that depend on the above parameter are derived, and are associated to the computed transition probabilities of the MC, thus obtaining a MSC. We show that one can arbitrarily increase the accuracy of the abstraction by tuning the controllable parameter, albeit at an increase of the cardinality of the MSC. Resorting to a number of results from the MSC literature allows the analysis of the dynamics of the original dt-SHS. In the present work, the asymptotic behavior of the dt-SHS dynamics is assessed within the abstracted framework.

Electronic downloads

• http://hybrid.stanford.edu/~aabate/pubs.htm
• http://dx.doi.org/10.1007/978-3-540-78929-1_1

• HTML

  Alessandro Abate, Alessandro D'Innocenzo, Maria D Di
  Benedetto, Shankar Sastry. <a
  href="http://chess.eecs.berkeley.edu/pubs/436.html"
  ><i>Markov Set-Chains as Abstractions of Stochastic
  Hybrid Systems</i></a>, M. Egerstedt and B.
  Misra (eds.), 1, Springer Verlag, 2008.

• Plain text

  Alessandro Abate, Alessandro D'Innocenzo, Maria D Di
  Benedetto, Shankar Sastry. "Markov Set-Chains as
  Abstractions of Stochastic Hybrid Systems". M.
  Egerstedt and B. Misra (eds.), 1, Springer Verlag, 2008.

• BibTeX

  @inbook{AbateDInnocenzoDiBenedettoSastry08_MarkovSetChainsAsAbstractionsOfStochasticHybridSystems,
      author = {Alessandro Abate and Alessandro D'Innocenzo and
                Maria D Di Benedetto and Shankar Sastry},
      editor = {M. Egerstedt and B. Misra},
      title = {Markov Set-Chains as Abstractions of Stochastic
                Hybrid Systems},
      volume = {1},
      publisher = {Springer Verlag},
      year = {2008},
      abstract = {The objective of this study is to introduce an
                abstraction procedure that applies to a general
                class of dynamical systems, that is to
                discrete-time stochastic hybrid systems (dt-SHS).
                The procedure abstracts the original dt-SHS into a
                Markov set-chain (MSC) in two steps. First, a
                Markov chain (MC) is obtained by partitioning the
                hybrid state space, according to a controllable
                parameter, into non-overlapping domains and
                computing transition probabilities for these
                domains according to the dynamics of the dt-SHS.
                Second, explicit error bounds for the abstraction
                that depend on the above parameter are derived,
                and are associated to the computed transition
                probabilities of the MC, thus obtaining a MSC. We
                show that one can arbitrarily increase the
                accuracy of the abstraction by tuning the
                controllable parameter, albeit at an increase of
                the cardinality of the MSC. Resorting to a number
                of results from the MSC literature allows the
                analysis of the dynamics of the original dt-SHS.
                In the present work, the asymptotic behavior of
                the dt-SHS dynamics is assessed within the
                abstracted framework.},
      URL = {http://chess.eecs.berkeley.edu/pubs/436.html}
  }
  

Posted by Alessandro Abate on 16 Jun 2008.
Groups: chess
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