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Approximation of General Stochastic Hybrid Systems by Switching Diffusions with Random Hybrid Jumps
Alessandro Abate, Maria Prandini, John Lygeros, Shankar Sastry

Citation
Alessandro Abate, Maria Prandini, John Lygeros, Shankar Sastry. "Approximation of General Stochastic Hybrid Systems by Switching Diffusions with Random Hybrid Jumps". M. Egerstedt and B. Misra (eds.), 598 - 601, Springer Verlag, 2008; Chapter in "Hybrid Systems: Computation and Control," 2008 .

Abstract
In this work we propose an approximation scheme to transform a general stochastic hybrid system (SHS) into a SHS without forced transitions due to spatial guards. Such switching mechanisms are replaced by spontaneous transitions with state-dependent transition intensities (jump rates). The resulting switching diffusion process with random hybrid jumps is shown to converge in distribution to the original stochastic hybrid system execution. The obtained approximation can be useful for various purposes such as, on the computational side, simulation and reachability analysis, as well as for the theoretical investigation of the model. More generally, it is suggested that SHS which are endowed exclusively with random jumping events are simpler than those that present spatial forcing transitions. In the opening of this work, the general SHS model is presented, a few of its basic properties are discussed, and the concept of generator is introduced. The second part of the paper describes the approximation procedure, introduces the new SHS model, and proves, under some assumptions, its weak convergence to the original system.

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  • HTML
    Alessandro Abate, Maria Prandini, John Lygeros, Shankar
    Sastry. <a
    href="http://chess.eecs.berkeley.edu/pubs/437.html"
    ><i>Approximation of General Stochastic Hybrid
    Systems by Switching Diffusions with Random Hybrid
    Jumps</i></a>, M. Egerstedt and B. Misra (eds.),
    598 - 601, Springer Verlag, 2008; Chapter in "Hybrid
    Systems: Computation and Control," 2008 .
  • Plain text
    Alessandro Abate, Maria Prandini, John Lygeros, Shankar
    Sastry. "Approximation of General Stochastic Hybrid
    Systems by Switching Diffusions with Random Hybrid
    Jumps". M. Egerstedt and B. Misra (eds.), 598 - 601,
    Springer Verlag, 2008; Chapter in "Hybrid Systems:
    Computation and Control," 2008 .
  • BibTeX
    @inbook{AbatePrandiniLygerosSastry08_ApproximationOfGeneralStochasticHybridSystemsBySwitching,
        author = {Alessandro Abate and Maria Prandini and John
                  Lygeros and Shankar Sastry},
        editor = {M. Egerstedt and B. Misra},
        title = {Approximation of General Stochastic Hybrid Systems
                  by Switching Diffusions with Random Hybrid Jumps},
        pages = {598 - 601},
        publisher = {Springer Verlag},
        year = {2008},
        note = {Chapter in "Hybrid Systems: Computation and
                  Control," 2008 },
        abstract = {In this work we propose an approximation scheme to
                  transform a general stochastic hybrid system (SHS)
                  into a SHS without forced transitions due to
                  spatial guards. Such switching mechanisms are
                  replaced by spontaneous transitions with
                  state-dependent transition intensities (jump
                  rates). The resulting switching diffusion process
                  with random hybrid jumps is shown to converge in
                  distribution to the original stochastic hybrid
                  system execution. The obtained approximation can
                  be useful for various purposes such as, on the
                  computational side, simulation and reachability
                  analysis, as well as for the theoretical
                  investigation of the model. More generally, it is
                  suggested that SHS which are endowed exclusively
                  with random jumping events are simpler than those
                  that present spatial forcing transitions. In the
                  opening of this work, the general SHS model is
                  presented, a few of its basic properties are
                  discussed, and the concept of generator is
                  introduced. The second part of the paper describes
                  the approximation procedure, introduces the new
                  SHS model, and proves, under some assumptions, its
                  weak convergence to the original system.},
        URL = {http://chess.eecs.berkeley.edu/pubs/437.html}
    }
    

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