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.

Electronic downloads

• http://hybrid.stanford.edu/~aabate/pubs.htm
• http://dx.doi.org/10.1007/978-3-540-78929-1_43

• 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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