Citation
Alessandro Abate, Maria Prandini, John Lygeros, Shankar Sastry. "Probabilistic Reachability and Safety for Controlled Discrete Time Stochastic Hybrid Systems". Automatica, 44(11):2724-2734, November 2008.

Abstract
In this work, probabilistic reachability over a finite horizon is investigated for a class of discrete time stochastic hybrid systems with control inputs. A suitable embedding of the reachability problem in a stochastic control framework reveals that it is amenable to two complementary interpretations, leading to dual algorithms for reachability computations. In particular, the set of initial conditions providing a certain probabilistic guarantee that the system will keep evolving within a desired 'safe' region of the state space is characterized in terms of a value function, and 'maximally safe' Markov policies are determined via dynamic programming. These results are of interest not only for safety analysis and design, but also for solving those regulation and stabilization problems that can be reinterpreted as safety problems. The temperature regulation problem presented in the paper as case study is one such case.

Electronic downloads

• http://hybrid.stanford.edu/~aabate/pubs.htm
• http://dx.doi.org/10.1016/j.automatica.2008.03.027

• HTML

  Alessandro Abate, Maria Prandini, John Lygeros, Shankar
  Sastry. <a
  href="http://chess.eecs.berkeley.edu/pubs/435.html"
  >Probabilistic Reachability and Safety for Controlled
  Discrete Time Stochastic Hybrid Systems</a>,
  <i>Automatica</i>, 44(11):2724-2734, November
  2008.

• Plain text

  Alessandro Abate, Maria Prandini, John Lygeros, Shankar
  Sastry. "Probabilistic Reachability and Safety for
  Controlled Discrete Time Stochastic Hybrid Systems".
  <i>Automatica</i>, 44(11):2724-2734, November
  2008.

• BibTeX

  @article{AbatePrandiniLygerosSastry08_ProbabilisticReachabilitySafetyForControlledDiscrete,
      author = {Alessandro Abate and Maria Prandini and John
                Lygeros and Shankar Sastry},
      title = {Probabilistic Reachability and Safety for
                Controlled Discrete Time Stochastic Hybrid Systems},
      journal = {Automatica},
      volume = {44},
      number = {11},
      pages = {2724-2734},
      month = {November},
      year = {2008},
      abstract = {In this work, probabilistic reachability over a
                finite horizon is investigated for a class of
                discrete time stochastic hybrid systems with
                control inputs. A suitable embedding of the
                reachability problem in a stochastic control
                framework reveals that it is amenable to two
                complementary interpretations, leading to dual
                algorithms for reachability computations. In
                particular, the set of initial conditions
                providing a certain probabilistic guarantee that
                the system will keep evolving within a desired
                'safe' region of the state space is characterized
                in terms of a value function, and 'maximally safe'
                Markov policies are determined via dynamic
                programming. These results are of interest not
                only for safety analysis and design, but also for
                solving those regulation and stabilization
                problems that can be reinterpreted as safety
                problems. The temperature regulation problem
                presented in the paper as case study is one such
                case.},
      URL = {http://chess.eecs.berkeley.edu/pubs/435.html}
  }
  

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