Citation
Alessandro Abate. "Probabilistic Reachability for Stochastic Hybrid Systems: Theory, Computations, and Applications". PhD thesis, University of California, Berkeley, November, 2007.

Abstract
Stochastic Hybrid Systems are probabilistic models suitable at describing the dynamics of variables presenting interleaved and interacting continuous and discrete components.

Engineering systems like communication networks or automotive and air traffic control systems, financial and industrial processes like market and manufacturing models, and natural systems like biological and ecological environments exhibit compound behaviors arising from the compositions and interactions between their heterogeneous components. Hybrid Systems are mathematical models that are by definition suitable to describe such complex systems.

The effect of the uncertainty upon the involved discrete and continuous dynamics---both endogenously and exogenously to the system---is virtually unquestionable for biological systems and often inevitable for engineering systems, and naturally leads to the employment of stochastic hybrid models.

The first part of this dissertation introduces gradually the modeling framework and focuses on some of its features. In particular, two sequential approximation procedures are introduced, which translate a general stochastic hybrid framework into a new probabilistic model. Their convergence properties are sketched. It is argued that the obtained model is more predisposed to analysis and computations.

The kernel of the thesis concentrates on understanding the theoretical and computational issues associated with an original notion of probabilistic reachability for controlled stochastic hybrid systems. The formal approach is based on formulating reachability analysis as a stochastic optimal control problem, which is solved via dynamic programming. A number of related and significant control problems, such as that of probabilistic safety, are reinterpreted with this approach. The technique is also computationally tested on a benchmark case study throughout the whole work. Moreover, a methodological application of the concept in the area of Systems Biology is presented: a model for the production of antibiotic as a component of the stress response network for the bacterium Bacillus subtilis is described. The model allows one to reinterpret the survival analysis for the single bacterial cell as a probabilistic safety specification problem, which is then studied by the aforementioned technique.

In conclusion, this dissertation aims at introducing a novel concept of probabilistic reachability that is both formally rigorous, computationally analyzable and of applicative interest. Furthermore, by the introduction of convergent approximation procedures, the thesis relates and positively compares the presented approach with other techniques in the literature.

Advisor: S. Shankar Sastry

Electronic downloads

• http://www.eecs.berkeley.edu/Pubs/TechRpts/2007/EECS-2007-132.html

• HTML

  Alessandro Abate. <a
  href="http://chess.eecs.berkeley.edu/pubs/440.html"
  ><i>Probabilistic Reachability for Stochastic
  Hybrid Systems: Theory, Computations, and
  Applications</i></a>, PhD thesis,  University of
  California, Berkeley, November, 2007.

• Plain text

  Alessandro Abate. "Probabilistic Reachability for
  Stochastic Hybrid Systems: Theory, Computations, and
  Applications". PhD thesis,  University of California,
  Berkeley, November, 2007.

• BibTeX

  @phdthesis{Abate07_ProbabilisticReachabilityForStochasticHybridSystems,
      author = {Alessandro Abate},
      title = {Probabilistic Reachability for Stochastic Hybrid
                Systems: Theory, Computations, and Applications},
      school = {University of California, Berkeley},
      month = {November},
      year = {2007},
      abstract = {Stochastic Hybrid Systems are probabilistic models
                suitable at describing the dynamics of variables
                presenting interleaved and interacting continuous
                and discrete components. <p>Engineering systems
                like communication networks or automotive and air
                traffic control systems, financial and industrial
                processes like market and manufacturing models,
                and natural systems like biological and ecological
                environments exhibit compound behaviors arising
                from the compositions and interactions between
                their heterogeneous components. Hybrid Systems are
                mathematical models that are by definition
                suitable to describe such complex systems. <p>The
                effect of the uncertainty upon the involved
                discrete and continuous dynamics---both
                endogenously and exogenously to the system---is
                virtually unquestionable for biological systems
                and often inevitable for engineering systems, and
                naturally leads to the employment of stochastic
                hybrid models. <p>The first part of this
                dissertation introduces gradually the modeling
                framework and focuses on some of its features. In
                particular, two sequential approximation
                procedures are introduced, which translate a
                general stochastic hybrid framework into a new
                probabilistic model. Their convergence properties
                are sketched. It is argued that the obtained model
                is more predisposed to analysis and computations.
                <p>The kernel of the thesis concentrates on
                understanding the theoretical and computational
                issues associated with an original notion of
                probabilistic reachability for controlled
                stochastic hybrid systems. The formal approach is
                based on formulating reachability analysis as a
                stochastic optimal control problem, which is
                solved via dynamic programming. A number of
                related and significant control problems, such as
                that of probabilistic safety, are reinterpreted
                with this approach. The technique is also
                computationally tested on a benchmark case study
                throughout the whole work. Moreover, a
                methodological application of the concept in the
                area of Systems Biology is presented: a model for
                the production of antibiotic as a component of the
                stress response network for the bacterium Bacillus
                subtilis is described. The model allows one to
                reinterpret the survival analysis for the single
                bacterial cell as a probabilistic safety
                specification problem, which is then studied by
                the aforementioned technique. <p>In conclusion,
                this dissertation aims at introducing a novel
                concept of probabilistic reachability that is both
                formally rigorous, computationally analyzable and
                of applicative interest. Furthermore, by the
                introduction of convergent approximation
                procedures, the thesis relates and positively
                compares the presented approach with other
                techniques in the literature. <p>Advisor: S.
                Shankar Sastry},
      URL = {http://chess.eecs.berkeley.edu/pubs/440.html}
  }
  

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