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Probabilistic Reachability for Stochastic Hybrid Systems: Theory, Computations, and Applications
Alessandro Abate

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

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  • 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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