Towards supervisory control for interactive Markov chains: plant minimization

J. Markovski

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    Abstract

    We extend a model-based systems engineering framework for supervisory control of nondeterministic stochastic discrete-event systems with controllability-preserving minimization of the unsupervised system. This is a second out of four phases outlined in the development of the framework. In the first phase, we proposed a process theory that captures the notion of controllability of the underlying model of Interactive Markov Chains using a behavioral relation termed Markovian partial bisimulation. Interactive Markov Chains extend (nondeterministic) labeled transition systems with Markovian (exponential) delays. The Markovian partial bisimulation is a stochastic extension of partial bisimulation that captures controllability by stating that controllable events should be simulated, whereas uncontrollable events should be bisimulated. The stochastic behavior is preserved up to lumping of Markovian delays. We develop a minimization algorithm for the preorder and equivalence induced by the Markovian partial bisimulation based on the most efficient algorithms for simulation and Markovian bisimulation.
    Original languageEnglish
    Title of host publicationProceedings of the 9th IEEE International Conference on Control & Automation (IEEE ICCA'11)
    Place of PublicationPiscataway
    PublisherInstitute of Electrical and Electronics Engineers
    Pages1195-1200
    Number of pages6
    ISBN (Electronic)978-1-4577-1476-4
    ISBN (Print)978-1-4577-1475-7
    DOIs
    Publication statusPublished - 2011
    Event9th IEEE International Conference on Control and Automation (ICCA) - Santiago, Chile
    Duration: 19 Dec 201121 Dec 2011

    Conference

    Conference9th IEEE International Conference on Control and Automation (ICCA)
    Country/TerritoryChile
    CitySantiago
    Period19/12/1121/12/11

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