Discretization of Continuous Dynamical Systems Using UPPAAL

Stefano Schivo, Romanus Langerak

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    Abstract

    We want to enable the analysis of continuous dynamical systems (where the evolution of a vector of continuous state variables is described by differential equations) by model checking. We do this by showing how such a dynamical system can be translated into a discrete model of communicating timed automata that can be analyzed by the UPPAAL tool. The basis of the translation is the well-known Euler approach for solving differential equations where we use fixed discrete value steps instead of fixed time steps. Each state variable is represented by a timed automaton in which the delay for taking the next value is calculated on the fly using the differential equations. The state variable automata proceed independently but may notify each other when a value step has been completed; this leads to a recalculation of delays. The approach has been implemented in the tool ANIMO for analyzing biological kinase networks in cells. This tool has been used in actual biological research on osteoarthritis dealing with systems where the dimension of the state vector (the number of nodes in the network) is in the order of one hundred.
    Original languageEnglish
    Title of host publicationModelEd, TestEd, TrustEd
    Subtitle of host publicationEssays Dedicated to Ed Brinksma on the Occasion of His 60th Birthday
    EditorsJoost-Pieter Katoen, Rom Langerak, Arend Rensink
    PublisherSpringer
    Pages297-315
    Number of pages19
    ISBN (Electronic)978-3-319-68270-9
    ISBN (Print)978-3-319-68269-3
    DOIs
    Publication statusPublished - 27 Sep 2017

    Publication series

    NameLecture Notes in Computer Science
    PublisherSpringer
    Volume10500
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Keywords

    • Discretization
    • Euler method
    • Model Checking
    • Timed Automata
    • Systems Biology

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