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Finite Abstractions of Stochastic Max-Plus-Linear Systems

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Quantitative Evaluation of Systems (QEST 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8657))

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Abstract

This work investigates the use of finite abstractions to study the finite-horizon probabilistic invariance problem over Stochastic Max-Plus-Linear (SMPL) systems. SMPL systems are probabilistic extensions of discrete-event MPL systems that are widely employed in the engineering practice for timing and synchronisation studies. We construct finite abstractions by re-formulating the SMPL system as a discrete-time Markov process, then tailoring formal abstraction techniques in the literature to generate a finite-state Markov Chain (MC), together with precise guarantees on the level of the introduced approximation. This finally allows to probabilistically model check the obtained MC against the finite-horizon probabilistic invariance specification. The approach is practically implemented via a dedicated software, and elucidated in this work over numerical examples.

The first two authors have equally contributed to this work. This work has been supported by the European Commission via STREP project MoVeS 257005, Marie Curie grant MANTRAS 249295, and IAPP project AMBI 324432.

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Author information

Authors and Affiliations

  1. Delft Center for Systems and Control, TU Delft, Delft University of Technology, The Netherlands

    Dieky Adzkiya, Sadegh Esmaeil Zadeh Soudjani & Alessandro Abate

  2. Department of Computer Science, University of Oxford, United Kingdom

    Alessandro Abate

Authors
  1. Dieky Adzkiya
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  2. Sadegh Esmaeil Zadeh Soudjani
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  3. Alessandro Abate
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Editor information

Editors and Affiliations

  1. School of Computing Science, University of Glasgow, G12 8RZ, Glasgow, UK

    Gethin Norman

  2. University of Illinois, 61801-2918, Urbana, IL, USA

    William Sanders

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Adzkiya, D., Esmaeil Zadeh Soudjani, S., Abate, A. (2014). Finite Abstractions of Stochastic Max-Plus-Linear Systems. In: Norman, G., Sanders, W. (eds) Quantitative Evaluation of Systems. QEST 2014. Lecture Notes in Computer Science, vol 8657. Springer, Cham. https://doi.org/10.1007/978-3-319-10696-0_7

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  • DOI: https://doi.org/10.1007/978-3-319-10696-0_7

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10695-3

  • Online ISBN: 978-3-319-10696-0

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