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Optimal Control for Multi-mode Systems with Discrete Costs

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Formal Modeling and Analysis of Timed Systems (FORMATS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10419))

Abstract

This paper studies optimal time-bounded control in multi-mode systems with discrete costs. Multi-mode systems are an important subclass of linear hybrid systems, in which there are no guards on transitions and all invariants are global. Each state has a continuous cost attached to it, which is linear in the sojourn time, while a discrete cost is attached to each transition taken. We show that an optimal control for this model can be computed in NExpTime and approximated in PSpace. We also show that the one-dimensional case is simpler: although the problem is NP-complete (and in LogSpace for an infinite time horizon), we develop an FPTAS for finding an approximate solution.

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Acknowledgement

This work was supported by EPSRC EP/M027287/1 grant “Energy Efficient Control”.

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Authors and Affiliations

  1. University of Liverpool, Liverpool, UK

    Mahmoud A. A. Mousa, Sven Schewe & Dominik Wojtczak

Authors
  1. Mahmoud A. A. Mousa
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  2. Sven Schewe
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  3. Dominik Wojtczak
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Corresponding author

Correspondence to Mahmoud A. A. Mousa .

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Editors and Affiliations

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

    Alessandro Abate

  2. Dept. d’Informatique, Université Libre de Bruxelles, Brussels, Belgium

    Gilles Geeraerts

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Mousa, M.A.A., Schewe, S., Wojtczak, D. (2017). Optimal Control for Multi-mode Systems with Discrete Costs. In: Abate, A., Geeraerts, G. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2017. Lecture Notes in Computer Science(), vol 10419. Springer, Cham. https://doi.org/10.1007/978-3-319-65765-3_5

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  • DOI: https://doi.org/10.1007/978-3-319-65765-3_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-65764-6

  • Online ISBN: 978-3-319-65765-3

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