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Scheduling of Controllers’ Update-Rates for Residual Bandwidth Utilization

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Book cover Formal Modeling and Analysis of Timed Systems (FORMATS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9884))

Abstract

We consider the problem of incorporating control tasks on top of a partially loaded shared computing resource, whose current task execution pattern is characterizable using a window based pattern. We consider that the control task to be scheduled is allowed to switch between multiple controllers, each with different associated sampling rate, in order to adjust its requirement of computational bandwidth as per availability. We provide a novel control theoretic analysis that derives a Timed Automata (TA) based specification of allowable switchings among the different controller options while retaining the asymptotic stability of the closed loop. Our scheduling scheme computes a platform level residual bandwidth pattern from individual task level execution patterns. We then leverage the TA based controller specification and the residual bandwidth pattern in order to synthesize a Linearly Priced Timed Automata for which the minimum cost reachability solution provides realizable multi-rate control schedules. The provided scheduler not only guarantees the asymptotic stability of the control loop but also increases the robustness and control performance of the implementation by maximizing the bandwidth utilization.

This work is partially supported by the German Research Foundation (DFG) through the grant ZA 873/1-1.

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Notes

  1. 1.

    A square matrix A is called Hurwitz if the real parts of its eigenvalues are negative.

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Author information

Authors and Affiliations

  1. Technical University of Munich, Munich, Germany

    Majid Zamani

  2. Indian Institute of Technology, Kharagpur, India

    Soumyajit Dey, Sajid Mohamed & Pallab Dasgupta

  3. Delft University of Technology, Delft, The Netherlands

    Manuel Mazo Jr.

Authors
  1. Majid Zamani
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  2. Soumyajit Dey
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  3. Sajid Mohamed
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  4. Pallab Dasgupta
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  5. Manuel Mazo Jr.
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Corresponding author

Correspondence to Majid Zamani .

Editor information

Editors and Affiliations

  1. Carl von Ossietzky Universität , Oldenburg, Germany

    Martin Fränzle

  2. LSV, ENS de Cachan , Cachan Cedex, France

    Nicolas Markey

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Zamani, M., Dey, S., Mohamed, S., Dasgupta, P., Mazo, M. (2016). Scheduling of Controllers’ Update-Rates for Residual Bandwidth Utilization. In: Fränzle, M., Markey, N. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2016. Lecture Notes in Computer Science(), vol 9884. Springer, Cham. https://doi.org/10.1007/978-3-319-44878-7_6

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  • DOI: https://doi.org/10.1007/978-3-319-44878-7_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44877-0

  • Online ISBN: 978-3-319-44878-7

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