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Logic, Rewriting, and Concurrency pp 114–134Cite as

Hybrid Multirate PALS

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9200))

Abstract

Multirate PALS reduces the design and verification of a virtually synchronous distributed real-time system to the design and verification of the underlying synchronous model. This paper introduces Hybrid Multirate PALS, which extends Multirate PALS to virtually synchronous distributed multirate hybrid systems, such as aircraft and power plant control systems. Such a system may have interrelated local physical environments, each of whose continuous behaviors may periodically change due to actuator commands. We define continuous interrelated local physical environments, and the synchronous and asynchronous Hybrid Multirate PALS models, and give a trace equivalence result relating a synchronous and an asynchronous model. Finally, we illustrate by an example how invariants can be verified using SMT solving.

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Notes

  1. 1.

    “Remote” sensors and actuators that are not tightly integrated can be considered as parts of another controller that communicates with M through the network.

  2. 2.

    From the physical state \(\varvec{v}\), the physical state \(\varvec{v'}\) is reachable through some trajectory \(\varvec{\tau }\) of duration \(\alpha _{\max _M}\) by the control command a.

  3. 3.

    E.g., if \(\psi \equiv x > 3 \wedge y = z\), then for \(\delta = 0.1\), its syntactic numerical perturbation by \(\delta \) is \(x - 3 > -0.1 \wedge y - z \ge -0.1 \wedge z - y \ge -0.1\).

  4. 4.

    The analysis took 28 min on Intel Xeon 2.0 GHz with 64 GB memory.

  5. 5.

    The analysis took 10 h 27 min on the same machine.

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Acknowledgments

José Meseguer has been a mentor and role model for both of us. We would like to thank you, José, for showing us how beautiful, and at the same time practical, theoretical computer science can be. We thank you for your exemplary guidance and your support throughout our research careers. But first and foremost, we thank you for many years of true friendship.

Author information

Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, USA

    Kyungmin Bae

  2. University of Oslo, Oslo, Norway

    Peter Csaba Ölveczky

Authors
  1. Kyungmin Bae
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  2. Peter Csaba Ölveczky
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Corresponding author

Correspondence to Kyungmin Bae .

Editor information

Editors and Affiliations

  1. Universidad Complutense de Madrid, Madrid, Spain

    Narciso Martí-Oliet

  2. University of Oslo, Oslo, Norway

    Peter Csaba Ölveczky

  3. SRI International, Menlo Park, California, USA

    Carolyn Talcott

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Bae, K., Ölveczky, P.C. (2015). Hybrid Multirate PALS. In: Martí-Oliet, N., Ölveczky, P., Talcott, C. (eds) Logic, Rewriting, and Concurrency. Lecture Notes in Computer Science(), vol 9200. Springer, Cham. https://doi.org/10.1007/978-3-319-23165-5_5

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  • DOI: https://doi.org/10.1007/978-3-319-23165-5_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23164-8

  • Online ISBN: 978-3-319-23165-5

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