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DOI: 10.4230/LIPIcs.ECRTS.2020.21

Control-System Stability Under Consecutive Deadline Misses Constraints

Authors: Martina Maggio, Arne Hamann, Eckart Mayer-John, and Dirk Ziegenbein

Published in: LIPIcs, Volume 165, 32nd Euromicro Conference on Real-Time Systems (ECRTS 2020)

Abstract

This paper deals with the real-time implementation of feedback controllers. In particular, it provides an analysis of the stability property of closed-loop systems that include a controller that can sporadically miss deadlines. In this context, the weakly hard m-K computational model has been widely adopted and researchers used it to design and verify controllers that are robust to deadline misses. Rather than using the m-K model, we focus on another weakly-hard model, the number of consecutive deadline misses, showing a neat mathematical connection between real-time systems and control theory. We formalise this connection using the joint spectral radius and we discuss how to prove stability guarantees on the combination of a controller (that is unaware of deadline misses) and its system-level implementation. We apply the proposed verification procedure to a synthetic example and to an industrial case study.

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Martina Maggio, Arne Hamann, Eckart Mayer-John, and Dirk Ziegenbein. Control-System Stability Under Consecutive Deadline Misses Constraints. In 32nd Euromicro Conference on Real-Time Systems (ECRTS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 165, pp. 21:1-21:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{maggio_et_al:LIPIcs.ECRTS.2020.21,
  author =	{Maggio, Martina and Hamann, Arne and Mayer-John, Eckart and Ziegenbein, Dirk},
  title =	{{Control-System Stability Under Consecutive Deadline Misses Constraints}},
  booktitle =	{32nd Euromicro Conference on Real-Time Systems (ECRTS 2020)},
  pages =	{21:1--21:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-152-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{165},
  editor =	{V\"{o}lp, Marcus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2020.21},
  URN =		{urn:nbn:de:0030-drops-123845},
  doi =		{10.4230/LIPIcs.ECRTS.2020.21},
  annote =	{Keywords: Real-Time Control, Deadline Misses, Weakly Hard Models}
}

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Control-System Stability Under Consecutive Deadline Misses Constraints

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