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Control-System Stability Under Consecutive Deadline Misses Constraints

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

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Author Details

Martina Maggio
  • Saarland University, Department of Computer Science, Saarbrücken, Germany
  • Lund University, Department of Automatic Control, Sweden
  • Robert Bosch GmbH, Renningen, Germany
Arne Hamann
  • Robert Bosch GmbH, Renningen, Germany
Eckart Mayer-John
  • Robert Bosch GmbH, Renningen, Germany
Dirk Ziegenbein
  • Robert Bosch GmbH, Renningen, Germany

Funding

This work was supported by: the ELLIIT Strategic Research Area, the project ARAMiS II of the German Federal Ministry for Education and Research with the funding ID 01IS16025. The project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 871259 (ADMORPH). The responsibility for the content remains with the authors.

Acknowledgements

This research was developed while Martina Maggio was on sabbatical at Robert Bosch GmbH.

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.ECRTS.2020.21

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.

Subject Classification

ACM Subject Classification
  • Computer systems organization → Real-time systems
  • Computer systems organization → Embedded and cyber-physical systems
  • Mathematics of computing → Mathematical analysis
  • Computer systems organization → Dependable and fault-tolerant systems and networks
Keywords
  • Real-Time Control
  • Deadline Misses
  • Weakly Hard Models

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