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Time-Regularized and Periodic Event-Triggered Control for Linear Systems

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Book cover Control Subject to Computational and Communication Constraints

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 475))

Abstract

In this chapter, we provide an overview of our recent results for the analysis and design of Event-Triggered controllers that are tailored to linear systems as provided in Heemels et al., IEEE Trans Autom Control 58(4):847–861, 2013, Heemels et al., IEEE Trans Autom Control 61(10):2766–2781, 2016, Borgers et al., IEEE Trans Autom Control, 2018. In particular, we discuss two different frameworks for the stability and contractivity analysis and design of (static) periodic Event-Triggered control (PETC) and time-regularized continuous Event-Triggered control (CETC) systems: the lifting-based framework of Heemels et al., IEEE Trans Autom Control 61(10):2766–2781, 2016, which applies to PETC systems, and the Riccati-based framework of Heemels et al., IEEE Trans Autom Control 58(4):847–861, 2013, Borgers et al., IEEE Trans Autom Control (2018), which applies to both PETC systems and time-regularized CETC systems. Moreover, we identify the connections and differences between the two frameworks. Finally, for PETC and time-regularized CETC systems, we show how the Riccati-based analysis leads to new designs for dynamic Event-Triggered controllers, which (for identical stability and contractivity guarantees) lead to a significantly reduced consumption of communication and energy resources compared to their static counterparts.

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Notes

  1. 1.

    This condition implies that each region has a non-empty interior thereby avoiding redundant regions of zero measure.

  2. 2.

    In the sense that Definitions 7.1 and 7.2 hold along solutions to the dynamic PETC system (7.45) with (7.39) and (7.40a) or (7.41a).

  3. 3.

    In the sense that Definitions 7.1 and 7.2 hold along solutions to the dynamic CETC system (7.57) with (7.53) and (7.54) or (7.55).

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Acknowledgements

This work is part of the research programmes “Wireless control systems: A new frontier in automation” with project number 11382 and “Integrated design approach for safety-critical real-time automotive systems” with project number 12698, which are (partly) financed by the Netherlands Organisation for Scientific Research (NWO).

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Authors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    D. P. Borgers, V. S. Dolk & W. P. M. H. Heemels

  2. University of Illinois, Urbana, IL, USA

    G. E. Dullerud

  3. University of California, Santa Barbara, CA, USA

    A. R. Teel

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  1. D. P. Borgers
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  2. V. S. Dolk
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  3. G. E. Dullerud
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  4. A. R. Teel
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  5. W. P. M. H. Heemels
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Correspondence to D. P. Borgers .

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Editors and Affiliations

  1. LAAS-CNRS, Université de Toulouse, Toulouse, France

    Sophie Tarbouriech

  2. Laboratoire des Signaux et Systèmes, CNRS, CentraleSupélec, Université Paris-Sud, Université Paris-Saclay, Gif-sur-Yvette, France

    Antoine Girard

  3. CNRS, Centrale Lille, UMR 9189—Centre de Recherche en Informatique Signal et Automatique de Lille (CRIStAL), Université Lille, Lille, France

    Laurentiu Hetel

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Borgers, D.P., Dolk, V.S., Dullerud, G.E., Teel, A.R., Heemels, W.P.M.H. (2018). Time-Regularized and Periodic Event-Triggered Control for Linear Systems. In: Tarbouriech, S., Girard, A., Hetel, L. (eds) Control Subject to Computational and Communication Constraints. Lecture Notes in Control and Information Sciences, vol 475. Springer, Cham. https://doi.org/10.1007/978-3-319-78449-6_7

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