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Control of mechanical systems using set based methods

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Abstract

This paper considers large discrete-time linear systems obtained from discretized partial differential equations, and controlled by a quantized law, i.e., a piecewise constant time function taking a finite set of values. We show how to generate the control by, first, applying model reduction to the original system, then using a “state-space bisection” method for synthesizing a control at the reduced-order level, and finally computing an upper bound on the deviations between the controlled output trajectories of the reduced-order model and those of the original model. The effectiveness of our approach is illustrated on several examples of the literature.

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Acknowledgments

This work is supported by Institut Farman through the project SWITCHDESIGN, by the French National Research Agency through the “iCODE Institute project” funded by the IDEX Paris-Saclay, ANR-11-IDEX-0003-02, and by the Labex DigiCosme ANR-11-LABEX-0045-DIGICOSME.

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Authors and Affiliations

  1. CMLA, ENS Cachan CNRS, Université Paris-Saclay, 61 av. du Président Wilson, 94235, Cachan cedex, France

    Adrien Le Coënt & Florian De Vuyst

  2. Safran Tech, 1 Rue GeneviÃĺve AubÃl’, 78772, Magny les Hameaux, France

    Christian Rey

  3. LMT Cachan, ENS Cachan, CNRS, Université Paris-Saclay, 61 av. du Président Wilson, 94235, Cachan cedex, France

    Ludovic Chamoin

  4. LSV, ENS Cachan, CNRS, Université Paris-Saclay, 61 av. du Président Wilson, 94235, Cachan cedex, France

    Laurent Fribourg

Authors
  1. Adrien Le Coënt
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  2. Florian De Vuyst
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  3. Christian Rey
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  4. Ludovic Chamoin
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  5. Laurent Fribourg
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Correspondence to Adrien Le Coënt.

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Le Coënt, A., De Vuyst, F., Rey, C. et al. Control of mechanical systems using set based methods. Int. J. Dynam. Control 5, 496–512 (2017). https://doi.org/10.1007/s40435-016-0245-y

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  • DOI: https://doi.org/10.1007/s40435-016-0245-y

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