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Discrete-Event Systems in a Dioid Framework: Control Theory

  • Chapter
Control of Discrete-Event Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 433))

Abstract

In this chapter, we will recall contributions to dioid theory dealing with control that were achieved during the last two decades. Just like in classical control engineering, control is to be understood as having an action on the inputs so as to adapt to given specifications. For instance, one could aim at finding an optimal control in order to track an a priori known output trajectory. Since inversion, which would be necessary for such a computation, does not exist in general in a dioid framework, we will also present notions of residuation theory, which introduces pseudo-inverses that are suitable to our needs. Provided a model of a system and a specified output for it, it can be shown that there exists a greatest input that leads to an output which is lower than or equal to the specified one. In practice, this greatest solution implies that all the events occur as late as possible while ensuring that the output events occur before the ones given by the specified output. In a production management context, this comes down to delaying as much as possible the input of raw parts in the manufacturing system, while ensuring a predefined throughput; hence the internal stock is reduced as much as possible. The control strategy is then optimal according to the just-in-time criterion. This chapter will provide the results allowing to synthesize this optimal control. But this kind of open-loop strategy does not take the real-time response of the system into account. So we will also extend control strategies to closed-loop ones, which allow to react to possible disturbances. For each control strategy an illustrative example dealing with a High-Throughput Screening system, which has served as a case study within the DISC project, will be given.

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Author information

Authors and Affiliations

  1. LUNAM, University of Angers, LISA, ISTIA, 62 Av. Notre-Dame du Lac, 49000, Angers, France

    Laurent Hardouin, Bertrand Cottenceau & Thomas Brunsch

  2. Calle Santiago 2 – 4∘C, 11005, Cadiz, Spain

    Olivier Boutin

  3. Fachgebiet Regelungssysteme, Technische Universität Berlin, Einsteinufer 17, 10587, Berlin, Germany

    Thomas Brunsch & Jörg Raisch

  4. Fachgruppe System- und Regelungstheorie, Max-Planck-Institut für Dynamik komplexer technischer Systeme, Sandtorstr. 1, 39106, Magdeburg, Germany

    Jörg Raisch

Authors
  1. Laurent Hardouin
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  2. Olivier Boutin
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  3. Bertrand Cottenceau
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  4. Thomas Brunsch
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  5. Jörg Raisch
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Corresponding author

Correspondence to Laurent Hardouin .

Editor information

Editors and Affiliations

  1. , Department of Electrical, University of Cagliari, Piazza D'Armi, Cagliari, 09124, Italy

    Carla Seatzu

  2. , Department of Computer Science, University of Zaragoza, Calle María de Luna 1, Zaragoza, 50018, Spain

    Manuel Silva

  3. Centrum Wiskunde & Informatica, Amsterdam, 1090 GB, Netherlands

    Jan H. van Schuppen

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Hardouin, L., Boutin, O., Cottenceau, B., Brunsch, T., Raisch, J. (2013). Discrete-Event Systems in a Dioid Framework: Control Theory. In: Seatzu, C., Silva, M., van Schuppen, J. (eds) Control of Discrete-Event Systems. Lecture Notes in Control and Information Sciences, vol 433. Springer, London. https://doi.org/10.1007/978-1-4471-4276-8_22

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  • DOI: https://doi.org/10.1007/978-1-4471-4276-8_22

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-4275-1

  • Online ISBN: 978-1-4471-4276-8

  • eBook Packages: EngineeringEngineering (R0)

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