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Timed and Hybrid Models

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Introduction to Discrete Event Systems

Abstract

In this chapter we concentrate on timed models of DES. We also explore what happens when a system combines time-driven dynamics with event-driven dynamics giving rise to what are referred to as hybrid systems, which were introduced at the end of Chapter 1. The simplest instance of time-driven dynamics is the case of adjoining one or more clocks to the untimed DES model, resulting in a timed model. In the case of timed DES models, the sample paths are no longer specified as event sequences \(\{e_{1},e_{2},\ldots \}\) or state sequences \(\{x_{0},x_{1},\ldots \}\), but they must include some form of timing information.

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Notes

  1. 1.

    Our choice of the terminology “timed automaton with guards” was made to avoid confusion with the timed automata with clock structures considered so far in this chapter and to highlight the fact that guards constitute the distinguishing feature of this formalism.

  2. 2.

    Example adapted from Bérard et al., 2001, p. 60.

  3. 3.

    Named after the Greek philosopher Zeno of Elea, born around 490 BC.

  4. 4.

    Example adapted from Laroussinie et al., CONCUR’04, LNCS 3170, pp. 387–401, Springer.

  5. 5.

    Technical report STAN-CS-92-1411, Department of Computer Science, Stanford University, March 1992.

  6. 6.

    Adapted from Alur & Dill, 1994, p. 205.

  7. 7.

    Adapted from Tripakis, FTRTFT 2002, LNCS 2469, pp. 205–221, 2002.

  8. 8.

    As we noted in Chapter 1 (see “Manufacturing Systems” example in Section 1.3.4), the term “blocking” here refers to time-blocking, which is different from the logical notion of blocking that was considered in Chapters 2 and 3.

  9. 9.

    Example from Max Plus at Work by B. Heidergott et al., 2006.

  10. 10.

    See, e.g., Alur & Dill, 1994.

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Authors and Affiliations

  1. Division of Systems Engineering, Department of Electrical and Computer Engineering, and Center for Information and Systems Engineering, Boston University, Boston, MA, USA

    Christos G. Cassandras

  2. Department of Eletrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA

    Stéphane Lafortune

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  1. Christos G. Cassandras
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  2. Stéphane Lafortune
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Correspondence to Christos G. Cassandras .

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Cite this chapter

Cassandras, C.G., Lafortune, S. (2021). Timed and Hybrid Models. In: Introduction to Discrete Event Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-72274-6_5

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  • DOI: https://doi.org/10.1007/978-3-030-72274-6_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-72272-2

  • Online ISBN: 978-3-030-72274-6

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