Abstract
We have seen how discrete event systems (DES) differ from continuous-variable dynamic systems (CVDS) and why DES are not adequately modeled through differential or difference equations. Our first task, therefore, in studying DES is to develop appropriate models, which both adequately describe the behavior of these systems and provide a framework for analytical techniques to meet the goals of design, control, and performance evaluation. When considering the state evolution of a DES, our first concern is with the sequence of states visited and the associated events causing these state transitions. To begin with, we will not concern ourselves with the issue of when the system enters a particular state or how long the system remains at that state.
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Notes
- 1.
“:=” denotes “equal to by definition”.
- 2.
We shall use the notation \(\subset \) for “strictly contained in” and \(\subseteq \) for “contained in or equal to”.
- 3.
In the original definition of Moore, the output is emitted when the state is exited; we have changed this convention in our discussion.
- 4.
This version is a variation of Example 2.2 in C. Baier and J.-P. Katoen, Principles of Model Checking, The MIT Press, 2008.
- 5.
The dining philosophers example is revisited in the context of supervisory control in Chap. 3, Example 3.18.
- 6.
Readers unfamiliar with the \(O(\cdot )\) notation for complexity of algorithms may consult the end of chapter references.
- 7.
The verifier is often called the “twin-automaton” in the literature.
- 8.
General information about DES software tools and links to relevant web sites can be found at the web site of the IEEE Technical Committee on DES.
- 9.
From W. M. Wonham, “Notes on Control of Discrete-Event Systems,” Dept. of Elec. and Comp. Eng., Univ. of Toronto.
- 10.
Our model follows that in Computer Networks - 3rd Ed., by A. Tanenbaum, Prentice-Hall, 1996, Sects. 3.3.3 and 3.5.1.
- 11.
Problem due I. Aleksander, Designing Intelligent Systems, Unipub, New York, 1984.
- 12.
From P. J. Ramadge & W. M. Wonham, “Supervisory Control of a Class of Discrete-Event Processes,” SIAM J. Contr. Opt., May 1987.
- 13.
From the viewpoint of the theory of computation.
- 14.
This brief list excludes Petri Nets, which are considered in Chap. 4.
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Cassandras, C.G., Lafortune, S. (2021). Languages and Automata. In: Introduction to Discrete Event Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-72274-6_2
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DOI: https://doi.org/10.1007/978-3-030-72274-6_2
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