Abstract
In supervisory control, formal languages provide a level of abstraction at which control concepts can be formulated in a way that is independent of any specific concrete implementation of the plant and controller. Some basic definitions are presented, leading to the Nerode equivalence relation as the bridge from a language to its dynamical state description. Emphasis is placed on regular (finite-state) languages as the class that is simplest and most directly applicable in the control context.
The original version of this chapter was revised: Belated corrections have been incorporated. The correction to this chapter is available at https://doi.org/10.1007/978-3-319-77452-7_10
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Change history
29 May 2019
In the original version of the book, the Chapters 7, 8, 12, 17 and 23 were revised.
Notes
- 1.
The software package TCT will be introduced in Example 3.2.1.
- 2.
If \(\eta (y,\sigma )!\) for all \((y,\sigma )\in Y \times \Sigma \), \(\eta \) may be called a total function (\(\eta \) is then an ‘ordinary’ function, as in Sect. 2.4).
- 3.
Not needed in the sequel.
- 4.
The symbol \( \vdash \) may be pronounced ‘bu’.
- 5.
The symbol
may be pronounced ‘shang’.
may be pronounced ‘shang’.References
Carroll J, Long D (1989) Theory of finite automata. Prentice-Hall, Englewood Cliffs
Hopcroft JE, Ullman JD (1979) Introduction to automata theory, languages and computation. Addison-Wesley, Boston
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Wonham, W.M., Cai, K. (2019). Linguistic Preliminaries. In: Supervisory Control of Discrete-Event Systems. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-77452-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-77452-7_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-77451-0
Online ISBN: 978-3-319-77452-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)