Abstract
This chapter provides a framework for the study of theoretical issues in the design of supervisory controls for timed discrete-event systems. The model incorporates both time delays and hard deadlines, and admits both forcing and disablement as means of control. In addition it supports composition of modular subsystems and systematic synthesis.
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
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Change history
29 May 2019
In the original version of the book, the Chapters 7, 8, 12, 17 and 23 were revised.
Notes
- 1.
Here the fact that A, and so Q, are finite sets is crucial.
- 2.
While this convention respects physical behavior in many applications it need not be considered sacrosanct for all future modeling exercises.
- 3.
The language generated is the closure of the string pair \(\{ tick ~\alpha ~ tick^2 ~ \beta ~ tick^2 ~( \gamma ~ tick ~|~ tick ~ \gamma ) \}\).
- 4.
An instance: air defense could force a plane to land within 20 min (say) but not prevent it from landing eventually; the landing is forcible but not controllable.
- 5.
For instance, if a forcible event \(\sigma \) = ‘stop’ is to strictly preempt \(\kappa \) = ‘collision’, our model requires interposing at least one tick between \(\sigma \) and \(\kappa \), and a structure in which \(\sigma \) causes transition to an activity where \(\kappa \) ceases to be enabled. This seems quite intuitive on physical grounds.
- 6.
Since breakdown can occur only when a machine is working, the upper time bound \(u_\lambda \) assigned to a breakdown event need not exceed the (finite) upper time bound \(u_\beta \) for completion of the corresponding work cycle. The \(u_\lambda \) could be replaced by anything larger, including \(\infty \), without affecting behavior.
- 7.
We refer to any DES over an alphabet which includes tick as a generalized TDES; it need not be a (strict) TDES constructed according to the rules in Sect. 9.2. Generalized TDES are needed to model specifications and supervisors.
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Wonham, W.M., Cai, K. (2019). Supervisory Control of Timed Discrete-Event Systems. In: Supervisory Control of Discrete-Event Systems. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-77452-7_9
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DOI: https://doi.org/10.1007/978-3-319-77452-7_9
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