Abstract
Supervisory control is an important area of discrete control theory that received a growing attention since the seminal work of Ramadge and Wonham (see, for example [119, 77, 78, 8, 25]). In this chapter we apply the techniques for language equation solving to supervisory control problems, taking into account that methods for language equation solving cannot be directly used in supervisory control, and vice versa. The reason is that from one side the topology addressed in supervisory control is a special case of the general topology addressed by language equation solving; from another side in supervisory control one is required to model also partial controllability and partial observability, which are formalized in a different way when solving language equations.
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Notes
- 1.
Another definition of progressive or non-blocking solution is reported in the literature, see [78, 38, 104, 102], by which a non-blocking controller C cannot block in the product P ∩ C any action that is allowed by the specification.
- 2.
If C w is a weak controller, then \({C}_{w} \subseteq {C}_{w}^{\Uparrow {\Sigma }_{uc}} \subseteq {(\overline{P} \cup S)}^{\mathit{Pref }}\).
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Villa, T., Yevtushenko, N., Brayton, R.K., Mishchenko, A., Petrenko, A., Sangiovanni-Vincentelli, A. (2012). Supervisory Control. In: The Unknown Component Problem. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-68759-9_15
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DOI: https://doi.org/10.1007/978-0-387-68759-9_15
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