Abstract
In this chapter, we present the supervisor localization approach in detail. After reviewing the basics of supervisory control theory, we formulate the distributed control problem for discrete-event systems: compute one local controller for each agent, such that these local controllers collectively enforce the same controlled behavior as the monolithic supervisor. The central concept of localization is that of control cover, which proves to be both sufficient and necessary for the controllers obtained by localization to solve the formulated problem. An algorithm is then presented that automates the localization procedure, and a language interpretation of localization is provided. Finally, two boundary cases of localization are identified which indicate, as a property of the localization problem itself, an extreme degree of ‘easiness’ or ‘hardness’, respectively.
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Notes
- 1.
In Appendix B we recall the concept of NP-hardness, and prove that the computation of state-minimal local controllers is indeed as stated.
- 2.
If the check turns out negative, \(\mathbf {SUP} \) might still be fully-localizable, as conceivably there could exist other instances of local controllers (referring to the Localization Procedure in Sect. 2.3) for which the check turns out positive.
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© 2016 Springer International Publishing Switzerland
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Cai, K., Wonham, W.M. (2016). Localization: Fundamental Results. In: Supervisor Localization. Lecture Notes in Control and Information Sciences, vol 459. Springer, Cham. https://doi.org/10.1007/978-3-319-20496-3_2
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DOI: https://doi.org/10.1007/978-3-319-20496-3_2
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Online ISBN: 978-3-319-20496-3
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