On Algebraic Properties of Delay-Nonconflicting Languages in Supervisory Control under Communication Delays

Jung-Min YANG  Seong-Jin PARK  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A    No.8    pp.2237-2239
Publication Date: 2008/08/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.8.2237
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Systems and Control
delay-nonconflicting languages,  discrete event systems,  supervisors,  communication delays,  

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In networked control systems, uncontrollable events may unexpectedly occur in a plant before a proper control action is applied to the plant due to communication delays. In the area of supervisory control of discrete event systems, Park and Cho [5] proposed the notion of delay-nonconflictingness for the existence of a supervisor achieving a given language specification under communication delays. In this paper, we present the algebraic properties of delay-nonconflicting languages which are necessary for solving supervisor synthesis problems under communication delays. Specifically, we show that the class of prefix-closed and delay-nonconflicting languages is closed under intersection, which leads to the existence of a unique infimal prefix-closed and delay-nonconflicting superlanguage of a given language specification.