{"title":"Algebraic and geometric characterization of Petri net controllers using the theory of regions","authors":"A. Ghaffari, N. Rezg, Xiaolan Xie","doi":"10.1109/WODES.2002.1167691","DOIUrl":null,"url":null,"abstract":"This paper presents a formal treatment of Petri net controller design problems. Two supervisory control problems of plant Petri net models, forbidden state and forbidden state-transition problems, are defined. The theory of regions is used to provide algebraic characterizations of pure and impure control places for both problems. Thanks to Farkas-Minkowski's lemma, the algebraic characterizations lead to nice geometric characterization for the existence of control places for the two supervisory problems.","PeriodicalId":435263,"journal":{"name":"Sixth International Workshop on Discrete Event Systems, 2002. Proceedings.","volume":"46 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2002-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"21","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Sixth International Workshop on Discrete Event Systems, 2002. Proceedings.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/WODES.2002.1167691","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 21
Abstract
This paper presents a formal treatment of Petri net controller design problems. Two supervisory control problems of plant Petri net models, forbidden state and forbidden state-transition problems, are defined. The theory of regions is used to provide algebraic characterizations of pure and impure control places for both problems. Thanks to Farkas-Minkowski's lemma, the algebraic characterizations lead to nice geometric characterization for the existence of control places for the two supervisory problems.
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