Algebraic and geometric characterization of Petri net controllers using the theory of regions

A. Ghaffari, N. Rezg, Xiaolan Xie
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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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利用区域理论对Petri网控制器进行代数和几何表征
本文给出了Petri网控制器设计问题的形式化处理方法。定义了植物Petri网模型的两个监督控制问题:禁止状态问题和禁止状态转移问题。利用区域理论给出了这两个问题的纯控制点和非纯控制点的代数表征。借助于法卡斯-闵可夫斯基引理,代数表征得到了两个监督问题控制点存在的良好几何表征。
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