利用全跨模與覆點擬陣設計自動化工廠的偵查法則

本文提出擬陣理論來設計自動化工廠的偵查器法則。傳統上，可程式控制器是用來控制自動化工廠的運作。當可程式控制器控制下的工廠出現不正常運作時，經過設計的偵查法則就可用來提供即時的警告訊息。所以如何設計出更好的法則來偵查出可程式控制器掌握下的不正常運作就成為研究上的一大挑戰。本文將可程式控制器與偵查器的數學模式視為擬陣理論裡的對偶關係。特別是可程式控制器的運作可用記號圖表達時，記號圖可視為擬陣理論裡的全跨模。由於全跨模的對偶擬陣為覆點擬陣，所以偵查器運作的數學模式可視為覆點擬陣。由於屬性方程式為隱性的偵查法則，故要實作的偵查法則可由覆點擬陣移除屬性方程式後產生。

A matroid-theoretical approach has been proposed for designing the monitor rules of automated factory. In the traditional approach, Programmable Logic Controllers (PLCs) are used to control the operations of a given automated factory. Also monitor rules are designed to offer real-time alert messages once an abnormal operation under the PLCs occurs in the factory. Consequently how to design better rules for monitoring the unexpected operations under the PLCs becomes a research challenge. In this new approach, both the mathematical models of the PLCs and the monitor are treated as a dual relationship in matroid theory. Especially when the operational model under the PLCs is represented as marked graphs, the marked graphs naturally become a strict gammoid in matroid theory. Since the dual matroid of the strict gammoid is transversal matroid, the corresponding monitor model becomes a transversal matroid. Because the attribute equations are implicit and inherent monitor rules, the implemented monitor rules are generated from the transversal matroid after removing its attribute equations.