Robustness Analysis in Automated Manufacturing Systems Allowing Multiple Server Failures Using Generalized Reduced Reachability Graphs
本文研究允许多次服务器故障的自动化制造系统的最大许可鲁棒性分析，通过广义危险变迁将子系统分类，构建广义缩减可达图，并推导出识别标记鲁棒性的充要条件。
This article concentrates on maximally permissive robustness analysis for automated manufacturing systems (AMSs) that allow multiple server failures in the paradigm of Petri nets (PNs). First, we fully describe resource failures in a more general perspective, formalized as generalized dangerous transitions, and develop an algorithm for computing the set of these transitions. The presence of such transitions results in all subnet systems being divided into two types: dangerous subnet systems and nondangerous subnet systems. Second, based on the number of nondangerous subnets consistently operated, the more general definitions of strongly robust, weakly robust, and nonrobust markings are established. Third, generalized reduced reachability graphs (R<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>Gs) are constructed to provide a formal tool for robustness analysis. An algorithm is formulated to compute the maximum nondangerous elementary circuits (NDE circuits) for each marking in generalized R<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>G. Subsequently, by analyzing the transitions involved in the maximum NDE circuits, we derived the necessary and sufficient conditions for identifying the robustness of markings. Finally, examples are provided to demonstrate the proposed methods and illustrate their advantages over existing approaches.