ABSTRACT This paper develops a concept of control transition equation (CTE) and the corresponding deadlock control algorithm (DCA) using control transitions (CTs) to eliminate deadlocks in Petri nets. By analysing the reachability graph (RG) of an original net with deadlocks, this DCA firstly find all deadlock markings (DMs) and then the corresponding CTs are solved on the basis of the proposed CTE. Secondly, a linear programming problem that can minimise the number of CTs is applied to these CTs. In addition, in order to furtherly simplify the structure of these CTs, the reconstruction of the necessarily added CTs is performed by a circulating sequence number method. Finally, a live controlled system with the simpler structure is obtained by adding the desired CTs to , which can reach the same number of states as the original plant model , i. e. live maximally reachable number. The proposed DCA is different from deadlock prevention policies using control places (CPs) in most existing literature and whose correctness and efficiency are verified via the theoretical analysis and the relevant several examples.

中文翻译：

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一种使用控制转换的死锁控制算法，用于使用 Petri 网建模的柔性制造系统

摘要 本文开发了控制转换方程 (CTE) 的概念和相应的死锁控制算法 (DCA)，使用控制转换 (CT) 来消除 Petri 网中的死锁。通过分析具有死锁的原始网络的可达图（RG），该 DCA 首先找到所有死锁标记（DM），然后根据所提出的 CTE 求解相应的 CT。其次，将可以最小化 CT 数量的线性规划问题应用于这些 CT。另外，为了进一步简化这些CT的结构，对必须添加的CT进行重构，采用循环序列号的方法。最后，通过将所需的 CT 添加到 中，得到结构更简单的实时控制系统，可以达到与原始设备模型相同的状态数，即 活最大可达数。所提出的 DCA 与大多数现有文献中使用控制位 (CP) 的死锁预防策略不同，其正确性和效率通过理论分析和相关的几个例子得到验证。