Deadlock recovery for flexible manufacturing systems modeled with Petri nets

The main contribution of this correspondence paper consists in a linear algebraic characterization of the admissible marking set relative to a Petri net with uncontrollable transitions, subject to a linear constraint. In more detail, given a linear constraint that limits the number of tokens in one place, an algorithm is proposed to compute an approximation of the admissible marking set in terms of a disjunction of transformed linear constraints. The optimality of the solution is guaranteed provided that certain conditions are satisfied during the intermediate steps of the iterative approach. In all the other cases, the set of markings described by the transformed constraints could be surely contained in the admissible marking set.

A Novel Approach for Constraint Transformation in Petri Nets With Uncontrollable Transitions

For bounded Petri nets, Cabasino et al. propose a diagnosability test method that is based on the analysis of a modified basis reachability graph and a basis reachability diagnoser. However, its complexity is exponential in the number of nodes of the basis reachability diagnoser. In order to reduce the complexity of their method, this paper presents a new diagnosability test approach for bounded Petri nets. We present the concept of an extended basis reachability graph and prove that our approach is of polynomial complexity in the number of nodes of extended basis reachability graphs. An example is given to illustrate the application of the presented approach.

An improved approach to test diagnosability of bounded petri nets

Siphons, as a structural object of Petri nets (PNs), are closely related to deadlock-freedom in PNs. Efficient siphon computation is of great importance in developing siphon-based deadlock control strategies with good performance. This paper is concerned with the enumeration of minimal siphons in a subclass of PNs called systems of sequential systems with shared resources (S4PR). First, a method with polynomial complexity is proposed to decide whether a subset of resource places can generate a minimal siphon. Next, by utilizing the technique of problem partitioning, we develop an approach to compute all minimal siphons in S4PR. The proposed approach is illustrated by an example and its advantage is finally demonstrated via a comparison with other approaches.

An Approach for Enumerating Minimal Siphons in a Subclass of Petri Nets

Complex and customized manufacturing requires a high level of collaboration between production and logistics in a flexible production system. With the widespread use of Internet of Things technology in manufacturing, a great amount of real-time and multi-source manufacturing data and logistics data is created, that can be used to perform production-logistics collaboration. To solve the aforementioned problems, this paper proposes a timed colored Petri net simulation-based self-adaptive collaboration method for Internet of Things-enabled production-logistics systems. The method combines the schedule of token sequences in the timed colored Petri net with real-time status of key production and logistics equipment. The key equipment is made ‘smart’ to actively publish or request logistics tasks. An integrated framework based on a cloud service platform is introduced to provide the basis for self-adaptive collaboration of production-logistics systems. A simulation experiment is conducted by using colored Petri nets (CPN) Tools to validate the performance and applicability of the proposed method. Computational experiments demonstrate that the proposed method outperforms the event-driven method in terms of reductions of waiting time, makespan, and electricity consumption. This proposed method is also applicable to other manufacturing systems to implement production-logistics collaboration.

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A Timed Colored Petri Net Simulation-Based Self-Adaptive Collaboration Method for Production-Logistics Systems

Optimal supervisor synthesis for petri nets with uncontrollable transitions

Linear constraint transformation is an important technique to solve the forbidden state problem in Petri nets containing uncontrollable transitions. This work develops an algorithm to perform the transformation of a linear constraint in Petri nets with arbitrary structures. Particularly, two rules are given to specify the priority of transitions for transformation. Moreover, a condition is proposed, under which a complementary marking set appearing during transformation can be directly added to the final transformation result rather than being continuously transformed. Examples are finally presented to illustrate the application of the proposed algorithm.

Chengying Wang

Papers

Optimal supervisor synthesis for petri nets with uncontrollable transitions

An algorithm for linear constraint transformation in Petri nets