Perfect Resource-transition Circuits Research Articles

Robust Deadlock Detection and Control of Automated Manufacturing Systems With Multiple Unreliable Resources Using Petri Nets

In recent years, the research on robust deadlock control has become increasingly popular in automated manufacturing systems (AMSs) because resource failures may lead any system to stagnation, e.g., deadlock. In this article, we study robust supervisory control issues in AMSs with multiple unreliable resources. Petri nets are used to model the considered AMSs that allow multi-quantity and multi-type of resource acquisitions. A set of integer linear programming formulations are introduced to detect a class of deadlocks that have the maximal number of dead transitions. By analysis, a deadlock is characterized by a saturated circuit, which only consists of a set of unmarked resources and a set of critical transitions. Based on the circuit, a linear marking constraint is developed to prevent such circuits from being saturated. A control place (monitor) with its control variable is thus designed for the constraint to prevent the deadlock from appearing even if some resource failures occur. Therefore, we can synthesize a robust deadlock supervisor, which can guarantee that the controlled system can implement the continual operations even if some unreliable resources fail. Finally, the theoretical analysis and comparative study are provided to elucidate the effectiveness and efficiency of our proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In practice, resource failures in automated manufacturing systems (AMSs) are common. Deadlock prevention control in AMSs allowing resource failures has gained more and more attention from researchers and practitioners. Most prior research is based on the enumeration of either siphons or perfect resource transition circuits whose number exponentially increases with the system scale. This means that the synthesized supervisor has a much complex structure. In this article, based on a special kind of circuits at a deadlock marking detected by using a set of mathematical formulations, we develop an effective and efficient method for AMSs with multiple unreliable resources to iteratively control deadlocks such that the controlled system can continue to operate smoothly even if some unreliable resources fail. The computational and comparative results show that our proposed approach can acquire more permissive states with a simpler supervisor.

Improved Multi-Step Look-Ahead Control Policies for Automated Manufacturing Systems

The deadlock control problem in automated manufacturing systems (AMSs) has received much attention in recent years due to the flexibility of an AMS. In the framework of Petri nets, resource-transition circuits and siphons are often used to characterize and derive a deadlock control policy for an AMS. This paper mainly focuses on a class of Petri nets, namely, the system of simple sequential processes with resources, which contains some special resource places. For such a class of Petri nets, the relationship between a multi-step look-ahead deadlock avoidance control method and the structure of the model is established and expanded in a mathematical way. Unlike the one-step look-ahead deadlock avoidance policy (DAP) proposed in the literature, the DAPs reported in this research are applicable to more complex situations, including a model with one-unit resource shared by two or more perfect resource-transition circuits that do not contain each other. Compared with the existing work, some results are archived for expanded models. Finally, for the model with two shared one-unit resources, specific solutions are also presented. Meanwhile, examples are used to demonstrate the proposed results.

A Polynomial Algorithm for Computing Elementary Siphons in a Class of Petri Nets

A set of elementary siphons plays a key role in the development of deadlock prevention policies for automated manufacturing systems. This paper addresses the computation problem for elementary siphons in a subclass of Petri nets which are basic systems of simple sequential processes with resources (BS3PR) and can model many automated manufacturing systems. An algorithm for enumerating elementary siphons is established by the one-to-one relationship between maximal perfect resource-transition circuits (MPCs) and strict minimal siphons. A set of MPCs is first computed, followed by a set of elementary siphons in a BS3PR. The presented algorithm is proved to have polynomial-time complexity. An example is used to illustrate the algorithm.

Optimal Petri-Net-Based Polynomial-Complexity Deadlock-Avoidance Policies for Automated Manufacturing Systems

Even for a simple automated manufacturing system (AMS), such as a general single-unit resource allocation system, the computation of an optimal or maximally permissive deadlock-avoidance policy (DAP) is NP-hard. Based on its Petri-net model, this paper addresses the deadlock-avoidance problem in AMSs, which can be modeled by systems of simple sequential processes with resources. First, deadlock is characterized as a perfect resource-transition circuit that is saturated at a reachable state. Second, for AMSs that do not have one-unit resources shared by two or more perfect resource-transition circuits that do not contain each other, it is proved that there are only two kinds of reachable states: safe states and deadlock. An algorithm for determining the safety of a new state resulting from a safe one is then presented, which has polynomial complexity. Hence, the optimal DAP with polynomial complexity can be obtained by a one-step look-ahead method, and the deadlock-avoidance problem is polynomially solved with Petri nets for the first time. Finally, by reducing a Petri-net model and applying the design of optimal DAP to the reduced one, a suboptimal DAP for a general AMS is synthesized, and its computation is of polynomial complexity.