In this paper, a type of specifications called OR-AND Generalized Mutual Exclusion Constraints (GMEC) for place/transition nets is defined. Such a specification consists of a disjunction of conjunction of several single GMECs, i.e., the requirement is that, at any given time, the controlled system should satisfy at least one set of conjunctive GMECs. We show that a bounded OR-AND GMEC can be enforced by a special control structure composed by a set of AND-GMEC monitor places plus a switcher that determines the current active ones. We also show that such a simple control structure can be modified to ensure maximal permissiveness. This approach can be used in the framework of supervisory control in Petri nets.

Design of Optimal Petri Net Controllers for Disjunctive Generalized Mutual Exclusion Constraints

This paper presents a new Petri net structure, namely, an interval inhibitor arc, and its application to the optimal supervisory control of Petri nets. An interval inhibitor arc is an arc from a place to a transition labeled with an integer interval. The transition is disabled by the place if the number of tokens in the place is between the labeled interval. The formal definition and the firing rules of Petri nets with interval inhibitor arcs are developed. Then, an optimal Petri net supervisor based on the interval inhibitor arcs is designed to prevent a system from reaching illegal markings. Two techniques are developed to simplify the supervisory structure by compressing the number of control places. The proposed approaches are general since they can be applied to any bounded Petri net models. A marking reduction approach is also introduced if they are applied to Petri net models of flexible manufacturing systems. Finally, a number of examples are provided to demonstrate the proposed approaches and the experimental results show that they can obtain optimal Petri net supervisors for some net models that cannot be optimally controlled by pure net supervisors. Furthermore, the obtained supervisor is structurally simple.

New Petri Net Structure and Its Application to Optimal Supervisory Control: Interval Inhibitor Arcs

This work proposes a novel structure in Petri nets, namely data inhibitor arcs, and their application to the optimal supervisory control of Petri nets. A data inhibitor arc is an arc from a place to a transition labeled with a set of integers. A transition is disabled by a data inhibitor arc if the number of tokens in the place is in the set of integers labeled on it. Its formal definitions and properties are given. Then, we propose a method to design an optimal Petri net supervisor with data inhibitor arcs to prevent a system from reaching illegal markings with respect to control specifications. Two techniques are developed to reduce the supervisor structure by compressing the number of control places. Finally, a number of examples are used to illustrate the proposed approaches and experimental results show that they can obtain optimal Petri net supervisors for the net models that cannot be optimally controlled by pure net supervisors. A significant result is that the proposed approach can always lead to an optimal supervisor with only one control place for bounded Petri nets on the premise that such a supervisor exists.

Compact Supervisory Control of Discrete Event Systems by Petri Nets With Data Inhibitor Arcs

In the context of automated manufacturing systems (AMSs), Petri nets are widely adopted to solve the modeling, analysis, and control problems. So far, nearly all known approaches to liveness-enforcing supervisory control study AMSs with flexible routes, whereas little work investigates the ones with synchronization operations. Compared with flexibility, synchronization allows the disassembly and assembly operations that correspond to splitting to and merging from different subprocesses, respectively. Such structures bring difficulties to establish a liveness condition of the Petri net model of AMSs. In this paper, we propose a novel class of systems, which can well deal with these features so as to facilitate the investigation of such complex systems. Using structural analysis, we show that their liveness can be attributed to deadlock freeness, which is much easier to analyze, detect, and control by synthesizing a proper supervisory controller. Furthermore, a set of mathematical formulations is proposed to describe and extract the corresponding deadlocks. This facilitates the synthesis of liveness enforcing supervisors as it avoids the consideration of deadlock-free but nonlive scenarios. The effectiveness and efficiency of this new method is shown by AMS examples.

A Petri Net-Based Discrete-Event Control of Automated Manufacturing Systems With Assembly Operations

Petri-net-based dynamic scheduling of flexible manufacturing system via deep reinforcement learning with graph convolutional network

Strict minimal siphons (SMS) play an important role in the development of deadlock control policies for flexible manufacturing systems (FMS). For a class of Petri nets called Systems of Simple Sequential Processes with Resources (S3PR), the resource circuit-based method is an effective way to compute SMS. In this paper, a more effective one to compute SMS is proposed. First, the concepts of loop resource subsets and their characteristic resource subnets are proposed. Next, sufficient and necessary conditions for loop resource subsets to generate SMS are established. Finally, an algorithm is given to find all the SMS based on loop resource subsets. Since the number of loop resource subsets is much less than that of resource circuits and their combinations, the computational efficiency of the SMS enumeration task is significantly improved by the proposed method. An FMS example is used to illustrate the application of the proposed method, and computational time comparisons are provided on several S3PRs to show its superior efficiency.

A Method to Compute Strict Minimal Siphons in a Class of Petri Nets Based on Loop Resource Subsets

Strict minimal siphons (SMSs) play a key role in the development of deadlock prevention policies by using Petri nets for flexible manufacturing systems (FMSs). In this paper, given two SMSs and their resultant siphon, the concept of key resource subsets is proposed which is shown to be the critical factor in deciding the controllability conditions of the latter. A necessary and sufficient condition is then proposed under which the resultant siphon can be always marked if its two SMSs are M-controlled, i.e., invariant controlled via the method proposed by Moody and Antsaklis. As for a resultant siphon that is composed by more than two composable SMSs, a sufficient condition is proposed under which it can be always marked if its SMSs are M-controlled. They are established by analyzing the structural characteristics and markings of the resource subnets in a class of Petri nets called L-S3PR. When they are applied to some classes of S3PR nets, i.e., those whose controlled ones are maximally permissive and live once their original SMSs are M-controlled, the number of monitors may be reduced. An FMS example is used to illustrate the application of the results.

Controllability Conditions of Resultant Siphons in a Class of Petri Nets

For a class of Petri nets whose uncontrollable influence subnets are forward synchronization and backward conflict-free nets, this paper proposes an algorithm to transform a given generalized mutual exclusion constraint (GMEC) into an optimal admissible one. Based on the proposed constraint transformation, a method is given to synthesize an optimal monitor-based supervisors. The proposed method utilizes an optimal monitor-based supervisor to enforce a GMEC containing infinite elements, which has not been seen in any prior research. Moreover, it has higher computational efficiency at the expense of application scope than some existing methods. An example is used to illustrate the application of the proposed method.

Design of Optimal Monitor-Based Supervisors for a Class of Petri Nets With Uncontrollable Transitions

This paper proposes a new modified reachability tree (NMRT) approach for a class of unbounded generalized Petri nets called ω-independent nets. The NMRT of an ω-independent net consists of all and only reachable markings from its initial marking. Moreover, the applications of the NMRT to deadlock analysis for ω-independent nets are developed. The proposed method has a larger application scope than all the existing methods. Several examples are provided to show its superiority over them.

A New Modified Reachability Tree Approach and Its Applications to Unbounded Petri Nets

A siphon-based algorithm for deadlock prevention of Petri nets called Algorithm H2 is proposed in the above paper. However, the illustrative examples for Algorithm H2 are incorrect because of the redundant weighted control (WC) places which control some marked siphons. This correspondence modifies the illustrative examples by removing the redundant control places and getting a maximally permissive control for the original net. As no WC place is presented in the modified examples, the examples cannot well illustrate Algorithm H2.

ChengYing Wang

Papers

A Method to Compute Strict Minimal Siphons in a Class of Petri Nets Based on Loop Resource Subsets

Controllability Conditions of Resultant Siphons in a Class of Petri Nets

Design of Optimal Monitor-Based Supervisors for a Class of Petri Nets With Uncontrollable Transitions

A New Modified Reachability Tree Approach and Its Applications to Unbounded Petri Nets

Comments on "Siphon-Based Deadlock Prevention Policy for Flexible Manufacturing Systems