Liveness-enforcing Petri Net Supervisor Research Articles

Synthesis of Liveness-Enforcing Petri Net Supervisors Based on a Think-Globally-Act-\Łocally Approach and a Structurally Minimal Method for Flexible Manufacturing Systems

This paper proposes a deadlock prevention policy for flexible manufacturing systems (FMSs) based on a think-globally-act-locally approach and a structurally minimal method. First, by using the think-globally-act-locally approach, a global idle place is temporarily added to a Petri net model with deadlocks. Then, at each iteration, an integer linear programming problem is formulated to design a minimal number of maximally permissive control places. Therefore, a supervisor with a low structural complexity is obtained since the number of control places is greatly compressed. Finally, by adding the designed supervisor, the resulting net model is optimally or near-optimally controlled. Three examples from the literature are used to illustrate the proposed method.

Most permissive liveness-enforcing Petri net supervisors for discrete event systems via linear monitors

This paper proposes a deadlock prevention method to design a maximally permissive liveness-enforcing pure Petri net supervisor for a discrete event system, if such a supervisor exists; otherwise, it obtains the most permissive one in the sense that no other pure liveness-enforcing supervisors via linear monitors can be more permissive than it. This paper exploits an iterative method. At each iteration, a first-met bad marking (FBM) is singled out and an integer linear programming problem (ILPP) is configured. If a feasible solution can be found for the ILPP, then a place invariant (PI) is designed to prohibit the FBM from being reached while no legal marking is forbidden. If the ILPP has no solution, we collect all these FBMs that cannot be optimally controlled. For each of such FBMs, another ILPP is designed to find the least number of legal markings whose reachability conditions contradict the current considered FBM and enumerate all the optimal solutions of this ILPP. Based on it, we develop a 0–1 linear programming problem to find the maximal number of legal markings after removing all the contradictory legal markings. Then, the new sets of legal markings and FBMs are obtained, and we return to the iteration stage to redesign a PI to control each FBM if the ILPP has a feasible solution. Repeat the above process until no FBM can be reached. Finally, a most permissive pure liveness-enforcing supervisor via linear monitors is derived. Two Petri net models are used to illustrate the proposed method.

Deadlock analysis and control using Petri net decomposition techniques

Petri nets are an effective tool for modeling and analyzing deadlock problems of flexible manufacturing systems (FMSs). Based on Petri nets, this paper proposes a decomposition method for deadlock control of a class of Petri net modeling FMSs. It first decomposes a Petri net into two (or more) subnets via shared transitions and designs a liveness-enforcing Petri net supervisor for each subnet. Then the root of causing deadlocks is analyzed when merging the controlled subnets. Finally, control places are adjoined to the merged net to obtain a liveness-enforcing Petri net supervisor. The proposed method only needs to calculate the reachability graphs of the subnets, which are in general much smaller than that of the whole original net system. This method in general reduces significantly the computational overhead of designing a liveness-enforcing Petri net supervisor. A subnet can be further decomposed in a hierarchical way, which can further mitigate the computational burden. Typical examples are used to demonstrate the proposed methods.

On structural reduction of liveness-enforcing Petri net supervisors for flexible manufacturing systems: an algebraic approach

On structural reduction of liveness-enforcing Petri net supervisors for flexible manufacturing systems: an algebraic approach

Synthesis of Liveness-Enforcing Petri Net Supervisors Based on a Think-Globally-Act-Locally Approach and Vector Covering for Flexible Manufacturing Systems

This paper proposes the synthesis of Petri net supervisors based on a think-globally-act-locally (TGAL) approach and a vector covering technique for flexible manufacturing systems. Given a Petri net model with deadlocks, the TGAL approach first temporarily adds a global idle place (GP). A GP has initially only one token. Then, we generate the reachability graph of the net model with the GP. If there are deadlocks, we find all the legal markings and first-met bad markings (FBMs). The legal markings and FBMs that need to be considered can be reduced by using a vector covering approach. An integer linear programming problem is formulated to design a set of control places to forbid all FBMs but no legal markings. Meanwhile, the redundancy of the obtained control places is checked to remove the redundant ones. Then, we increase one token in the GP and compute a set of control place again. This process is carried out until the reachable markings of the Petri net model do not increase when the number of tokens in the GP is increased. As a result, we can find a set of control places to make the Petri net model live. Finally, some Petri net examples from the literature are used to demonstrate the proposed methods. It can be verified that the obtained supervisors can lead to more reachable markings, since the obtained control places are maximally permissive at each iteration.

Update to "Extraction of elementary siphons in a class of generalized Petri nets using graph theory" [Engineering Computations (2014) 31(2)331-352

Purpose The purpose of this paper is to correct some mistakes in recently published paper (Hou, Y.F., Li, Z.W., Zhao, M., and Liu, D. (2014) “Extraction of elementary siphons in a class of generalized Petri nets using graph theory”, Engineering Computations, Vol.31, No.2, pp.331-352). Design/methodology/approach In (Hou et al., 2014), based on the concepts of initial resource weighted digraphs and restricted subgraphs, a structurally simple liveness-enforcing supervisor for WS3PR was designed. To demonstrate the effectiveness and applicability of the proposed method, a flexible manufacturing system (FMS) example was presented. However, there are some mistakes in the considered example. The derived monitors were incorrect, which caused the result that the final controlled net system is not live. Findings In order to correct the errors in (Hou et al., 2014), a liveness-enforcing Petri nets supervisor with revised monitors for the considered example was redesigned by applying the method in (Hou et al., 2014). Originality/value This paper corrected the mistakes in (Hou et al., 2014). Consequently, a liveness-enforcing Petri net supervisor is redesigned.

Comparison and Evaluation of Deadlock Prevention Methods for Different Size Automated Manufacturing Systems

In automated manufacturing systems (AMSs), deadlocks problems can arise due to limited shared resources. Petri nets are an effective tool to prevent deadlocks in AMSs. In this paper, a simulation based on existing deadlock prevention policies and different Petri net models are considered to explore whether a permissive liveness-enforcing Petri net supervisor can provide better time performance. The work of simulation is implemented as follows. (1) Assign the time to the controlled Petri net models, which leads to timed Petri nets. (2) Build the Petri net model using MATLAB software. (3) Run and simulate the model, and simulation results are analyzed to determine which existing policies are suitable for different systems. Siphons and iterative methods are used for deadlocks prevention. Finally, the computational results show that the selected deadlock policies may not imply high resource utilization and plant productivity, which have been shown theoretically in previous publications. However, for all selected AMSs, the iterative methods always lead to structurally and computationally complex liveness-enforcing net supervisors compared to the siphons methods. Moreover, they can provide better behavioral permissiveness than siphons methods for small systems. For large systems, a strict minimal siphon method leads to better behavioral permissiveness than the other methods.

On Nonexistence of a Maximally Permissive Liveness-Enforcing Pure Net Supervisor

Behavioral permissiveness is one of the well-accepted criteria for evaluating the performance of a liveness-enforcing Petri net supervisor. However, a maximally permissive liveness-enforcing pure net supervisor does not always exist for any Petri net. This paper focuses on the nonexistence of maximally permissive liveness-enforcing pure net supervisors for a subclass of Petri nets. It shows that if a net contains a siphon that cannot be optimally controlled by a P-invariant, the net does not have a maximally permissive liveness-enforcing pure net supervisor. For a class of Petri nets that can model flexible manufacturing systems, sufficient conditions are proposed to decide whether there exists a siphon that cannot be optimally controlled. This paper also shows that a Petri net system does not have a maximally permissive liveness-enforcing pure net supervisor if it contains some special reachable markings.

Most permissive liveness-enforcing Petri net supervisors for flexible manufacturing systems

This paper presents a deadlock prevention approach to find a maximally permissive liveness-enforcing pure Petri net supervisor, expressed by a set of monitors, for a flexible manufacturing system (FMS), if such a supervisor exists. Otherwise, it derives the most permissive one in the sense that there are no other Petri net supervisors that are more permissive than it. The proposed approach computes the reachability graph of a plant model only once. By using a vector covering approach, the sets of legal markings and first-met bad markings (FBMs) are reduced to two smaller ones, namely the minimal covering set of legal markings and the minimal covered set of FBMs. At each iteration, an FBM is selected. By solving an integer linear programming problem (ILPP), a place invariant (PI) is designed to prevent the FBM from being reached while no marking in the minimal covering set of legal markings is forbidden. If the ILPP has no solution, implying that there is no maximally permissive Petri net supervisor for the plant net model, another ILPP is designed to remove the least number of legal markings whose reachability conditions contradict others. Then, a PI is redesigned to ensure that the remaining legal markings are reachable. This process is carried out until no FBM can be reached. Finally, a most permissive liveness-enforcing supervisor is obtained. FMS examples are presented to illustrate the proposed approaches.

On structural minimality of optimal supervisors for flexible manufacturing systems

This paper develops a place invariant based deadlock prevention method to obtain an optimal, i.e., maximally permissive, liveness-enforcing Petri net supervisor with a minimal supervisory structure that means the minimal number of control places. Maximal permissiveness can be achieved by designing place invariants that make all legal markings reachable while all first-met bad markings unreachable. An integer linear programming problem is formulated to compute all place invariants and its objective function minimizes the number of place invariants, aiming to yield a minimal supervisory structure. Importantly, we develop a technique to greatly improve the efficiency of the proposed method by reducing the number of constraints and variables in the integer linear programming problem under consideration. A number of examples from the literature are used to illustrate the proposed approaches.

Corrections to “Design of a Maximally Permissive Liveness-Enforcing Petri Net Supervisor for Flexible Manufacturing Systems” [Apr 11 374-393

Presents corrections to the second paragraph of Section V-B in the above titled paper (ibid., vol. 8, no. 2, pp. 374-393, Apr. 2011).

A deadlock prevention policy for a class of Petri net models of flexible manufacturing systems

This paper focuses on the problem of deadlocks in automated flexible manufacturing systems (FMS). Based on Petri nets, a deadlock prevention policy is proposed for a special class of Petri nets, S3PR. We embed the deadlock avoidance policy (DAP) of conjunctive/disjunctive resources upstream neighbourhood (C/D RUN) into the deadlock prevention policy (DPP), and allocate the underlying (sequential) resources reasonably to guarantee the absence of deadlock states and processes. First, siphons in a net model are distinguished by elementary and dependent ones. From the set of elementary siphons, a set of linear inequality constraints expressed by the state vector can be formalised. After being modified by the proposed policy, a set of generalised mutual exclusion constraints (GMEC) expressed by the marking vector can be found. Then monitors based on the GMEC are added to the plant model such that the elementary siphons in the S3PR net are all invariant-controlled and no emptiable siphon is generated due to the addition of the monitors. This novel deadlock prevention policy can usually lead to a more permissive supervisor by adding a smaller number of monitors and arcs than the existing methods for the design of liveness-enforcing Petri net supervisors. Two manufacturing examples are utilised to illustrate the proposed method and compared with the existing ones.

Design of a maximally permissive liveness-enforcing supervisor with a compressed supervisory structure for flexible manufacturing systems

In this paper, a deadlock prevention policy for flexible manufacturing systems (FMS) is proposed, which can obtain a maximally permissive liveness-enforcing Petri net supervisor while the number of control places is compressed. By using a vector covering approach, the sets of legal markings and first-met bad markings (FBM) are reduced to two small ones, i.e., the minimal covering set of legal markings and the minimal covered set of FBM. A maximally permissive control purpose can be achieved by designing control places such that all markings in the minimal covered set of FBM are forbidden and no marking in the minimal covering set of legal markings is forbidden. An integer linear programming problem is designed to minimize the number of control places under an assumption that a control place is associated with a P-semiflow. The resulting net has the minimal number of control places on the premise that the assumption holds, and possesses all permissive states of a plant. The only problem of the proposed method is its computational complexity that makes it inapplicable to large-scale Petri net models. An FMS example from the literature is presented to illustrate the proposed method.

A deadlock prevention approach for flexible manufacturing systems with uncontrollable transitions in their Petri net models

Deadlocks are a highly undesired situation in a fully automated flexible manufacturing system, whose occurrences are tied to the existence of shared resources that are competed by different production processes. In the last two decades, a fair amount of research has been done on deadlock analysis and control for flexible manufacturing systems, leading to a variety of strategies in the literature. Petri nets are a promising mathematical tool to handle deadlock problems in flexible manufacturing systems. However, most deadlock control policies based on a Petri net formalism assume that all the transitions in a plant model are controllable. However, uncontrollability of events are a natural feature in a real-world production system. This paper proposes a deadlock prevention policy for a class of Petri nets by considering the existence of uncontrollable transitions. Deadlocks are prevented by adding monitors to a plant Petri net model, whose addition does not inhibit the firings of uncontrollable transitions. Linear programming techniques are employed to find transitions to which a monitor points in order that a more permissive liveness-enforcing Petri net supervisor can be found. A number of manufacturing examples are used to demonstrate the proposed methods. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Structure reduction of liveness-enforcing Petri nets using mixed integer programming

Many deadlock prevention policies existing in the literature are to add control places (CPs) to cope with deadlocks in practical systems modeled with Petri nets. Since the number of CPs determined by these policies is not minimal under the condition that a controlled systems is live, this usually leads to a liveness-enforcing Petri net supervisor with redundant CPs. Based on mixed integer programming (MIP) and the concept of implicit places (IPs), this paper develops a novel iterative algorithm of simplifying the structural complexity for a live Petri net. Under the condition that liveness is preserved in the iteration, this algorithm computes a feasible solution of an MIP for each CP to confirm whether redundant CPs exist in the live controlled system. Necessary and redundant CPs are then kept in or removed from the simplified live Petri net, respectively. As a result, a live controlled system with simpler structure is obtained, which directly reduces computational cost in further design and verification phases and possibly leads to more permissive behavior. Effectiveness of this algorithm is proved via a theoretic analysis and examples. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Identification of controllable transitions to decide the existence of an optimal liveness-enforcing supervisor for a class of Petri nets

Behaviour permissiveness is an important criterion in evaluating the performance of a liveness-enforcing supervisor for discrete event systems. The existence of uncontrollable events is a standard feature in the supervisory control of discrete event systems. A natural problem arising in this area is the existence of an optimal supervisor when there exist uncontrollable events in a plant. For a class of Petri net models of flexible manufacturing systems, whose optimal liveness-enforcing Petri net supervisors can be synthesized by a particular method through the addition of a set of monitors, this paper aims to identify a set of transitions such that the existence of an optimal liveness-enforcing net supervisor depends on their controllability. The controllability of a transition is decided by solving a linear programming problem to verify whether a monitor with arcs to the transition can act to inhibit it when it is otherwise enabled. A number of examples are presented to demonstrate the application of the proposed methods.

Smart deadlock prevention policy for flexible manufacturing systems using Petri nets

Deadlocks are a highly undesired situation in automated production systems including flexible manufacturing systems. Based on a Petri net formalism, a novel deadlock prevention policy is proposed for a class of Petri nets, S3PR, by using an MIP-based deadlock detection method and elementary siphons of Petri nets. Deadlock prevention is achieved by synthesising a set of monitors that are added to the plant net model. The concept of dominated transitions is proposed, to which the output arcs of the monitors are led. The monitors are computed according to a set of elementary siphons in a plant net model, which is found by using an established algorithm in the literature. When compared with the existing policies, the proposed method leads to a liveness-enforcing Petri net supervisor with a small number of monitors but more permissive behaviour. Examples are used to demonstrate the proposed method.

A Divide-and-Conquer Strategy to Deadlock Prevention in Flexible Manufacturing Systems

Petri nets are a popular mathematical tool to investigate the deadlock problems in resource allocation systems. As an important problem solution paradigm in computer science, the divide-and-conquer strategy is used in this paper to investigate the deadlock prevention for flexible manufacturing systems (FMSs) that are modeled with Petri nets. Based on the concept of resource circuits, a plant net model is divided into an idle subnet, an autonomous subnet, and a number of small but independent subnets, called toparchies, from the viewpoint of deadlock control. A liveness-enforcing supervisor, called toparch, is designed for each toparchy. If a particular separation condition holds in a plant net model, the computational complexity of toparches is significantly reduced. This research shows that the resultant net, called monarch, by composing the toparches derived for the toparchies can serve as a liveness-enforcing Petri net supervisor for the whole plant model. FMS examples are given to illustrate the proposed method.

A deadlock prevention approach for flexible manufacturing systems without complete siphon enumeration of their Petri net models

Siphons are very important in the analysis and control of deadlocks in a Petri net. However, it is quite time-consuming or even impossible to get the complete siphon enumeration of a Petri net. This paper focuses on the deadlock prevention problems in flexible manufacturing systems that are modeled with S4PR, a general class of Petri nets. The analysis of S4PR leads us to characterize deadlock situations in terms of insufficiently marked siphons. The method proposed in this paper is an iterative approach. At each iteration, a non-max-marked siphon is computed by solving a mixed integer linear programming problem. Then the siphon is max-marked through a P-invariant by adding a monitor place. This process is carried out until no non-max-marked siphon can be found in the net. As a result all the siphons in the net are max-controlled. Then the net becomes live. Without computing all the siphons, a monitor-based liveness-enforcing Petri net supervisor can be found with more permissive behavior. A number of flexible manufacturing examples are used to demonstrate the proposed methods.

A Deadlock Prevention Policy for a Class of Petri Nets S^3PMR

This paper focuses on the problem of deadlocks in automated flexible manufacturing systems (FMS) where deadlocks are caused by unmarked siphons in their Petri net models. A deadlock prevention policy is proposed for a subclass of Petri nets, S^3PMR that can well model a large class of FMS. We distinguish siphons in such a net model by elementary and dependent ones. For each elementary siphon, a monitor is added to the plant model such that it is invariant-controlled. The monitor addition way guarantees that no emptiable control-induced siphon is generated due to the presence of monitors in the resultant net. This novel deadlock prevention policy can usually lead to a more permissive supervisor by adding a small number of monitors and arcs than the existing methods for the design of liveness-enforcing Petri net supervisors. Experimental study indicates that the proposed policy appears to be more permissive than closely related approaches in the literature.