Generalized Mutual Exclusion Constraints Research Articles

Control laws synthesis to satisfy generalized mutual exclusion constraints for timed event graphs networks using min-plus algebra

The paper focuses on the Generalized Mutual Exclusion Constraints (GMECs) problem in the Network of Timed Event Graphs (NTEGs). A new formal method for state feedback control using Min-Plus algebra formalisms is proposed. For this purpose, the dynamic behavior of the NTEGs and GMECs are respectively described by linear equations and weighted inequalities in Min-Plus algebra. Based on these mathematical tools, control laws are computed to satisfy the constraints that are imposed on the NTEGs in case sufficient conditions are verified. The established controllers are represented by monitor places which supervise the system to ensure all GMECs. Finally, a case study of an AGV network is carried out to illustrate theoretical results and demonstrate the efficiency of developed approaches.

Feedback control laws to ensure generalized mutual exclusion constraints in a network of partially observable timed event graphs

This paper deals with the control problem of partially-observable Discrete Event Systems (DESs) which are modelled by Networks of Timed Event Graphs (NTEGs) and subject to Generalized Mutual Exclusion Constraints (GMECs). A new mathematical methodology based on the use of Min-Plus formalisms to synthesize control laws that guarantee the concerned constraints is suggested. For this, the dynamic behavior of the NTEGs is described by linear equations in Min-Plus algebra and the GMECs are represented by weighted inequalities in Min-Plus algebra too. Sufficient conditions are supplied to verify the existence of feedback gains guaranteeing the satisfaction of GMECs. Eventually, to verify the analytical results, it is important to examine a real case study of manufacturing systems.

Online verification of [formula omitted]-step opacity by Petri nets in centralized and decentralized structures

This paper presents an online approach to deal with the problem of state-based K-step opacity of a discrete event system modeled with labeled Petri nets. The secret states can be described by a set of either markings or generalized mutual exclusion constraints (GMECs), which is more general than the existing approaches in which the secret states are characterized by GMECs only. We formulate an integer linear programming (ILP) model to find a marking outside the set of secret states from each of the K-delayed state estimates, avoiding a complete enumeration of reachability set. Based on the ILP model, an online algorithm is developed to verify K-step opacity of an observation (i.e., an observed sequence). As an extension of K-step opacity, we define the notion of jointK-step opacity in a decentralized structure with two local sites and extend the proposed algorithm to verify the joint K-step opacity of an observation. In addition, the relationship between joint K-step opacity and K-step opacity is formally discussed.

An approach for enforcing a class of GMECs on time Petri nets with uncontrollable transitions

Real-time control is of great significance for practical plants such as intelligent manufacturing systems and transportation systems, and timing information should be integrated in their discrete models. The existing specifications expressed by generalized mutual exclusion constraints (GMECs) do not consider timing specifications in the control design of these models, which would be restrictive for the control specifications of a timed system. In the framework of time Petri net (TPN) models, this paper introduces a class of GMECs, called time GMECs (TGMECs), in which each GMEC is associated with a restricted time interval. By restricting the firing intervals of controllable transitions, an efficient method based on control functions is proposed to implement TGMECs on a TPN system in presence of uncontrollable transitions. The core of the reported method is to employ the transitions-related timing constraints in a partial modified state class graph (PMSCG) to solve mathematical programming problems. Such a PMSCG is a graph recently introduced to enhance the supervisor permissiveness for a TPN system with GMECs. In particular, the terminal condition for the construction of a PMSCG is modified. By taking advantage of the PMSCG, an online control procedure is presented to implement the supervision for TGMECs in a maximally permissive way.

Implementation of Generalized Mutual Exclusion Constraints Using Critical Places and Marking Estimation

Generalized mutual exclusion constraints (GMECs) are a class of state specifications on Petri nets (PNs). They are generally enforced on the nets by a simple control structure called control places (monitors). Unfortunately, this conventional procedure is implemented in an offline and monolithic manner, which suffers from computational difficulty and is arduous for the control of a system in real time. Additionally, the flexibility and fault tolerance of such a method are somewhat unacceptable, and the method suffers from a lack of adaptability to net variations incurred by system reconfiguration, communication failure, and constraint integration. This article aims to enforce GMECs for a live PN model by using critical places and marking estimation. First, we define GMECs on some so-called critical places, such that the satisfaction of the GMECs can be determined by only monitoring the number of tokens in their corresponding critical places during runtime. Then, an efficient and effective control strategy is developed such that the controllers forbid all those transition firings that lead to the violated GMECs based on the estimated markings of critical places derived by observers from a resource perspective rather than exploring the markings of the entire system. Finally, we present procedures to deal with decision deadlocks, which are induced by one-sided decisions made by some controllers and may prevent all enabled transitions from firing. Global GMECs are always implemented through the local observation and control of processes without knowing an extra information.

Closed-Loop Deadlock-Free Supervision for GMECs in Time Petri Net Systems

This article investigates the enforcement of generalized mutual exclusion constraints (GMECs) and deadlock-freeness on a time Petri net (TPN) system with uncontrollable transitions, motivated by the fact that the existing methods enforcing GMECs may degrade the performance of a closed-loop system and lead to deadlock states. A supervisor enforcing a set of GMECs and deadlock-freeness on an underlying untimed Petri net system is assumed to be available. By exploiting timing information and mathematical programming, a control function is designed to restrict the firing intervals of transitions such that a TPN system can avoid entering forbidden states. The key idea behind the proposed approach is the online computation of a graph, called reduced modified state class graph (RMSCG), that is an extension of the partial modified state class graph recently introduced by the authors. Based on the RMSCG, an online control synthesis procedure is developed, which can enforce the originally given GMECs and deadlock-freeness in a maximally permissive way.

A Reduced Computation of State Space to Enforce GMECs and Deadlock-Freeness on TPN Systems

Abstract This paper analyzes the enforcement of Generalized Mutual Exclusion Constraints (GMECs) and deadlock-freeness on a Time Petri net (TPN) system with uncontrollable transitions, motivated by the fact that the existing methods enforcing GMECs may degrade the performance of a closed-loop system and lead to deadlock states. By exploiting timing information and mathematical programming, a control function is designed to restrict the firing intervals of transitions such that a TPN system can avoid entering forbidden states. The key idea behind the proposed approach is the online computation of a graph, called Reduced Modified State Class Graph, that is derived from another graph recently presented in the literature.

Static and Dynamic Partitions of Inequalities: A Unified Methodology for Supervisor Simplification

In the context of automated manufacturing systems, supervisor simplification is drawing increasing attention. As a special class of state specifications, generalized mutual exclusion constraints (GMECs) are a typical kind of supervisory control of Petri nets. In this note, we first propose static and dynamic partitions to reduce the size of supervisor by partitioning inequalities, i.e., GMECs, into redundant and necessary ones. The former considers the specifications themselves and exhibits higher efficiency; while the latter takes into account both specifications and reachable markings and achieves more economical supervisors. In an incremental manner, we develop Type I supervisor simplification method which has a compromised efficiency and complexity. In an integrated manner, we propose Type II supervisor simplification method that further improves efficiency and eases computational complexity. All techniques proposed in this note can be realized in an algebraic manner. Examples are presented for the sake of illustration as well as demonstration.

Online Fault Diagnosis in Discrete Event Systems with Partially Observed Petri Nets

This paper investigates the fault detection problem for Discrete Event Systems (DES) which can be modeled by Partially Observed Petri Nets (POPN). To overcome the problem of low diagnosability in the POPN online fault diagnoser in current use, we propose an improved online fault diagnosis algorithm that integrates Generalized Mutual Exclusion Constraints (GMEC) and Integer Linear Programming (ILP).We assume that the POPN structure and its initial markings are known, and the faults are modeled as unobservable transitions. First, the event sequence is observed and recorded. We use GMEC for elementary diagnosis of the system behavior,then the ILP problem of POPN is solved for further diagnosis. Finally, we modeled and analyzed an example of a real DES to test the new fault diagnoser. The proposed algorithm increased the diagnosability of the DES remarkably, and the effectiveness of the new algorithm integrating GMEC and ILP was verified.

A Minimal Supervisory Structure to Optimally Enforce Liveness on Petri Net Models for Flexible Manufacturing Systems

This paper presents a new method of computing a minimal supervisory structure that optimally enforces liveness on the Petri net models for flexible manufacturing systems (FMSs). The proposed method utilizes the structural properties of a Petri net model to avoid the computation of its reachability graph, which in general leads to the state explosion problem. This paper aims to design a single control place for each concurrent process of a Petri net model or a sub-net model, which thus provides a constant number of control places in a supervisor regardless of the number of resource places in a Petri net or sub-net model. It is shown that the structural size of a supervisor is minimal as the number of control places depends on the number of concurrent processes in the Petri net model. Precisely, two algorithms are developed in this paper. The first aims to compute active uncontrolled transitions and the second is concerned with a method to compute the generalized mutual exclusion constraints (GMECs) for each process of the Petri net model of an FMS. Furthermore, it provides an approach to design control places for each computed GMEC without solving integer linear programming problems, which greatly reduces the computational costs. When the computed control places are coupled with the uncontrolled Petri net model for an FMS, it optimally enforces liveness behavior of the Petri net model, and hence ensures the high utilization of resources in a considered system.

Online Fault Diagnoser for Partially Observed Petri Nets

This paper investigates the fault detection problem for Discrete Event Systems which can be modeled by Partially Observed Petri Nets (POPN). To overcome the shortage of the low diagnosability of the currently POPN online fault diagnoser, we propose an improved on-line fault diagnosis algorithm that integrates Generalized Mutual Exclusion Constraints(GMEC) and Integer Linear Programming (ILP). We assume that the POPN structure and its initial markings are known, the faults are modeled as unobservable transitions. First, the event sequence is observed and recorded. The ILP problem of POPN is solved for elementary diagnosis for the system behavior. While the system is diagnosed that some faults may have happened, we use the GMEC for the further diagnosis. Finally, a real discrete event system is taken as an example, we model and analyse the discrete event system, the proposed algorithm increases the diagnosablity remarkably.

Characterization of Admissible Marking Sets in Petri Nets with Uncontrollable Transitions

This work studies the equivalent transformation from a legal marking set to its admissible marking set. First, the concepts of escaping-marking set and transforming marking set are defined, and two algorithms are provided to compute the transforming marking set and the admissible marking set. Second, the equivalent transformation of a disjunction of linear constraints expressed in terms of generalized mutual exclusion constraints (GMECs) with non-negative weights via uncontrollable transitions is established.

Confusion diagnosis and avoidance of discrete event systems using supervisory control

Nondeterministic firing of concurrent transitions in Petri nets (PNs) may lead to the disappearance of conflicts. The disappearance implies that the partial conflicting transitions in a conflict become disabled before the resolution of the conflict. The phenomenon is called confusions that are caused by the interlacement of conflicting and concurrent transitions in PNs, which generates incomplete and faulty system conflicting behavior such that conflicts cannot be correctly resolved. In this paper, conflict‐increasing confusions (CICs) and conflict‐decreasing confusions (CDCs) in a PN are investigated. The relation graph of conflicts and confusions (RGC2) in a PN is proposed to detect the structure of confusions. To avoid the occurrence of confusions in a PN, an algorithm based on generalized mutual exclusion constraints (GMECs) is proposed, which can generate confusion‐avoidance supervisors such that the occurrence of conflicts can be ensured in a PN. Finally, an example of confusion detection and avoidance in a flexible assembly system is presented. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

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

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.

Integrated design of optimal supervisors for the enforcement of static and behavioral specifications in Petri net models

Petri net (PN) supervisory control is often performed through a sequential procedure that introduces additional constraint layers over an initial unconstrained PN model, using generalized mutual exclusion constraints (GMECs) implemented as monitor places. This is typical, e.g., in the context of flexible manufacturing systems, where the initial model represents the production sequences and the constraints are used to express static specifications, such as job limitations or the usage of resources, and behavioral ones, as liveness, controllability, etc. This sequential procedure may yield a redundant model, that is not easily reduced a posteriori. Also, it is difficult to ensure maximal permissivity with respect to multiple behavioral specifications. This paper, building on recent results regarding optimal supervisor design with branch & bound methods, proposes an integrated modeling approach that can be used to derive a minimal supervisor guaranteeing the attainment of an arbitrary set of static and behavioral specifications in a maximally permissive way. Among behavioral specifications, deadlock-freeness, liveness, reversibility and behavioral controllability are considered in the paper. The supervisor comes in the form of a simple set of GMECs or of a disjunction of sets of GMECs. Some examples emphasize the potential model size reductions that can be achieved.

Synthesis of Structurally Simple Supervisors Enforcing Generalized Mutual Exclusion Constraints in Petri Nets

Generalized mutual exclusion constraints (GMECs) are a typical class of specifications for the supervisory control of discrete event systems in a Petri net formalism. This paper classifies the given constraints into elementary and dependent ones according to the linear dependency of their characteristic transition vectors that indicate the token count change of the concerned places. The dependent constraints are further divided into strongly and weakly dependent ones. A constraint is usually enforced by explicitly adding a monitor to a plant model. This research develops the conditions under which a dependent constraint is enforced due to the enforcement of the elementary constraints. The results developed in this paper are applied to the existing manufacturing-oriented Petri net classes. An algorithm is also proposed to identify a set of elementary constraints. Examples are used to demonstrate the proposed methods. Some potential extensions and applications are also discussed. This research improves the existing methods in computational efficiency and structure simplification of the supervisor, given a set of GMECs.

Supervisor Synthesis for Enforcing a Class of Generalized Mutual Exclusion Constraints on Petri Nets

The considered class of generalized mutual exclusion constraints (GMECs) on a controlled Petri net are such that the influence-uncontrollable subnets are forward-concurrent-free nets. Some structural properties of forward-concurrent-free nets are firstly proposed. Utilizing these properties, a method is then proposed to transform a given conjunction of GMECs into a conjunction of admissible GMECs. Furthermore, the necessary and sufficient condition of the existence of the permissive supervisor is obtained, and the optimal supervisor with a complexity of polynomial time is designed. The theoretic results are illustrated by an example that synthesizes a maximally permissive supervisor for a manufacturing system.

Closed-loop Live Marked Graphs under Generalized Mutual Exclusion Constraint Enforcement

Enforcing a supervisory control policy to avoid forbidden states on a discrete event system modeled by a Petri net may result in a non live system. This may happen even if the admissible states are specified by Generalized Mutual Exclusion Constraints (GMECs). This leads to the problem of synthesizing a maximally permissive control policy preserving liveness of the system under a GMEC. This problem is very interesting in practice, but difficult even for a restricted class of systems. In this paper, we focus on systems which can be modeled as live and safe Marked Graphs (MGs). On such systems, when some of the transitions are uncontrollable, a GMEC can be forced by a monitor place if a not maximally permissive policy is accepted, otherwise a more complex control has to be adopted. Anyway, liveness of the closed-loop system (plant plus control) is not guaranteed. Two sufficient conditions to verify the closed-loop liveness of a live and safe MG plant controlled by a monitor are derived. A sufficient condition for closed loop liveness of MGs where a GMEC has been enforced on is derived. In addition, a set of predicates is provided that enforces, in a maximally permissive way, a GMEC while preserving closed-loop liveness on live and safe MG systems under some restrictions.

Some New Results on Supervisory Control of Petri Nets with Decentralized Monitor Places

This paper presents two new results on the problem of determining a set of decentralized controllers for place/transition nets to enforce a global specification on the net behavior. Both the global specification and the decentralized specifications are given in terms of Generalized Mutual Exclusion Constraints (GMECs). First, an algorithm to select a decentralized specification that finds a compromise between fairness among variables and the maximal cardinality is proposed assuming that the support of each decentralized GMEC is a singleton. Then, a maximal solution in terms of permissiveness and fairness among places is proposed removing the previous assumption.

Suboptimal supervisory control of Petri nets in presence of uncontrollable transitions via monitor places

This paper deals with the problem of enforcing generalized mutual exclusion constraints (GMEC) on place/transition nets with uncontrollable transitions. An efficient control synthesis technique, which has been proposed in the literature, enforces GMEC constraints by introducing monitor places to create suitable place invariants. The method has been shown to be maximally permissive and to give a unique control structure in the case that the set of legal markings is controllable. This paper investigates on and formally shows that the class of controllers obtained by this technique may not have a supremal element for uncontrollable specifications. Moreover, it is shown that the family of monitor places enforcing an uncontrollable specification can be parameterized with respect to the solution of a linear system of equation. An algorithm to obtain such parameterization is presented here.