Forbidden State Problem Research Articles

Design of Controllers Considering the Number of Control Places for Forbidden State Problem of Petri Nets

Design of Controllers Considering the Number of Control Places for Forbidden State Problem of Petri Nets

Optimal Petri net supervisor synthesis for forbidden state problems using marking mask

This article addresses the forbidden state problem in discrete-event systems (DESs) modeled with Petri nets. Given a control specification, we first decide the sets of forbidden and admissible markings. Then, the minimal mask set of first-met forbidden markings (FFMs) and the minimal root set of admissible markings are computed by marking mask that is implemented using a class of special places in a plant, called competitive places. Marking mask can effectively filtrate the markings to be processed such that the two obtained sets are in general much smaller than the sets of originally specified forbidden and admissible markings, respectively. Monitors computed by place invariants are used to forbid the forbidden markings. It is shown that a maximally permissive (optimal) supervisor can be computed if it exists. Integer linear programming is used to optimize the structure of a supervisor. The minimal mask set of FFMs and root set of admissible markings efficiently reduce the computational overhead because of much fewer constraints and variables in the formulated programming problem. The developed methodology is illustrated by parameterized examples.

Supervisory control of a class of Petri nets with unobservable and uncontrollable transitions

This paper uses Petri nets (PNs) as a modeling tool to deal with the forbidden state problem of discrete event systems (DESs) in the presence of both unobservable and uncontrollable events. First of all, it is proved that two state specifications are equivalent if their admissible marking sets coincide. Motivated by this result, we focus on studying how to compute optimal policies with respect to a state specification that is an admissible linear constraint. Thanks to many approaches in the literature that allow one to efficiently transform an arbitrary linear constraint into an admissible one with the admissible marking set unchanged, the proposed result remains useful in the more general case of arbitrary linear constraints. Specifically, focusing on ordinary PNs subject to an admissible linear constraint, we propose an optimal control policy whose computation mainly lies in the computation of the unobservable minimal decrease, a parameter depending on the current observation and the given constraint. A procedure to compute such a parameter with polynomial complexity is proposed provided that a particular subnet, called observation subnet, is acyclic and backward-conflict and backward-concurrent free (BBF). As a result, under such assumptions, the optimal control policy could be computed with polynomial complexity.

Theory of Regions for Control Synthesis without Computing Reachability Graph

This paper addresses the design of Petri net (PN) supervisor using the theory of regions for forbidden state problem with a set of general mutual exclusion constraints. In fact, as any method of supervisory control based on reachability graph, the theory of regions suffers from a technical obstacle in control synthesis, which is the necessity of computing the graph at each iteration step. Moreover, based on the reachability graph, which may contain a large number of states, with respect to the structural size of the system, the computation of PN controllers becomes harder and even impossible. The main contribution of this paper, compared to previous works, is the development of a control synthesis method in order to decrease significantly the computation cost of the PN supervisor. Thus, based on PN properties and mathematical concepts, the proposed methodology provides an optimal PN supervisor for bounded Petri nets following the interpretation of the theory of regions. Finally, case studies are solved by CPLEX software to compare our new control policy with previous works which use the theory of regions for control synthesis.

Computation of an Optimal Transformed Linear Constraint in a Class of Petri Nets With Uncontrollable Transitions

Deciding how to prevent discrete event systems (DESs) from reaching forbidden states is an important problem in the field of DES supervisory control. For DESs with uncontrollable events, linear constraint transformation becomes a popular technique for solving the forbidden state problem when Petri nets are used as a modeling tool and control specifications are given in the form of linear constraints. This paper proposes a novel linear constraint transformation approach that is applicable to PT-ordinary Petri nets with uncontrollable subnets being forward-concurrent-free. For such nets, a linear constraint can be transformed into an optimal transformed one (i.e., a linear constraint that exactly characterizes the admissible marking set) by using the proposed approach, which is computationally shown to be of polynomial complexity with respect to the net size. An example is presented to illustrate the developed technique.

Solving the Problem of Forbidden States in Discrete Event Systems: A Novel Systematic Method for Reducing the Number of Control Places

AbstractThis paper deals with the problem of forbidden states in Discrete Event Systems modelled by non‐safe Petri Nets. To avoid these states, some Generalized Mutual Exclusion Constraints can be assigned to them. These constraints limit the weight sum of tokens in some places and can be enforced on the system using control places. When the number of these constraints is large, a large number of control places should be added to the system. In this paper, a method is presented to assign the small number of constraints to forbidden states using some states which cover the forbidden states. So, a small number of control places are added to the system leading to obtaining a maximally permissive controller.

Safety analysis of discrete event systems using a simplified Petri net controller

This paper deals with the problem of forbidden states in discrete event systems based on Petri net models. So, a method is presented to prevent the system from entering these states by constructing a small number of generalized mutual exclusion constraints. This goal is achieved by solving three types of Integer Linear Programming problems. The problems are designed to verify the constraints that some of them are related to verifying authorized states and the others are related to avoiding forbidden states. The obtained constraints can be enforced on the system using a small number of control places. Moreover, the number of arcs related to these places is small, and the controller after connecting them is maximally permissive.

Supervisor synthesis for discrete event systems under partial observation and arbitrary forbidden state specifications

In this paper, we consider the forbidden state problem in discrete event systems modeled by partially observed and partially controlled Petri nets. Assuming that the reverse net of the uncontrollable subnet of the Petri net is structurally bounded, we compute a set of weakly forbidden markings from which forbidden markings can be reached by firing a sequence of uncontrollable/unobservable transitions. We then use reduced consistent markings to represent the set of consistent markings for Petri nets with structurally bounded unobservable subnets. We determine the control policy by checking if the firing of a certain controllable transition will lead to a subsequent reduced consistent marking that belongs to the set of weakly forbidden markings; if so, we disable the corresponding controllable transition. This approach is shown to be minimally restrictive in the sense that it only disables behavior that can potentially lead to a forbidden marking. The setting in this paper generalizes previous work by studying supervisory control for partially observed and partially controlled Petri nets with a general labeling function and a finite number of arbitrary forbidden states. In contrast, most previous work focuses on either labeling functions that assign a unique label to each observable transition or forbidden states that are represented using linear inequalities. More importantly, we demonstrate that, in general, the separation between observation and control (as considered in previous work) may not hold in our setting.

Controller Synthesis with Highly Simplified Linear Constraints

AbstractThis paper deals with the problem of forbidden states in safe Petri nets to obtain a maximally permissive controller. To prevent the system from entering the forbidden states, assigning some constraints to them is possible. The constraints can be enforced on the system using control places. When the number of forbidden states is large, a large number of constraints should be assigned to them. This results in a large number of control places being added to the model of the system, which causes a complicated model. Some methods have been proposed to reduce the number of constraints. Nevertheless, they do not always give the best results. In this paper, two ideas are offered to reduce the number of constraints, giving a more simplified controller.

On Almost-Sure Properties of Probabilistic Discrete Event Systems

Although randomization often increases the degree of flexibility in system design, analyzing system properties in the probabilistic framework introduces additional difficulties and challenges in comparison with their nonprobabilistic counterparts. In this paper, we focus on probabilistic versions of two problems frequently encountered in discrete event systems, namely, the reachability and forbidden-state problems. Our main concern is to see whether there exists a (or for every) non-blocking or fair control policy under which a given finite- or infinite-state system can be guided to reach (or avoid) a set of goal states with probability one. For finite-state systems, we devise algorithmic approaches which result in polynomial time solutions to the two problems. For infinite-state systems modelled as Petri nets, the problems are undecidable in general. For the class of persistent Petri nets, we establish a valuation approach through which the convergence behavior of a system is characterized, which in turn yields solutions to the reachability and forbidden-state problems.

Structural optimal control for safe Petri nets

This article addresses the problem of forbidden states in both conservative and non-conservative safe Petri net (PN) models. The property of conservativeness is discussed, and its implications are analysed. The construction and formulation of control conditions in the context of safe and non-conservative PN models is investigated, emphasising the problem of control optimality. The fundamental issue studied is that of the equivalence between a forbidden state and its associated constraint. A new fashion of writing control conditions is proposed and used, in conjunction with the place-invariant synthesis method, for the generation of a control solution. The final controlled model obtained is a PN similar in size to the initial model. Finally, the approach is illustrated via a simple example.

On Almost-Sure Properties of Probabilistic Discrete Event Systems

Although randomization often increases the degree of flexibility in system design, analyzing system properties in the probabilistic framework introduces additional difficulties and challenges in comparison with their nonprobabilistic counterparts. In this paper, we focus on probabilistic versions of two problems frequently encountered in discrete event systems, namely, the reachability and forbidden-state problems. Our main concern is to see whether there exists a non-blocking or fair control policy under which a given finite- or infinite-state system can be guided to reach (or avoid) a set of goal states with probability one. For finite-state systems, we devise algorithmic approaches which result in polynomial time solutions to the two problems. For infinite-state systems modelled as Petri nets, the problems are undecidable in general. For the class of persistent Petri nets, we establish a valuation approach through which the convergence behavior of a system is characterized, which in turn yields solutions to the reachability and forbidden-state problems.

Supervisory Control of partially observable Marked Graph based on Marking Exclusion Constraint

This paper presents a control synthesis approach for discrete event systems modelled by partially observable marked graphs. It solves the forbidden state problem for discrete event systems modelled by partially observable event graphs subject to Marking Exclusion Constraints (MEC). Two kind of MEC specifications are considered: MEC-AND or MEC-OR. The main advantage of MEC specifications is an increased modelling power regarding to General Mutual Exclusion Constraints GMEC. We provide a simple optimal controller to enforce MEC specifications with independent critical places. We also propose a suboptimal controller for MEC-OR with dependent critical places belonging to the same direct path.

FUZZY AUTOMATION CONTROLLER FOR FLEXIBLE MANUFACTURING SYSTEMS

The behavior mapping of systems has undergone rapid change with advances in technology. The representation has become digital with state description of the behavior. This manifestation is called Discrete Event Systems (DES), exhibiting properties such as non – determinism, conflict and parallelism[1]-[3]. Supervisory Control Theory (SCT)[8],[9] is chosen as a modeling paradigm and Programmable Logic Controllers (PLC) [10] – [12] as an implementation tool for DES. This work investigates the use of Fuzzy Petri nets in supervisory control and suggests a modified and improved version called Fuzzy Automation Petri net (FAPN) as a modeling tool. It presents a systematic approach to the synthesis of Fuzzy Petri net based supervisor for the forbidden state problem using supervisory design procedure. The controlled model of the system can be constructed from this FAPN net structure. The implementation is using Flexible Manufacturing System (FMS) as an example of DES. The results can be interpreted and applied to high level manufacturing systems, where the role of the supervisor is to coordinate the control of multiple machines or to low level manufacturing systems, where the control function is to switch ON/OFF with respect to the dynamics between different valves.

Modular specification of forbidden states for supervisory control

A method for solving the forbidden state problem in the Supervisory Control Theory framework is presented. In many real-world applications both the plant and specification is given as a set of interacting automata or processes. In this work, we enable specification of forbidden states within such a modular structure. The aim with the method is to make each forbidden modular state combination uncontrollable. It is then possible to use efficient modular synthesis algorithms for calculation of a modular supervisor where the forbidden states are removed.

Combined Supervisor Synthesis for a Class of Forbidden State Problems in Petri Nets

Combined Supervisor Synthesis for a Class of Forbidden State Problems in Petri Nets

Controller synthesis with very simplified linear constraints in PN model

this paper addresses the problem of forbidden states for safe Petri Nets modeling discrete event systems. We present an efficient method to construct a controller. A set of linear constraints allow forbidding the reachability of specific states. The number of these so-called forbidden states and consequently the number of constraints are large and lead to a large number of control places. A systematic method for constructing very simplified controller is offered. By using a method based on Petri nets partial invariants, maximal permissive controllers are determined.

Feedback control logic synthesis for non safe Petri nets

This paper addresses the problem of forbidden states of non safe Petri Net (PN) modelling discrete events systems. To prevent the forbidden states, it is possible to use conditions or predicates associated with transitions. Generally, there are many forbidden states, thus many complex conditions are associated with the transitions. A new idea for computing predicates in non safe Petri nets will be presented. Using this method, we can construct a maximally permissive controller if it exists.

DECIDABILITY AND COMPLEXITY ANALYSIS OF FORBIDDEN STATE PROBLEMS FOR DISCRETE EVENT SYSTEMS

The conventional forbidden state problem for discrete event systems is concerned with the issue of synthesizing a maximally permissive control policy to prevent a discrete event system from reaching any forbidden state during the course of its computation. In this paper, we regard the forbidden state problem as a decision problem, and investigate the decidability/complexity issue of the problem under two new types of control policies, namely, non-blocking and fair policies, for finite state systems and Petri nets.

Control synthesis approach for DES modelled by Petri Nets

This paper presents a control synthesis approach for discrete event systems modelled by ordinary Petri Nets (PN) to solve a forbidden state problem. The PN herein considered are transitions controllable and contain measurable and non measurable transitions. The proposed PN controller is synthesised using the influence paths of the forbidden transitions. The latter are deduced from the PN reachability graph. The designed PN controller is maximally permissive because it prevents the occurrence of forbidden markings and guarantees exactly the desired behaviours. The proposed approach is illustrated by an example.