Supervisors For Discrete Event Systems Research Articles

On the Existence of Non-blocking Bounded Supervisors for Discrete Event Systems

On the Existence of Non-blocking Bounded Supervisors for Discrete Event Systems

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.

PLC-based implementation of supervisory control for flexible manufacturing systems using theory of regions

The supervisory control is a common theory for the synthesis of Petri net (PN) supervisors for discrete event systems given a PN model and a control specification for the maximum permissive behaviour. The theory of regions as one of control synthesis method generates a PN controller to satisfy the control specification. Though the theory of regions has for over a decade received a considerable attention in academy, still very few applications exist. The real cause of this seems to be a contradiction between the abstract controller and its physical implementation. This is evident in particular when the implementation is supposed to be based on a programmable logic controller (PLC), as is the case for flexible manufacturing systems. Indeed, since the synchronous PLC is based on signals, the PN supervisor remains asynchronous; this explains its implementation difficulty. In this work, a control synthesis method using the theory of regions is implemented with a Java application on PLCs of a flexible manufacturing system (FMS) installed in our research laboratory in the University of Lorraine in Metz, France.

Compositional synthesis of supervisors in the form of state machines and state maps

This paper investigates the compositional abstraction-based synthesis of least restrictive, controllable, and nonblocking supervisors for discrete event systems that are given as a large number of finite-state machines. It compares a previous algorithm that synthesises modular supervisors in the form of state machines, with an alternative that records state maps after each abstraction step and uses these to control the system. The state map-based algorithm supports all abstraction methods used previously, and in addition allows for nondeterminism, hiding, and transition removal. It has been implemented in the software tool Supremica and applied to several large industrial models. The experimental results and the complexity analysis show that state maps can be computed efficiently and in many cases require less memory than state machine-based supervisors.

Reinforcement Learning of Optimal Supervisor for Discrete Event Systems with Different Preferences

In this paper, we propose an optimal supervisory control method for discrete event systems (DESs) that have different preferences. In our previous work, we proposed an optimal supervisory control method based on reinforcement learning. In this paper, we extend it and consider a system that consists of several local systems. This system is modeled by a decentralized DES (DDES) that consists of local DESs, and is supervised by a central supervisor. In addition, we consider that the supervisor and each local DES have their own preferences. Each preference is represented by a preference function. We introduce the new value function based on the preference functions. Then, we propose the learning method of the optimal supervisor based on reinforcement learning for the DDESs. The supervisor learns how to assign the control pattern so as to maximize the value function for the DDES. The proposed method shows the general framework of optimal supervisory control for the DDES that consists of several local systems with different preferences. We show the efficiency of the proposed method through a computer simulation.

Local Modular Control with Distinguishers applied to a Manufacturing System

Local Modular Control (LMC) is a decentralized method to synthesize supervisors for Discrete Event Systems (DES) and distinguishers define a design-oriented concept that allows to simplify specifications modeling. When associated with approximations, distinguishers can also reduce synthesis effort. In this paper, we show how to combine advantages from LMC, distinguishers and approximations, to solve DES control problems. The approach preserves controllability, nonblocking and least restrictiveness of supervisors, while providing important computational gains. Our contributions are applied to the control of a manufacturing system with material feedback.

A framework for synthesis of communicating decentralised supervisors for discrete-event systems

We propose a framework to study communication among decentralised supervisors for a (distributed) discrete-event system (DES), where system specifications lack co-observability. Using agent-wise labeling maps (ALMs), the framework explores the observation and control structures of an already designed centralised supervisor in a distributed manner, and represent them as polynomial equations over a finite field. Communication is naturally required to re-evaluate the equations, which depend on distributed information, correctly, and is formalised and implemented using communication events. The framework generalises the authors’ previous work on extended finite-state machines (EFSMs) by formalising system representation and communication events, proving the correctness of proposed communication policies, and algorithmic simplification of polynomial equations. This provides a systematic procedure for the synthesis of decentralised supervisors and formalisation, computation and implementation of the communication.

Supervision in Synthesis of Agents Cooperation

The discrete-event systems (DES) modularity and supervision are utilized at synthesis of the agents cooperation. The agents are understood to be (DES) modules. They are described by place/transition Petri-nets (P/T PN)[5]. A desired strategy of the agents behaviour during the cooperation is expressed by conditions for synthesizing the DES supervisor. Then the strategy is forced on agents. Such a procedure can be utilized step-by-step also at the synthesis of more complex structures of co-operating modules (groups of agents) in order to achieve a prescribed behaviour of the global structure. The approach is illustrated by examples.

Modeling and Synthesis of Event-Transferring Communicating Decentralized Supervisors for Discrete-Event Systems

This work models and synthesizes communicating decentralized supervisors for Discrete-Event System (DES) which communicate the information about observed events. This is done within the authors' framework of Distributed Supervised DESs (DSDESs), using agent-wise labeling maps to reveal the informational dependencies among the supervisors. Communication between every two supervisors is modeled by the maps from the sender's observable events to its set of recently observed event, or an empty set. Thereby, the synthesis of communicating decentralized supervisors is reduced to the design of these maps.

Multi-agent methodology for distributed and cooperative supervisory estimation subject to unreliable information

In this work, a novel multi-agent framework for cooperative supervisory estimation of linear time-invariant systems is proposed. This framework is developed based on the notion of subobservers and a discrete-event system (DES) supervisory control and is applicable to large-scale systems. We introduce a group of subobservers where each subobserver is estimating certain states that are conditioned on a given input, output and state information. The cooperation among the subobservers is managed by a DES supervisor. The supervisor makes decisions regarding the selection and configuration of a set of subobservers to successfully estimate all the system states, while the feasibility of the overall integrated cooperative subobservers is verified. When certain anomalies (faults) are present in the system, or the sensors and subobservers become unreliable, the supervisor reconfigures the set of selected subobservers so that the impacts of anomalies on the estimation performance are minimised to the extent that is possible. The application and capabilities of our proposed methodology in a practical industrial process is demonstrated through numerical simulations.

Modular Synthesis of Maximally Permissive Opacity-Enforcing Supervisors for Discrete Event Systems

In this paper, we study opacity-enforcing supervisory control of discrete event systems. We consider the case that the secrete behavior of the system is specified by multiple secret languages, and synthesize a maximally permissive supervisor that enforces opacity for all secret languages. We prove that, under a certain assumption on observable and uncontrollable events, a maximally permissive opacity-enforcing supervisor can be synthesized in a modular fashion.

Synthesis of Over-Approximating Inference-Based Decentralized Supervisors for Discrete Event Systems

In our past work, we presented a framework for the decentralized control of discrete event systems involving inferencing over ambiguities about the system state of various local decision-makers, and introduced the notion of N-inference-observability as an existence condition of a certain decentralized supervisor. When a given specification fails to satisfy the N-inference-observability property, a supervisor achieving the given specification does not exist, and a technique for synthesizing a decentralized supervisor that achieves an N-inference-observable superlanguage is presented here (a dual problem of computing an N-inference-observable sublanguage was studied in our past work).

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.

Efficient robust supervisors for discrete event systems

This paper is a sequel to a previous publication by the same authors, in which an efficient modular solution to a robust supervisory control problem for discrete event systems modeled by finite automata with prefix-closed specification languages has been presented. This solution is based on a general recursive robust control scheme, which has been successfully applied to a number of problems. The additional contributions of the present paper are: (a) a slight generalization of the problem assumptions; (b) an alternative derivation of some of the results and an alternative formulation of the controller; (c) a detailed description of a very efficient on-line implementation algorithm; and (d) an illustrative practical example.

An implementation methodology for supervisory control theory

In this study, a methodology for PLC implementation of Supervisory Control Theory is introduced and realized on a pneumatic manufacturing system. The implementation methodology resolves the problem of avalanche effect and enhances program readability. We use local modular approach, which exploits modular structure of the plant and of the specifications. Local modular approach, together with the implementation methodology presented in this study provides an effective way for synthesizing and realizing supervisors for Discrete Event Systems (DES) control problems. The resulting PLC program is also modular in structure, making it handable for modification and error detection.

Compositional Synthesis of Maximally Permissive Supervisors Using Supervision Equivalence

This paper presents a general framework for efficient synthesis of supervisors for discrete event systems. The approach is based on compositional minimisation, using concepts of process equivalence. In this context, a large number of ways are suggested how a finite-state automaton can be simplified such that the results of supervisor synthesis are preserved. The proposed approach yields a compact representation of a least restrictive supervisor that ensures controllability and nonblocking. The method is demonstrated on a simple manufacturing example to significantly reduce the number of states constructed for supervisor synthesis.

Maximally permissive mutually and globally nonblocking supervisors for discrete event systems

A supervisor is said to be mutually nonblocking with respect to a pair of specifications if upon completing a task in any of the specifications, it can continue on to complete the task in the other specification, i.e., the two specifications do not block each other. The notion of mutually nonblocking supervisor was introduced by Fabian and Kumar (2000). In this paper we present an algorithm of polynomial complexity for computing a maximally permissive mutually and globally nonblocking supervisor. The algorithm is based on a notion of attractability, and as a special case offers a new way of computing the maximally permissive nonblocking supervisors.

Synthesis and PLC Implementation of Supervisory Control via Place Invariants for a Manufacturing Cell

Based on the concept of place invariants of Petri Nets, supervisors for discrete-event systems can be synthesized so as to have a set of operation constraints respected by the controlled system. The implementation of this technique in a manufacturing cell is presented, with detailed description of modeling, supervisor design and programming, in STL language, of the PLC which controls the cell. Important issues such as: supervisor permissiveness, comparative analysis with techniques based on automata, as well as the systematization of the procedure for application to other systems are also discussed.

Exploiting symmetry in the synthesis of supervisors for discrete event systems

We investigate a method to exploit the symmetry inherent to many discrete-event systems in order to reduce the computational complexity of the supervisory control problem (SCP). We characterize symmetry using notions of group theory and derive conditions under which there exists a quotient (reduced) automaton representation for a language with, in general, a much smaller state space than the original minimal (in number of states) automaton representation for the language. We then propose an algorithm to synthesize a solution to the SCP which is similar to the classical one, but performed on reduced automata. Special attention is given to the particular case of systems whose models contain similar components. The approach is illustrated by an example of control of a small production line.

Synthesis of Supervisors Using Learning Algorithm of RegularLanguages

We propose an algorithm for the synthesis of supervisors in discrete event systems. The algorithm is based on a learning algorithm of regular languages proposed by Angluin, and constructs a supervisor realizing an unknown specification which is identified through the interaction between the designer and the algorithm. We also consider the synthesis problem for systems consisting of several processes which behave concurrently. One of serious problems in dealing with such a concurrent system is that the number of states required for describing the global behavior often grows exponentially in the size of the model. To improve this situation, we introduce the concept of dependency defined on the set of events. It prevents the algorithm from considering all interleavings of independent occurrences of events.