Class Of Discrete Event Systems Research Articles

State Estimation and Detectability of Networked Discrete Event Systems With Multi-Channel Communication Networks

In this paper, we extend existing results on detectability of Discrete Event Systems (DES) to Networked Discrete Event Systems (NDES), a class of DES whose communication between the plant and the agent (supervisor, diagnoser, prognoser, etc) is carried out through a network that can have several channels. We assume that each channel is subject to different communication delays, which may cause changes in the order of the event observations with respect to their actual occurrences in the system automaton, and also that event transmission may be lost in the communication channels causing loss of observations. We follow a previously presented approach to construct an equivalent nondeterministic untimed automaton, and, based on this model, we present a method for the state estimation of NDES. We extend existing D-detectability definitions of DES to NDES subject to delays and loss of observation, referred here to as strong networked D-detectability, weak networked D-detectability, strong periodic networked D-detectability, weak periodic networked D-detectability. Finally, necessary and sufficient conditions for the networked D-detectability notions proposed here are proposed and algorithms for their verification are developed. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —State estimation is an important problem that appear in several practical applications, e.g. industrial systems, aircraft control and business management. Of current interest is the problem of distinguishing in real time if the system is not in pairs of states, the so-called D-detectability. In practical terms, it is not necessary to actually know the current state of the system but if the system may not be in two or more conflicting states. With the use of communication networks, additional features such as communication delay must also be taken into account in the process of performing D-detectability. In this paper we consider discrete event systems, a class of systems used to model a wide class of practical engineering problems whose dynamic evolution is driven by event occurrences, that are embedded in a communication network; we will refer to these systems as networked discrete event systems. In this regard, we generalize existing notions of D-detectability, and we call them networked D-detectability. Algorithms for networked D-detectability verification and a method to perform online state estimation are given in the paper.

Control of a class of discrete event systems with disturbances and capacity constraints: Application to a disassembly problem

AbstractThis study proposes an analytical control method for the meeting of capacity constraints in discrete event systems with disturbances. More precisely, it consists of computing control laws for partially controllable and observable timed event graphs that are subject to marking constraints. To resolve the issue, linear Min‐Plus models are used to describe the behavior of these graphs, and the constraints are expressed by inequalities in Min‐Plus algebra. Sufficient conditions for the existence of causal control laws to guarantee marking specifications are established. Finally, to illustrate the efficiency of the proposed approaches in this paper, an application for a disassembly process with some disturbance inputs and limited component capacities is carried out.

Diagnosability of discrete event systems modeled by time-interval automata

We address, in this paper, the problem of diagnosability of time-interval discrete event systems (TIDES), a class of discrete event system that has a single clock structure and whose event occurrence takes place within a time interval after the previous event occurrence. The idea behind the diagnosability of TIDES is to leverage time information to distinguish faulty traces from non-faulty ones, increasing the accuracy of the fault diagnosis system. For this purpose, we use a recently proposed timed model called time-interval automaton (TIA), and, based on this model, we present necessary and sufficient conditions for diagnosability of discrete event systems modeled by TIA and an algorithm for its verification. Examples illustrate all of the results present in the paper.

Switching models and control of Petri Nets with shared resources under marking constraints

ABSTRACT Nowadays multi-option phenomena can generate potential problems related to industrial manufacturing systems. For instance, time and money loss are both expensive costs that should be paid when failing to make the right control choice decision, especially given the existence of various constraints. Therefore, the shared resource allocation between several processes can be transformed into a switching control problem that can be modeled using (Min, +) algebra. Due to the finite number of states and ergo of the application of this type of system, they are defined under the class of Discrete Event Systems. Accordingly, while taking into consideration modes of representation, this paper seeks to discuss a new modelling approach for competitive Timed Events Graphs under capacity constraints. The deduced switching models are then examined to solve the control problem issue of an industrial manufacturing process composed of cells of pick and place robots. To deduce the adequate control laws, an original solution based on the use of linear equations described by (Min, +) linear algebra is provided.

Analysis and control of max-plus linear discrete-event systems: An introduction

The objective of this paper is to provide a concise introduction to the max-plus algebra and to max-plus linear discrete-event systems. We present the basic concepts of the max-plus algebra and explain how it can be used to model a specific class of discrete-event systems with synchronization but no concurrency. Such systems are called max-plus linear discrete-event systems because they can be described by a model that is “linear” in the max-plus algebra. We discuss some key properties of the max-plus algebra and indicate how these properties can be used to analyze the behavior of max-plus linear discrete-event systems. Next, some control approaches for max-plus linear discrete-event systems, including residuation-based control and model predictive control, are presented briefly. Finally, we discuss some extensions of the max-plus algebra and of max-plus linear systems.

Diagnosability of a class of discrete event systems based on observations

The diagnosability of discrete event systems has been a topic of interest to many researchers. The diagnosability conditions for various systems have evolved based on a regularity condition that is imposed on faulty traces with respect to their observable continuations. Improving upon this weak but necessary condition, a new model of diagnosability that is based on sensor outputs, which are called observations, upon a command input is proposed in this paper. Necessary and sufficient conditions are derived for the proposed diagnosability model. The search performance of the proposed diagnosability condition is of linear complexity in terms of the power set of the system events and observations, compared to the exponential complexity of the search with the existing diagnosability regularity condition. Moreover, a system that is not diagnosable according to the existing diagnosability condition may be diagnosable in the proposed diagnosability model, which includes observations.

Optimal on-off control for a class of discrete event systems with real-time constraints

This paper studies an optimal ON-OFF control problem for a class of discrete event systems with real-time constraints. Our goal is to minimize the overall costs, including the operating cost and the wake-up cost, while still guaranteeing the deadline of each individual task. In particular, we consider the homogeneous case in which it takes the same amount of time to serve each task and each task needs to be served by d seconds upon arrival. The problem involves two subproblems: (i) finding the best time to wake up the system and (ii) finding the best time to let the system go to sleep. We study the two subproblems in both off-line and on-line settings. In the off-line case that all task information is known a priori, we combine sample path analysis and dynamic programming to come up with the optimal solution. In the on-line scenario where future task information is completely unknown, we show that the optimal time to wake up the system can be obtained without relying on future task arrivals. We also perform competitive analysis for on-line control and derive the competitive ratios for both deterministic and random controllers.

Near-Optimal Scheduling for Petri Net Models With Forbidden Markings

This paper is about control design for discrete event systems modeled with Petri nets. It addresses the problems of reachability and of firing sequence design. The untimed and timed cases are successively studied by searching control sequences from an initial marking to a reference one with length or duration that approach the minimal value, avoiding forbidden states and nonpromising branches. The proposed algorithms are applicable to a large class of discrete event systems in particular in the domain of flexible manufacturing, engineering. To accelerate the computation and make robust the control strategy, only a small area of the reachability graph is worked out and an approach inspired from model predictive control is used. The approach is suitable for deadlock-free scheduling and fault-tolerant control problems.

Dynamical Scheduling and Robust Control in Uncertain Environments with Petri Nets for DESs

This paper is about the incremental computation of control sequences for discrete event systems in uncertain environments where uncontrollable events may occur. Timed Petri nets are used for this purpose. The aim is to drive the marking of the net from an initial value to a reference one, in minimal or near-minimal time, by avoiding forbidden markings, deadlocks, and dead branches. The approach is similar to model predictive control with a finite set of control actions. At each step only a small area of the reachability graph is explored: this leads to a reasonable computational complexity. The robustness of the resulting trajectory is also evaluated according to a risk probability. A sufficient condition is provided to compute robust trajectories. The proposed results are applicable to a large class of discrete event systems, in particular in the domains of flexible manufacturing. However, they are also applicable to other domains as communication, computer science, transportation, and traffic as long as the considered systems admit Petri Nets (PNs) models. They are suitable for dynamical deadlock-free scheduling and reconfiguration problems in uncertain environments.

Design of receding-horizon estimators for the battery assembly system

Abstract The paper concerns the state estimation problem of a class of discrete-event systems. It is solved by defining a receding-horizon objective function that depends both on the prediction and output error. The system and its variables are described within the (max,+) algebra, which makes it possible to incorporate robustness within the overall framework. The paper also shows how to transform the interval cost function into the scalar one, and hence, making the computational procedure trackable within the quadratic programming framework. As a result, the proposed approach provided interval estimates of the system state, which can be used for both fault diagnosis and control purposes. An exemplary system is the battery assembly one, which is being designed and implemented in RAFI GmbH Company (one of the leading electronic manufacturing service providers in Germany). The final part of the paper shows illustrative examples, which exhibit the the performance of the proposed approach.

Object Oriented Design of Software Tool for Finite Abstractions of Max-Plus-Linear Systems using Unified Modeling Language

Max-Plus-Linear (MPL) systems are a class of discrete-event systems with a continuous state space characterizing the timing of the underlying sequential discrete events. There is a formal approach to analyze these systems based on finite abstractions. The abstraction algorithms have been in MATLAB using list data structure and in JAVA using tree data structure. The MATLAB implementation requires long computational time, whereas the JAVA one requires larger memory allocation. In this work, we discuss an object oriented design in C++ using tree data structure without recursive functions in the hope of improving the results obtained by the two previous implementations.

Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller

This paper presents that the structural controllability and observability can be used for a class of discrete event systems modeled by industry-standard N-squared diagrams. The main results of this paper provide analytical assessment of large scale industrial system properties before the software simulation and hardware demonstration; therefore it offers immense savings in verification time and cost. The dynamics of N-squared diagrams are represented by linear time-invariant systems over the Boolean algebra. Structural controllability and structural observability of discrete event systems are transformed to “standard” controllability and observability problems in traditional linear systems over real numbers. The rank of the controllability and observability matrices determine not only the structural controllability and observability, but also which discrete nodes cannot be reached by the initial states and which discrete states have no outgoing paths to the output nodes, respectively. This rank condition is extremely easy to be verified through computer software, such as MATLAB, it can be used in large scale industrial systems or communication networks.

Reduction and Analysis of a Max-Plus Linear System to a Constraint Satisfaction Problem for Mixed Integer Programming

This research develops a solution method for project scheduling represented by a max-plus-linear (MPL) form. Max-plus-linear representation is an approach to model and analyze a class of discrete-event systems, in which the behavior of a target system is represented by linear equations in max-plus algebra. Several types of MPL equations can be reduced to a constraint satisfaction problem (CSP) for mixed integer programming. The resulting formulation is flexible and easy-to-use for project scheduling; for example, we can obtain the earliest output times, latest task-starting times, and latest input times using an MPL form. We also develop a key method for identifying critical tasks under the framework of CSP. The developed methods are validated through a numerical example.

Conflict-free trajectory planning based on the model predictive control theory

Model Predictive Control (MPC) is a model-based control method based on a receding horizon approach and online optimization. A key advantage of MPC is that it can accommodate constraints on the inputs and outputs. This paper proposes a max-plus general modeling framework adapted to the robust optimal control of air traffic flow in the airspace. It is shown that the problem can be posed as the control of queues with safety separation-dependent service rate. We extend MPC to a class of discrete-event system that can be described by models that are linear in the max-plus algebra with noise or modeling errors. Regarding the single aircraft as a batch, the relationships between input variables, state variables and output variable are established. We discuss some key properties of the system model and indicate how these properties can be used to analyze the behavior of air traffic flow. The model predictive control design problems are defined for this type of discrete event system to help prepare the airspace for various robust regulation needs and we give some extensions of the air traffic max-plus linear systems.

Deadlock-free scheduling for flexible manufacturing systems using untimed Petri nets and model predictive control

This paper proposes algorithms that incrementally compute control sequences that drive the marking of untimed Petri nets from an initial value to a reference one, avoiding forbidden states with a length or duration that approaches the minimal value. The proposed algorithms are applicable to a large class of discrete event systems with or without temporal specifications in particular in the domain of flexible manufacturing, communication and computer science or transportation and traffic. To overcome the most burdensome part of the computations, the sequences encoded in a small area of the reachability graph are worked out. The main contribution is to propose an estimation of the minimal length or duration of the remaining sequences to the reference based on the computation of the firing count vectors. The approach is suitable for deadlock-free scheduling problems encountered with flexible manufacturing systems.

VeriSiMPL 2: An open-source software for the verification of max-plus-linear systems

This work presents a technique to generate finite abstractions of autonomous Max-Plus-Linear (MPL) systems, a class of discrete-event systems employed to characterize the dynamics of the timing related to the synchronization of successive events. Abstractions of MPL systems are derived as finite-state transition systems. A transition system is obtained first by partitioning the state space of the MPL system into finitely many regions and then by associating a unique state of the transition system to each partitioning region. Relations among the states of the transition system are then set up based on the underlying dynamical transitions between the corresponding partitioning regions of the MPL state space. In order to establish formal equivalences, the obtained finite abstractions are proven either to simulate or to bisimulate the original MPL system. The approach enables the study of general properties of the original MPL system formalized as logical specifications, by verifying them over the finite abstraction via model checking. The article presents a new, extended and improved implementation of a software tool (available online) for the discussed formal abstraction of MPL systems, and is tested on a numerical benchmark against a previous version.

Feedback control for a class of discrete event systems with critical time

This paper presents an algebraic approach for control laws synthesis of timed event graphs subjected to strict temporal constraints. This class of discrete event systems is deterministic, in the sense that its behaviour only depends on the initial marking and on the control that is applied. This behaviour can be modelled by a linear equations system in Min-Plus algebra. The temporal constraint is represented by an inequality that is also linear in the Min-Plus algebra. Then, a method for the synthesis of control laws ensuring the respect of constraints is described. We give explicit formulas characterising a control law, which ensures the validity of the temporal constraints. It is a causal feedback control, involving delays. The method is illustrated on an example.

Supervisory Control for a Class of Discrete Event Systems for Optimal Throughput

In this paper, we study the problem of supervisor synthesis for a class of discrete event systems for optimal throughput based on the timed discrete event modelling formalism. First, a language-based definition for the concept of throughput is presented. Then, we formulate the supervisor synthesis problem with both logic correctness and time-related optimal performance objective, namely throughput. After we show the existence of supremal controllable sublanguage with maximum throughput and minimum transient makespan, an algorithm is provided to compute such a supervisor.

Finite Abstractions of Max-Plus-Linear Systems

This work puts forward a novel technique to generate finite abstractions of autonomous and nonautonomous Max-Plus-Linear (MPL) models, a class of discrete-event systems used to characterize the dynamics of the timing related to successive events that synchronize autonomously. Nonautonomous versions of MPL models embed within their dynamics nondeterminism, namely a signal choice that is usually regarded as an exogenous control or schedule. In this paper, abstractions of MPL models are characterized as finite-state Labeled Transition Systems (LTS). LTS are obtained first by partitioning the state space (and, for the nonautonomous model, by covering the input space) of the MPL model and by associating states of the LTS to the introduced partitions, then by defining relations among the states of the LTS based on dynamical transitions between the corresponding partitions of the MPL state space, and finally by labeling the LTS edges according to the one-step timing properties of the events of the original MPL model. In order to establish formal equivalences, the finite abstractions are proven to either simulate or to bisimulate the original MPL model. This approach enables the study of general properties of the original MPL model by verifying (via model checking) equivalent logical specifications over the finite LTS abstraction. The computational aspects related to the abstraction procedure are thoroughly discussed and its performance is tested on a numerical benchmark.

Mathematical programming time-based decomposition algorithm for discrete event simulation

Mathematical programming has been proposed in the literature as an alternative technique to simulating a special class of Discrete Event Systems. There are several benefits to using mathematical programs for simulation, such as the possibility of performing sensitivity analysis and the ease of better integrating the simulation and optimisation. However, applications are limited by the usually long computational times. This paper proposes a time-based decomposition algorithm that splits the mathematical programming model into a number of submodels that can be solved sequentially to make the mathematical programming approach viable for long running simulations. The number of required submodels is the solution of an optimisation problem that minimises the expected time for solving all of the submodels. In this way, the solution time becomes a linear function of the number of simulated entities.