Diagnosability of fuzzy discrete event systems

In this paper, discrete event systems (DESs) are reformulated as fuzzy discrete event systems (FDESs) and fuzzy discrete event dynamical systems (FDEDSs). These frameworks include fuzzy states, events and IF-THEN rules. In these frameworks, all events occur at the same time with different membership degrees. Fuzzy states and events have been introduced to describe uncertainties that occur often in practical problems, such as fault diagnosis applications. To measure a diagnoser’s fault discrimination ability, a fuzzy diagnosability degree is proposed. If the diagnosability of the degree of the system yields one a diagnoser can be implemented to identify all possible fault types related to a system. For any degree less than one, researchers should not devote their time to distinguish all possible fault types correctly. Thus, two different diagnosability definitions FDEDS and FDES are introduced. Due to the specialized fuzzy rule-base embedded in the FDEDS, it is capable of representing a class of non-linear dynamic system. Computationally speaking, the framework of diagnosability of the FDEDS is structurally similar to the framework of diagnosability of a non-linear system. The crisp DES diagnosability has been turned into the term fuzzy diagnosability for the FDES. The newly proposed diagnosability definition allows us to define a degree of diagnosability in a class of non-linear systems. In addition, a simple fuzzy diagnosability checking method is introduced and some numerical examples are provided to illustrate this theoretical development. Finally, the potential applications of the proposed method are discussed.     

State estimation and detectability of probabilistic discrete event systems

A probabilistic discrete event system (PDES) is a nondeterministic discrete event system where the probabilities of nondeterministic transitions are specified. State estimation problems of PDES are more difficult than those of non-probabilistic discrete event systems. In our previous papers, we investigated state estimation problems for non-probabilistic discrete event systems. We defined four types of detectabilities and derived necessary and sufficient conditions for checking these detectabilities. In this paper, we extend our study to state estimation problems for PDES by considering the probabilities. The first step in our approach is to convert a given PDES into a nondeterministic discrete event system and find sufficient conditions for checking probabilistic detectabilities. Next, to find necessary and sufficient conditions for checking probabilistic detectabilities, we investigate the “convergence” of event sequences in PDES. An event sequence is convergent if along this sequence, it is more and more certain that the system is in a particular state. We derive conditions for convergence and hence for detectabilities. We focus on systems with complete event observation and no state observation. For better presentation, the theoretical development is illustrated by a simplified example of nephritis diagnosis.     

Detectability in stochastic discrete event systems

A discrete event system possesses the property of detectability if it allows an observer to perfectly estimate the current state of the system after a finite number of observed symbols, i.e., detectability captures the ability of an observer to eventually perfectly estimate the system state. In this paper we analyze detectability in stochastic discrete event systems (SDES) that can be modeled as probabilistic finite automata. More specifically, we define the notion of A-detectability, which characterizes our ability to estimate the current state of a given SDES with increasing certainty as we observe more output symbols. The notion of A-detectability is differentiated from previous notions for detectability in SDES because it takes into account the probability of problematic observation sequences (that do not allow us to perfectly deduce the system state), whereas previous notions for detectability in SDES considered each observation sequence that can be generated by the underlying system. We discuss observer-based techniques that can be used to verify A-detectability, and provide associated necessary and sufficient conditions. We also prove that A-detectability is a PSPACE-hard problem.     

Diagnosability of discrete event systems and its applications

As man-made systems become more and more complex, diagnostics of component failures is no longer an easy task that can be performed based on experience and intuition. Therefore, it is important to develop a systematic approach to diagnostic problems. Diagnostics can be done either on-line or off-line. By on-line diagnostics, we mean diagnostics performed while the system to be diagnosed is in normal operation. On the other hand, in off-line diagnostics, the system is not in normal operation. We will study both on-line and off-line diagnostics in this paper and identify main features and differences of these two types of diagnostics. We will also introduce the concept of diagnosability and study its properties, all in the framework of discrete event systems. This study is motivated by diagnostic problems in the automotive industry and we will emphasize its applications.     

Lagrange stability and boundedness of discrete event systems

Recently it has been shown that the conventional notions of stability in the sense of Lyapunov and asymptotic stability can be used to characterize the stability properties of a class of logical discrete event systems (DES). Moreover, it has been shown that stability analysis via the choice of appropriate Lyapunov functions can be used for DES and can be applied to several DES applications including manufacturing systems and computer networks (Passino et al. 1994, Burgess and Passino 1994). In this paper we extend the conventional notions and analysis of uniform boundedness, uniform ultimate boundedness, practical stability, finite time stability, and Lagrange stability so that they apply to the class of logical DES that can be defined on a metric space. Within this stability-theoretic framework we show that the standard Petri net-theoretic notions of boundedness are special cases of Lagrange stability and uniform boundedness. In addition we show that the Petri ent-theoretic approach to boundedness analysis is actually a Lyapunov approach in that the net-theoretic analysis actually produces an appropriate Lyapunov function. Moreover, via the Lyapunov approach we provide a sufficient condition for the uniform ultimate boundedness of General Petri nets. To illustrate the Petri net results, we study the boundedness properties of a rate synchronization network for manufacturing systems. In addition, we provide a detailed analysis of the Lagrange stability of a single-machine manufacturing system that uses a priority-based part servicing policy.     

Opacity generalised to transition systems

Recently, opacity has proved a promising technique for describing security properties. Much of the work has been couched in terms of Petri nets. Here, we extend the notion of opacity to the model of labelled transition systems and generalise opacity in order to better represent concepts from the literature on information flow. In particular, we establish links between opacity and the information flow concepts of anonymity and non-inference. We also investigate ways of verifying opacity when working with Petri nets. Our work is illustrated by two examples, one describing anonymity in a commercial context, and the other modelling requirements upon a simple voting system.     

Abstraction-based verification of codiagnosability for discrete event systems

In this paper, we investigate the verification of codiagnosability for discrete event systems (DES). That is, it is desired to ascertain if the occurrence of system faults can be detected based on the information of multiple local sites that partially observe the overall DES. As an improvement of existing codiagnosability tests that resort to the original DES with a potentially computationally infeasible state space, we propose a method that employs an abstracted system model on a smaller state space for the codiagnosability verification. Furthermore, we show that this abstraction can be computed without explicitly evaluating the state space of the original model in the practical case where the DES is composed of multiple subsystems.     

State observability and condition observability for a class of interacting discrete event systems

This paper introduces the concepts of state observability and condition observability for condition systems, a class of systems composed of discrete state components which interact via discrete binary signals called conditions. Given a set of externally observed conditions, state observability implies that the state of the system can be determined from the observations, and condition observability implies that all unobserved input and output conditions of the system can be determined from the observations. In this paper, we present a class of systems which is state observable and condition observable. We present a method to synthesize an observer system to provide state and condition signal estimates for a single component subsystem.     

Optimal sensor activation for diagnosing discrete event systems

The problem of dynamic sensor activation for event diagnosis in partially observed discrete event systems is considered. Diagnostic agents are able to activate sensors dynamically during the evolution of the system. Sensor activation policies for diagnostic agents are functions that determine which sensors are to be activated after the occurrence of a trace of events. The sensor activation policy must satisfy the property of diagnosability of centralized systems or codiagnosability of decentralized systems. A policy is said to be minimal if there is no other policy, with strictly less sensor activation, that achieves diagnosability or codiagnosability. To compute minimal policies, we propose language partition methods that lead to efficient computational algorithms. Specifically, we define “window-based” language partitions for scalable algorithms to compute minimal policies. By refining partitions, one is able to refine the solution space over which minimal solutions are computed at the expense of more computation. Thus a compromise can be achieved between fineness of solution and complexity of computation.     

The concept of residuals for fault localization in discrete event systems

In this paper an approach for fault localization in closed-loop Discrete Event Systems is proposed. The presented diagnosis method allows fault localization using a fault-free system model to describe the expected system behavior. Via a systematic comparison of the observed and the expected behavior, a fault can be detected and a set of fault candidates is determined. Inspired by residuals known from diagnosis in continuous systems, different set operations are introduced to generate the fault candidate set. After fault detection and a first fault localization, a procedure is given to render the fault localization more precisely by an analysis of the further observed system behavior. Special emphasis is given to the use of identified models for the fault-free system behavior. The approach is explained using a laboratory manufacturing facility.     

Delay-coobservability and its algebraic properties for the decentralized supervisory control of discrete event systems with communication delays

In networked control systems, uncontrollable events may unexpectedly occur at a plant before a proper control command is applied to it due to communication delays. In this paper, we address the problem of decentralized supervisory control under such communication delays based on the C&P (conjunctive and permissive) and D&A (disjunctive and antipermissive) decision architecture. In particular, for the existence of a decentralized supervisor, we present the notion of delay-coobservability of a given language specification and a polynomial-time algorithm for verifying it. In addition, algebraic properties of the delay-coobservability are investigated. We further present a synthesis method of the decentralized supervisor for practical usefulness.     

Fault prognosis of discrete event systems: An overview

Fault prognosis of discrete event systems (DES) is an active field of research and has become important due to the high demand on systems’ safety and reliability. The aim of this paper is to provide the state-of-the-art on fault prognosis of DES, as well as quick directions regarding many aspects of the research on this topic. This overview was carried out using a systematic approach, which allowed us to find and select papers with minimum bias. In total, 74 papers were selected and analyzed in this overview. A classification and an analysis of these papers are made regarding the modeling formalism and decision structure of prognosis of DES. Specific notions of prognosis are also presented. A survey on these papers was performed, regarding practical applications and related problems of prognosis. Results show that most papers present solutions based on languages & automata (56), and most papers consider the centralized decision structure (45). Also, we have found 17 different papers with examples of practical applications of prognosis of DES. We have identified research gaps, such as applications of distributed prognosis and distributed prognosis of Petri nets. Finally, the research activity on prognosis of DES is growing 16.14% by year on average, accordingly to the number of published papers on this topic between 2006 and 2020.     

Real time identification of discrete event systems using Petri nets

The paper defines the identification problem for Discrete Event Systems (DES) as the problem of inferring a Petri Net () model using the observation of the events and the available output vectors, that correspond to the markings of the measurable places. Two cases are studied considering different levels of the system knowledge. In the first case the place and transition sets are assumed known. Hence, an integer linear programming problem is defined in order to determine a modelling the DES. In the second case the transition and place sets are assumed unknown and only an upper bound of the number of places is given. Hence, the identification problem is solved by an identification algorithm that observes in real time the occurred events and the corresponding output vectors. The integer linear programming problem is defined at each observation so that the can be recursively identified. Some results and examples characterize the identified systems and show the flexibility and simplicity of the proposed technique. Moreover, an application to the synthesis of supervisory control of systems via monitor places is proposed.     

Jump modes analysis and observer design for discrete singular systems

This paper is concerned with the reconstructability and detectability of the jump modes of discrete singular systems. The notion of jump modes can be considered as the discrete counterpart of the impulsive modes of continuous singular systems which has been extensively studied. The effect of jump modes on the existence of reduced order normal Luenberger observers for discrete singular systems is investigated. Necessary and sufficient conditions for the existence of normal Luenberger observers and the corresponding observer design procedure are obtained.     

Decentralized control of networked discrete event systems with communication delays

In many practical systems, supervisory control is not performed by one centralized supervisor, but by multiple local supervisors. When communication networks are used in such a system as the medium of information transmission, the communication channels between local supervisors and the system to be controlled will unavoidably result in communication delays. This paper investigates how to use these local supervisors to control the system in order to satisfy given specifications even under communication delays. The specifications are described by two languages: a minimal required language which specifies the minimal required performance that the supervised system must have and a maximal admissible language which specifies the maximal boundary that the supervised system must be in. The results show that if the control problem is solvable, then there exists the minimal control policy which can be calculated based on state estimates. Furthermore, we derive algorithms to check whether the control problem is solvable or not.     

Control of large scale discrete event systems: Task allocation and coordination

To control a large scale discrete event system, decentralized control and hierarchical control can be used, where several local supervisors are used to control events in local sites and a coordinator is used to coordinate the local supervisors. Two important problems that need to be solved in such a control architecture are task allocation and coordination. That is, how to allocate tasks to the supervisors, and how to coordinate those tasks. We propose and solve a task allocation problem of assigning tasks to the local supervisors and a minimal intervention problem of coordinating tasks so that the intervention by the coordinator is minimal.     

An optimal effective controller for discrete event systems

An approach to the online synthesis of an optimal effective controller for discrete event systems is presented. The optimal effective controller can achieve the prescribed (cumulative) effectiveness measure while minimizing the total cost incurred for the execution of events. This approach is constructed over a generalized control framework for automata‐based discrete event systems, which allows event enforcement in addition to the (original) event disablement/enablement as the control mechanism. The optimal effective control policy generated by this approach is proved to be the least restrictive among all the possible optimal effective control policies for the given online expansion tree of the system behavior. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Decision making in fuzzy discrete event systems

The primary goal of the study presented in this paper is to develop a novel and comprehensive approach to decision making using fuzzy discrete event systems (FDES) and to apply such an approach to real-world problems. At the theoretical front, we develop a new control architecture of FDES as a way of decision making, which includes a FDES decision model, a fuzzy objective generator for generating optimal control objectives, and a control scheme using both disablement and enforcement. We develop an online approach to dealing with the optimal control problem efficiently. As an application, we apply the approach to HIV/AIDS treatment planning, a technical challenge since AIDS is one of the most complex diseases to treat. We build a FDES decision model for HIV/AIDS treatment based on expert’s knowledge, treatment guidelines, clinic trials, patient database statistics, and other available information. Our preliminary retrospective evaluation shows that the approach is capable of generating optimal control objectives for real patients in our AIDS clinic database and is able to apply our online approach to deciding an optimal treatment regimen for each patient. In the process, we have developed methods to resolve the following two new theoretical issues that have not been addressed in the literature: (1) the optimal control problem has state dependent performance index and hence it is not monotonic, (2) the state space of a FDES is infinite.     

Reliable supervisory control for general architecture of decentralized discrete event systems

In this paper, we investigate the reliable decentralized supervisory control of discrete event systems (DESs) under the general architecture, where the decision for controllable events is a combination of the conjunctive and disjunctive fusion rules. By reliable control, we mean that the performance of closed-loop systems will not be degraded even in the face of possible failures of some local supervisors. The main contributions are twofold. First, a necessary and sufficient condition for the existence of a k-reliable decentralized supervisor under the general architecture is presented after introducing notions of -controllability and k-reliable -coobservability. Second, a polynomial-time algorithm to verify the reliable -coobservability of a specification is proposed.     

Bisimilarity control of partially observed nondeterministic discrete event systems and a test algorithm

In this paper, the bisimilarity control of discrete event systems (DESs) under partial observations is investigated, where the plant and the specification are allowed to be nondeterministic. A notation of simulation-based controllability and a synchronization scheme for the supervised system are formalized based on the simulation relation between the specification and the plant. It is shown that the existence of bisimilarity supervisors is characterized by the notions of the simulation-based controllability and the language observability, which extends the traditional results of supervisory control from language equivalence to bisimulation equivalence. In addition, a polynomial algorithm to test the simulation-based controllability is developed by constructing a computing tree. This algorithm together with the test of language observability can be used to check the existence of bisimilarity supervisors.