Framework Of Discrete Event Systems Research Articles

Active fault tolerant control of discrete event systems using online diagnostics

The aim of this paper is to deal with the problem of fault tolerant control in the framework of discrete event systems modeled as automata. A fault tolerant controller is a controller able to satisfy control specifications both in nominal operation and after the occurrence of a fault. This task is solved by means of a parameterized controller that is suitably updated on the basis of the information provided by online diagnostics: the supervisor actively reacts to the detection of a malfunctioning component in order to eventually meet degraded control specifications. Starting from an appropriate model of the system, we recall the notion of safe diagnosability as a necessary step in order to achieve fault tolerant control. We then introduce two new notions: (i) “safe controllability”, which represents the capability, after the occurrence of a fault, of steering the system away from forbidden zones and (ii) “active fault tolerant system”, which is the property of safely continuing operation after faults. Finally, we show how the problem can be solved using a general control architecture based on the use of special kind of diagnoser, called “diagnosing controller”, which is used to safely detect faults and to switch between the nominal control policy and a bank of reconfigured control policies. A simple example is used to illustrate the new notions and the control architecture introduced in the paper.

관리 제어를 이용한 무선 TCP 성능 향상에 관한 방법

This paper proposes a systematic approach to the rate-based feedback control based on the supervisory control framework for discrete event systems. We design the supervisor to achieve the desired behavior for TCP wireless networks. From the analysis and simulation results, it is shown that the controlled networks guarantee the fair sharing of the available bandwidth and avoid the packet loss caused by the buffer overflow of TCP wireless networks.

Estimation of transitional probabilities of discrete event systems from cross-sectional survey and its application in tobacco control

In order to find better strategies for tobacco control, it is often critical to know the transitional probabilities among various stages of tobacco use. Traditionally, such probabilities are estimated by analyzing data from longitudinal surveys that are often time-consuming and expensive to conduct. Since cross-sectional surveys are much easier to conduct, it will be much more practical and useful to estimate transitional probabilities from cross-sectional survey data if possible. However, no previous research has attempted to do this. In this paper, we propose a method to estimate transitional probabilities from cross-sectional survey data. The method is novel and is based on a discrete event system framework. In particular, we introduce state probabilities and transitional probabilities to conventional discrete event system models. We derive various equations that can be used to estimate the transitional probabilities. We test the method using cross-sectional data of the National Survey on Drug Use and Health. The estimated transitional probabilities can be used in predicting the future smoking behavior for decision-making, planning and evaluation of various tobacco control programs. The method also allows a sensitivity analysis that can be used to find the most effective way of tobacco control. Since there are much more cross-sectional survey data in existence than longitudinal ones, the impact of this new method is expected to be significant.

Spectral analysis for performance evaluation in a bus network

This paper deals with the performance evaluation of a public transportation system in terms of waiting times at various connection points. The behaviour of a bus network is studied in the framework of Discrete Event Systems (DES). Two possible operating modes of buses can be observed at each connection stop: periodic and non-periodic mode. Two complementary tools, Petri nets and (max, +) algebra, are used to describe the network by a non-stationary linear state model. This one can be solved after solving the structural conflicts associated to the graphical representation. From the characteristic matrix of the mathematical model, we determine eigenvalues and eigenvectors that we use to evaluate the connection times of passengers. This work is finally illustrated with a numerical example.

非決定出力関数をもつＭｅａｌｙオートマトンで表される離散事象システムのスーパバイザ制御

In the conventional supervisory control frame-work for discrete event systems with partial event observation, it is assumed that, for each event, the corresponding output symbol is determined deterministically. However, this assumption does not hold in discrete event systems such as a system with sensor errors and a mobile system, where an output symbol depends on not only an event but also a state at which the event occurs. In this paper, we model such a discrete event system by a Mealy automaton with a nondeterministic output function. We consider two kinds of supervisors: one assigns its control action based on a permissive policy and the other based on an anti-permissive one. We present necessary and sufficient conditions for each of them to achieve a given specification. We then present algorithms for verifying these conditions. Moreover, we discuss the relationship between the two supervisors in the case that an output function is deterministic.

A Formula for the Supremal Controllable and Opaque Sublanguage Arising in Supervisory Control

In this paper, we study a property of opacity in the language-based framework of discrete event systems. The problem of synthesizing a supervisor that enforces opacity in a maximally permissive way...

A fault tolerant architecture for supervisory control of discrete event systems

In this paper the problem of Fault Tolerant Control (FTC) in the framework of Discrete Event Systems (DES) modeled as automata is considered. The approach we follow is the so-called active approach in which the supervisor actively reacts to the detection of a malfunctioning component in order to eventually meet degraded control specifications. Starting from an appropriate model of the system, we recall the notion of safe diagnosability as a necessary step in order to achieve fault tolerant supervision of DES. We then introduce two new notions: (i) “safe controllability”, which represents the capability, after the occurrence of a fault, of steering the system away from forbidden zones and (ii) “active fault tolerant system”, which is the property of safely continuing operation after faults. We show how it is possible to define a general control architecture to deal with the FTC problem by introducing a special kind of automaton, called a “diagnosing-controller”.

An Optimal Directed Control Framework for Discrete Event Systems

In an earlier paper, we introduced the notion of directed control, where a directed controller, which is simply referred to as a director, is one that selects at most one controllable event to be enabled at any instant. In this paper, we develop an optimization-based approach for the design of a director: starting from any state, the worst cost to the nearest reachable marked state is minimized. The motivation is that a pending task can be completed in the least possible cost. A necessary and sufficient condition for the existence of an optimal director is obtained. Furthermore, for systems that are cycle-free, we provide an algorithm of polynomial complexity to compute an optimal director.

Failure diagnosis and recovery based on DES framework

As many industrial systems become more complex, it becomes extremely difficult to diagnose the cause of failures. This paper presents a new failure diagnosis approach based on discrete-event systems (DES) framework. In particular, the approach is a hybrid of event-based and state-based ones leading to a simpler failure diagnoser with supervisory control capability. In our approach, we include the failure recovery events for failures in the system model in order to derive a diagnoser we refer to as a recoverable diagnoser. Further, in order to reduce the state size of the recoverable diagnoser, a procedure to construct a high-level diagnoser is presented. The design procedure for diagnoser is presented along with a pump-valve system as a illustrative example.

Max-Min Fair Rate Allocation Scheme in Multirate Multicast Networks Using Supervisory Control

This paper describes a max-min fair rate allocation scheme in multicast networks based on the supervisory control framework for discrete event systems. Based on the discrete event model of multicast networks, we design a supervisor to guarantee the max-min fair allocation of bandwidth. Analysis and simulations are used to show that the controlled networks guarantee the max-min fair sharing with a low message exchange overhead and fast convergence time.

SPECTRAL THEORY IN (MAX, PLUS) ALGEBRA FOR PERFORMANCE EVALUATION IN A TRANSPORT NETWORK

This paper deals with the performance evaluation of a public transportation system in terms of waiting times of passengers. A bus network is studied in the framework of Discrete Event Systems. Two complementary tools are used: Petri nets and dioid algebra. First we describe the network by a (max, plus) linear system deduced from a Petri net model. This system can be solved after solving the structural conflicts associated to the graphical model. From the characteristic matrix of the state model, we determine eigenvalues and eigenvectors that we use to evaluate the connection times. This work is finally illustrated with a numerical example.

The Verification and Control of Interacting Similar Discrete-Event Systems

This paper explore issues related to the control and verification of similar module systems in the discrete-event systems framework. Similar module systems are distributed systems comprised of subsystem modules that exhibit isomorphic local behavior coordinated on global event occurrences. When given a global model of these systems, it is shown how to decompose the global model into the component subsystems in polynomial time. It is also shown how to perform various verification tasks for these interacting systems while mitigating common state explosion difficulties by taking advantage of the special similar module system structure. Control properties of the similar module systems are also discussed. It is assumed that the local modules are supervised by exactly one local controller and the controllers enforce the same local control policy. Necessary and sufficient conditions for achieving local and global control specifications in this setting are identified.

Rate-based feedback control over TCP wireless networks using supervisory control

This paper proposes a systematic approach to the rate-based feedback control based on the supervisory control framework for discrete event systems. Since communication networks can be represented as discrete event systems, we design the supervisor to generate the admissible behavior for TCP wireless networks. It is shown that the controlled networks guarantee the fair sharing of the available bandwidth and avoid the packet loss caused by the-buffer overflow of TCP wireless networks.

Decentralised supervisory control of discrete event systems with mutual observability

An extended decentralised supervisory control framework of discrete event systems is considered, in which a certain number of local supervisors are required to disable a controllable event. The mutual observability, which is an extended concept of the conventional co-observability, is presented to increase the system's efficacy. Based on the mutual observability, the authors investigate the necessary and sufficient conditions for the existence of the extended decentralised supervisory control.

Undecidable problems of decentralized observation and control on regular languages

We introduce a decentralized observation problem, where the system under observation is modeled as a regular language L over a finite alphabet Σ and n subsets of Σ model distributed observation points. A regular language K⊆ L models a set of distinguished behaviors, say, correct behaviors of the system. The objective is to check the existence of a function which, given the n observations corresponding to a behavior ρ∈ L, decides whether ρ is in K or not. We prove that checking the existence of such a function is undecidable. We then use this result to show undecidability of a decentralized supervisory control problem in the discrete event system framework.

Modeling and control of fuzzy discrete event systems

In order to make it possible to effectively represent deterministic uncertainties and vagueness as well as the human subjective observation and judgement inherent to many real-world problems, especially those in biomedicine, we introduce, in this paper, fuzzy states and fuzzy events and generalize (crisp) discrete event systems (DES) to fuzzy DES. The largely graph-based current framework of the crisp DES is unsuitable for the expansion, and we have thus reformulated it using state vectors and event transition matrices which can be extended to fuzzy vectors and matrices by allowing their elements to take values between 0 and 1. To measure information related to fuzzy DES, we generalize the crisp DES observability. The new observability allows one to determine whether or not the system output observed is sufficient for decision making. Finally, we extend the optimal control of DES to fuzzy DES. The new fuzzy DES theory is consistent with the existing theory, both at the conceptual and the computation levels, in that the former contains the latter as a special case when the memberships must be either 0 or 1. Numerical examples are provided to illustrate the theoretical development.

Robust and nonblocking supervisor for discrete-event systems with model uncertainty under partial observation

Addresses a robust and nonblocking supervisory control problem based on a framework of discrete-event systems with model uncertainty under partial observation. The uncertainty introduced in the paper is associated with internal and unobservable events occurring in systems. The paper presents a systematic method for modeling uncertainty described as a /spl Delta/-transition representing the internal and unobservable events. In particular, at a state with the assigned positive integer value p a system is assumed to experience at most a p-step state transition by the internal and unobservable event. Under the framework for model uncertainty, the paper presents necessary and sufficient conditions for the existence of a robust supervisor with the nonblocking property.

Active diagnosis of discrete-event systems

The need for accurate and timely diagnosis of system failures and the advantages of automated diagnostic systems are well appreciated. However, diagnosability considerations are often not explicitly taken into account in the system design. In particular, design of the controller and that of the diagnostic subsystem are decoupled, and this may significantly affect the diagnosability properties of a system. The authors present an integrated approach to control and diagnosis. More specifically, they present an approach for the design of diagnosable systems by design of the system controller. This problem, which they refer to as the active diagnosis problem, is studied in the framework of discrete-event systems (DESs); it is based on prior and new results on the theory of diagnosis for DESs and on existing results in supervisory control under partial observations. They formulate the active diagnosis problem as a supervisory control problem where the legal language is an appropriate regular sublanguage of the regular language generated by the system. They present an iterative procedure for determining the supremal controllable, observable, and diagnosable sublanguage of the legal language and for obtaining the supervisor that synthesizes this language. This procedure provides both a controller that ensures diagnosability of the closed-loop system and a diagnoser for online failure diagnosis. The procedure can be implemented using finite-state machines and is guaranteed to converge in a finite number of iterations. The authors illustrate their approach using a simple pump-valve system.

Failure diagnosis using discrete-event models

Detection and isolation of failures in large, complex systems is a crucial and challenging task. The increasingly stringent requirements on performance and reliability of complex technological systems have necessitated the development of sophisticated and systematic methods for the timely and accurate diagnosis of system failures. We propose a discrete-event systems (DES) approach to the failure diagnosis problem. This approach is applicable to systems that fall naturally in the class of DES; moreover, for the purpose of diagnosis, continuous-variable dynamic systems can often be viewed as DES at a higher level of abstraction. We present a methodology for modeling physical systems in a DES framework and illustrate this method with examples. We discuss the notion of diagnosability, the construction procedure of the diagnoser, and necessary and sufficient conditions for diagnosability. Finally, we illustrate our approach using realistic models of two different heating, ventilation, and air conditioning (HVAC) systems, one diagnosable and the other not diagnosable. While the modeling methodology presented here has been developed for the purpose of failure diagnosis, its scope is not restricted to this problem; it can also be used to develop DES models for other purposes such as control.

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.