Full-state perturbation analysis of discrete event dynamic systems

Discrete event dynamic systems are studied within the framework of perturbation analysis in this paper. Perturbation is extended from the event times only to both event times and queue lengths. An approximate technique, full-state perturbation analysis (PA), is developed as an extension of the PA approach. Full-state PA is able to deal with problems involving queue length perturbations which often defy existing PA methods, while it still retains all the advantages of existing PA. Full-state PA is used to calculate the throughput sensitivity to the number of customers in closed queueing networks and the throughput sensitivity to routing change. Numerical examples are given. Experimental results verify the validity and accuracy.This work is supported in part by the National High Technology Project and by Southeast University Research Funds for Young Teachers.     

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.     

Fault detection and isolation in manufacturing systems with an identified discrete event model

In this article a generic method for fault detection and isolation (FDI) in manufacturing systems considered as discrete event systems (DES) is presented. The method uses an identified model of the closed-loop of plant and controller built on the basis of observed fault-free system behaviour. An identification algorithm known from literature is used to determine the fault detection model in form of a non-deterministic automaton. New results of how to parameterise this algorithm are reported. To assess the fault detection capability of an identified automaton, probabilistic measures are proposed. For fault isolation, the concept of residuals adapted for DES is used by defining appropriate set operations representing generic fault symptoms. The method is applied to a case study system.     

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.     

On-line control of partially observed discrete event systems

It is well known that the design of supervisors for partially observed discrete-event systems is an NP-complete problem and hence computationally impractical. Furthermore, optimal supervisors for partially observed systems do not generally exist. Hence, the best supervisors that can be designed directly for operation under partial observation are the ones that generate the supremal normal (and controllable) sublanguage. In the present paper we show that a standard procedure exists by which any supervisor that has been designed for operation under full observation, can be modified to operate under partial observation. When the procedure is used to modify the optimal full-observation supervisor (i.e., the one that generates the supremal controllable language), the resultant modified supervisor is at least as efficient as the best one that can be designed directly (that generates the supremal normal sublanguage). The supervisor modification algorithm can be carried out on-line with linear computational complexity and hence makes the control under partial observation a computationally feasible procedure.     

串行生产线的参数优化

对随机离散事件系统模型,用实验(或模拟)方法进行扰动分析(Perturbation Analysisi,简称PA),对固定的样本,得到性能指标(设为J(θ))对可调参数θ的梯度dJ(θ)/dθ的估计.用固定长度的观测值(如L个顾客)估计dJ(θ)/dθ,将估计值代入随机逼近算法,递推地求最优参数,得到了基于扰动分析的优化算法.实验结果表明.这种优化算法,有较好的收敛速度.对串行生产线,提出每离开L个顾客递推一次参数的优化算法,并证明了这种算法可收敛到使J(θ)达极小的θ.     

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.     

Modular nonblocking state feedback control of discrete event systems and its application to dynamic oligopolistic markets

This article addresses a modular state feedback supervisory control problem where two local controllers should achieve a common control objective against another local controller. Each local controller has its own control objective described as a predicate. This article also addresses a nonblocking modular control problem in which a discrete event system controlled by three local controllers tends to reach the common marked states of two local controllers that are, however, prohibited by the third local controller. For a case study, we apply the proposed theory to an oligopolistic market composed of two firms and one government. Two oligopolistic firms have a common objective to maximise their total profit through collusion. However, the government prevents them from engaging in collusion. We show that the modular supervisory control theory presented in this article can be used to solve the problem of ‘how can the firms maximise their total profit against the intervention of government’?     

Polynomial-time verification of diagnosability of fuzzy discrete event systems

A fuzzy approach to perform diagnosis of fuzzy discrete event systems(FDESs)is proposed by constructing diagnosers,which may more effectively cope with the problems of vagueness and fuzziness arising from failure diagnosis of fuzzy systems.However,the complexity of constructing this kind of diagnosers is exponential in the state space and the number of fuzzy events of the system.In this paper,we present an algorithm for verifying the diagnosability of FDESs based on the construction of a nondeterministic automaton called F-verifier instead of diagnosers.Both the construction of F-verifiers and the verification of diagnosability of FDESs can be realized with a polynomial-time complexity.     

On derivative estimation of single-server queues via structural infinitesimal perturbation analysis

In Dai and Ho (1994) we developed a method, referred to asstructural infinitesimal perturbation analysis (SIPA), to address the need for derivative estimation with respect to a special type of parameter. However, it was not clear how much computational effort is required to implement this method. Derivative estimation via SIPA can be complicated in implementation. Such computational problems, also arise in several other derivative estimation methods. In this paper we take SIPA as a typical method and apply it to a special class of DEDS-several variations of single-server queues, focusing on the issue of implementation. We demonstrate that SIPA can be efficiently implemented. In some cases, it can be as simple as theinfinitesimal perturbation analysis (IPA), method which is considered to be the most efficient method available so far. The main approach we take is to combine SIPA with finite perturbation analysis and cut-and-paste techniques. Explicit formulae are given to various problems, some being impossible to solve using the traditional IPA method. Numerical examples are employed to illustrate the results.     

A control synthesis approach for time discrete event systems

In this paper, we introduce a control synthesis method for discrete event systems whose behavior is dependent on explicit values of time. Our goal is to control the occurrence dates of the controllable events so that the functioning of the system respects given specifications. The system to be controlled is modeled by a time Petri net. In a previous work we proposed a systematic method to build the timed automaton which models the exact behavior of a time Petri net. Furthermore, the forbidden behaviors of the system are modeled by forbidden timed automaton locations. This paper focuses on the control synthesis method, which consists in computing new firing conditions for the timed automaton transitions so that the forbidden locations are no longer reachable.     

A graph-theoretic optimal control problem for terminating discrete event processes

Most of the results to date in discrete event supervisory control assume a zero-or-infinity structure for the cost of controlling a discrete event system, in the sense that it costs nothing to disable controllable events while uncontrollable events cannot be disabled (i.e., their disablement entails infinite cost). In several applications however, a more refined structure of the control cost becomes necessary in order to quantify the tradeoffs between candidate supervisors. In this paper, we formulate and solve a new optimal control problem for a class of discrete event systems. We assume that the system can be modeled as a finite acylic directed graph, i.e., the system process has a finite set of event trajectories and thus is terminating. The optimal control problem explicitly considers the cost of control in the objective function. In general terms, this problem involves a tradeoff between the cost of system evolution, which is quantified in terms of a path cost on the event trajectories generated by the system, and the cost of impacting on the external environment, which is quantified as a dynamic cost on control. We also seek a least restrictive solution. An algorithm based on dynamic programming is developed for the solution of this problem. This algorithm is based on a graph-theoretic formulation of the problem. The use of dynamic programming allows for the efficient construction of an optimal subgraph (i.e., optimal supervisor) of the given graph (i.e., discrete event system) with respect to the cost structure imposed. We show that this algorithm is of polynomial complexity in the number of vertices of the graph of the system.Research supported in part by the National Science Foundation under grant ECS-9057967 with additional support from GE and DEC.     

随机计时离散事件系统的软控制任务研究

本文通过引入马氏决策过程中的迭代算法,研究了计时离散事件系统的随机优化监控综合问题。为了对不确定的人造系统实施监控,在考虑事件的操作时间的基础上,利用带有发生事件概率分布函数的随机计时离散事件系统模型对系统建模。为了对这类随机系统实施监控,在传统方法中,采用控制任务的最大可控子语言设计控制器,不能体现系统模型的随机特性。本文提出利用软控制任务代替原控制任务的方法,使其超出原控制任务的概率在给定的容许度约束范围内。首先,通过在计时离散事件系统中定义计时事件的发生概率映射和发生费用函数,利用离散事件系统的逻辑特性,构造事件发生序列的期望费用函数,进而确立马氏决策过程的最优方程,建立软控制任务与期望费用函数之间的关系。然后,通过计算事件发生序列的费用值,提出利用有限费用值可以用来确定软控制任务,进而基于逻辑监控方法,确定最优监控器。最后,利用计算有限费用值的迭代过程,提出迭代算法,并给出了计算实例。     

On tolerable and desirable behaviors in supervisory control of discrete event systems

We formulate and solve a new supervisory control problem for discrete event systems. The objective is to design a logical controller—or supervisor—such that the discrete event system satisfies a given set of requirements that involve event ordering. The controller must deal with a limited amount of controllability in the form of uncontrollable events. Our problem formulation considers that the requirements for the behavior (i.e., set of traces) of the controlled system are specified in terms of a desired behavior and a larger tolerated behavior. Due to the uncontrollable events, one may wish to tolerate behavior that sometimes exceeds the ideal desired behavior if overall this results in achieving more of the desired behavior. The general solution of our problem is completely characterized. The nonblocking solution is also analyzed in detail. This solution requires the study of a new class of controllable languages. Several results are proved about this class of languages. Algorithms to compute certain languages of interest within this class are also presented.Research supported in part by the National Science Foundation under grants ECS-8707671, ECS-9057967, and ECS-9008947.     

Nonblocking supervisory control of timed discrete event systems under communication delays: The existence conditions

This paper addresses the problem of nonblocking supervisory control of timed discrete event systems under communication delays based on the framework proposed by Brandin and Wonham. For such a system, a supervisory control command could be applied to the system after some time-delay limited by a finite bound corresponding to the maximal number of tick occurrences, and some uncontrollable events may unexpectedly occur within this time-delay. This paper presents the necessary and sufficient conditions for the existence of a nonblocking supervisor that can achieve a given language specification in consideration of such delayed communications.     

State feedback control of real-time discrete event systems with infinite states

In this paper, we study a state feedback supervisory control of timed discrete event systems (TDESs) with infinite number of states modelled as timed automata. To this end, we represent a timed automaton with infinite number of untimed states (called locations) by a finite set of conditional assignment statements. Predicates and predicate transformers are employed to finitely represent the behaviour and specification of a TDES with infinite number of locations. In addition, the notion of clock regions in timed automata is used to identify the reachable states of a TDES with an infinite time space. For a real-time specification described as a predicate, we present the controllability condition for the existence of a state feedback supervisor that restricts the behaviour of the controlled TDES within the specification.     

Grid automata and supervisory control of dense real-time discrete event systems

We present a generalization of the classical supervisory control theory for discrete event systems to a setting of dense real-time systems modeled by Alur and Dill timed automata. The main problem involved is that in general the state space of a timed automaton is (uncountably) infinite. The solution is to reduce the dense time transition system to an appropriate finite discrete subautomaton, the grid automaton, which contains enough information to deal with the timed supervisory control problem (TSCP). The plant and the specifications region graphs are sampled for a granularity defined in a way that each state has an outgoing transition labeled with the same time amount. We redefine the controllability concept in the context of grid automata, and we provide necessary and sufficient solvability conditions under which the optimal solution to centralized supervisory control problems in timed discrete event systems under full observation can be obtained. The enhanced setting admits subsystem composition and the concept of forcible event. A simple example illustrates how the new method can be used to solve the TSCP.     

Supply management for cost minimization in assembly systems with random component yield times

This paper is concerned with inventory control in assembly systems for minimizing production costs. The system manufactures multiple products assembled from various components, and it operates according to a cyclic schedule. At the start of each cycle time, two decisions are made: the product volumes to be assembled during the current cycle, and the component-stock levels to be ordered. For a given decision, there is an associated cost incurred by backlogging of the finished products on one hand, and the component inventory holding cost, on the other hand. The objective here is to balance the two costs so as to minimize their sum. One complicating factor stems from uncertainties in both product demand levels and components yield times. These uncertainties can be modelled by probabilistic means, and hence the cost minimization problem becomes a stochastic problem. This problem can be quite difficult due to the nonlinearity of the equations involved, the mix of integer and continuous parameters, and their large number in moderate-size problems. Our approach in this paper is to first define certain control parameters and thus reduce the number of the variables involved in the optimization problem, and then solve the latter problem by using sophisticated optimization techniques in conjunction with heuristic modelling. We will demonstrate, by numerical means, the resolution of fairly difficult problems and thus establish the viability of the proposed numerical techniques.     

A new approach to the analysis of discrete event dynamic systems

We present a new, time domain approach to the study of discrete event dynamical systems (DEDS), typified by queueing networks and production systems. A general state-space representation is developed and perturbation analysis is carried out. Observation of a single sample realization of such a system can be used to predict behavior over other sample realizations, when some parameter is perturbed, without having to make additional observations. Conditions under which this is always possible are investigated and explicit results for some special cases are included.