Fault detection and isolation is a crucial and challenging task in the automatic control of large complex systems. We propose a discrete-event system (DES) approach to the problem of failure diagnosis. We introduce two related notions of diagnosability of DES's in the framework of formal languages and compare diagnosability with the related notions of observability and invertibility. We present a systematic procedure for detection and isolation of failure events using diagnosers and provide necessary and sufficient conditions for a language to be diagnosable. The diagnoser performs diagnostics using online observations of the system behavior; it is also used to state and verify off-line the necessary and sufficient conditions for diagnosability. These conditions are stated on the diagnoser or variations thereof. The approach to failure diagnosis presented in this paper is applicable to systems that fall naturally in the class of DES's; moreover, for the purpose of diagnosis, most continuous variable dynamic systems can be viewed as DES's at a higher level of abstraction. In a companion paper [20], we provide a methodology for building DES models for the purpose of failure diagnosis and present applications of the theory developed in this paper.

Abstruct-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. A detailed treatment of the theory underlying our approach can be found in a companion paper [27].

Abstract. We address the problem of failure diagnosis in discrete event systems with decentralized information. We propose a coordinated decentralized architecture consisting of local sites communicating with a coordinator that is responsible for diagnosing the failures occurring in the system. We extend the notion of diagnosability, originally introduced in Sampath et al. (1995) for centralized systems, to the proposed coordinated decentralized architecture. We specify three protocols that realize the proposed architecture; each protocol is defined by the diagnostic information generated at the local sites, the communication rules used by the local sites, and the coordinator's decision rule. We analyze the diagnostic properties of each protocol. We also state and prove conditions for a language to be diagnosable under each protocol. These conditions are checkable off-line. The on-line diagnostic process is carried out using the diagnosers introduced in Sampath et al. (1995) or a slight variation of these diagnosers. The key features of the proposed protocols are: (i) they achieve, each under a set of assumptions, the same diagnostic performance as the centralized diagnoser; and (ii) they highlight the "performance vs. complexity" tradeoff that arises in coordinated decentralized architectures. The correctness of two of the protocols relies on some stringent global ordering assumptions on message reception at the coordinator's site, the relaxation of which is briefly discussed.

Abstruct-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. A detailed treatment of the theory underlying our approach can be found in a companion paper [27].

Abstract. We address the problem of failure diagnosis in discrete event systems with decentralized information. We propose a coordinated decentralized architecture consisting of local sites communicating with a coordinator that is responsible for diagnosing the failures occurring in the system. We extend the notion of diagnosability, originally introduced in Sampath et al. (1995) for centralized systems, to the proposed coordinated decentralized architecture. We specify three protocols that realize the proposed architecture; each protocol is defined by the diagnostic information generated at the local sites, the communication rules used by the local sites, and the coordinator's decision rule. We analyze the diagnostic properties of each protocol. We also state and prove conditions for a language to be diagnosable under each protocol. These conditions are checkable off-line. The on-line diagnostic process is carried out using the diagnosers introduced in Sampath et al. (1995) or a slight variation of these diagnosers. The key features of the proposed protocols are: (i) they achieve, each under a set of assumptions, the same diagnostic performance as the centralized diagnoser; and (ii) they highlight the "performance vs. complexity" tradeoff that arises in coordinated decentralized architectures. The correctness of two of the protocols relies on some stringent global ordering assumptions on message reception at the coordinator's site, the relaxation of which is briefly discussed.

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In certain discrete event applications it may be desirable to find a particular controller, within the set of acceptable controllers, which optimizes some quantitative performance measure. In this paper we propose a theory of optimal control to meet such design requirements for deterministic systems. The discrete event system (DES) is modeled by a formal language. Event and cost functions are defined which induce costs on controlled system behavior. The event costs associated with the system behavior can be reduced, in general, only by increasing the control costs. Thus it is nontrivial to find the optimal amount of control to use, and the formulation captures the fundamental tradeoff motivating classical optimal control. Results on the existence of minimally restrictive optimal solutions are presented. Communication protocols are analyzed to motivate the formulation and demonstrate optimal controller synthesis. Algorithms for the computation of optimal controllers are developed for the special case of DES modeled by regular languages. It is shown that this framework generalizes some of the existing literature. AMS subject classifications. 93A99, 49-XX, 90C27PII. S0363012994260957 1. Introduction. This paper presents a new framework for the optimal control of discrete event systems (DESs). The aim is to find methods to handle numerical performance measures in the DES controller design process.The most influential paradigm for DES control is the supervisory control theory (SCT) suggested by Ramadge and Wonham [9,8]. SCT makes certain systemtheoretic assumptions which are appropriate for DES control problems. SCT as developed in [8] partitions all possible DES behavior into legal or illegal, and then addresses the problem of designing a DES controller that guarantees legal behavior. Here we enrich this view by accepting that some legal behaviors are better than others. For example, for a transaction submitted to a database management system (DBMS), all commit times below a certain threshold may be legal, but a smaller commit time is better. We propose numerical measures on the set of legal behaviors to capture such distinctions. The new problem, then, is to produce a controller that is not only legal but also "good" in the sense of the given numerical performance measures. We present our various findings collectively as a theory of optimal control for discrete event systems. It is our hope that this theory lays out the boundaries within which future work on the performance improvement or performance tuning of specific DESs can be attempted.In the historical development of control theory, optimal control has been considered interesting only after the design and analysis of other control-theoretic concepts such as controllability, stabilizability, etc. have attained some degree of maturity.

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