This thesis considers probabilistic supervisory control of probabilistic discrete event systems (PDES). PDES are modeled as generators of probabilistic languages. The probabilistic supervisors employed are a generalization of the deterministic ones previously employed in the literature. At any state, the supervisor enables/disables events with certain probabilities. The probabilistic supervisory control problem (PSCP) that has previously been considered in the literature is revisited: find, if possible, a supervisor under whose control the behavior of a plant is identical to a given probabilistic specification. The existing results are unified, complemented with a solution of a special case and the computational analysis of synthesis problem and the solution. The central place in the thesis is given to the solution of the optimal probabilistic supervisory control problem (OPSCP) in the framework: if the conditions for the existence of probabilistic supervisor for PSCP problem are not satisfied, find a probabilistic supervisor such that the achievable behaviour is as close as possible to the desired behaviour. The proximity is measured using the concept of pseudometric on states of generators. The distance between two systems is defined as the distance in the pseudometric between the initial states of the corresponding generators. The pseudometric is adopted from the research in formal methods community and is defined as the greatest fixed point of a monotone function. Starting from this definition, we suggest two algorithms for finding the distances in the pseudometric. Further, we give a logical characterization of the same pseudometric such that the distance between two systems is measured by a formula that distinguishes between the systems the most. A trace characterization of the pseudometric is then derived from the logical characterization by which the pseudometric measures the difference of (appropriately discounted) probabilities of traces and sets of traces generated by systems, as well as some more complicated properties of traces. Then, the solution to the optimal probabilistic supervisory control problem is presented. Further, the solution of the problem of approximation of a given probabilistic generator with another generator of a prespecified structure is suggested such that the new model is as close as possible to the original one in the pseudometric (probabilistic model fitting). The significance of the approximation is then discussed. While other applications are briefly discussed, a special attention is given to the use of ideas of probabilistic model fitting in the solution of a modified optimal probabilistic supervisory control problem. / Thesis / Doctor of Philosophy (PhD)

In the area of Discrete Event Systems (DES), formal verification techniques are important in examining a variety of system properties including controllability and nonblocking. Nonetheless, in reality, most software and hardware practitioners are not proficient in formal methods which holds them back from the formal representation and verification of their systems. Alternatively, it is a common observation that control engineers are typically familiar with Moore synchronous Finite State Machines (FSM) and use them to express their controllers’ behaviour. Taking this into consideration, we devise a generic and structured approach to automatically translate Moore synchronous FSM into timed DES (TDES) supervisors. In this thesis, we describe our FSM-TDES translation method, present a set of algorithms to realize the translation steps and rules, and demonstrate the application and correctness of our translation approach with the help of an example. In order to develop our automatic FSM-TDES translation approach, we exploit the structural similarity created by the sampled-data (SD) supervisory control theory between the two models. To build upon the SD framework, first we address a related issue of disabling the tick event in order to force an eligible prohibitable event in the SD framework. To do this, we introduce a new synchronization operator called the SD synchronous product (||SD), adapt the existing TDES and SD properties, and devise our ||SD setting. We formally verify the controllability and nonblocking properties of our ||SD setting by establishing logical equivalence between the existing SD setting and our ||SD setting. We present algorithms to implement our ||SD setting in the DES research tool, DESpot. The formulation of the ||SD operator provides twofold benefits. First, it simplifies the design logic of the TDES supervisors that are modelled in the SD framework. This results in improving the ease of manually designing SD controllable TDES supervisors, and reduced verification time of the closed-loop system. We demonstrate these benefits by applying our ||SD setting to an example system. Second, it bridges the gap between theoretical supervisors and physical controllers with respect to event forcing. This makes our FSM-TDES translation approach relatively uncomplicated. Our automatic FSM-TDES translation approach enables the designers to obtain a formal representation of their controllers without designing TDES supervisors by hand and without requiring formal methods expertise. Overall, this work should increase the adoption of the SD supervisory control theory in particular, and formal methods in general, in the industry by facilitating software and hardware practitioners in the formal representation and verification of their control systems. / Dissertation / Doctor of Philosophy (PhD)

A Graphical User Interface (GUI) is defined by its appearance and its behavior. A GUI’s behavior determines how it reacts to user and system events such as mouse, keyboard, or touchscreen presses, or changes to an underlying data model. Although many tools are effective in enabling designers to specify a GUI’s appearance, defining a custom behavior is difficult and error-prone. Many of the difficulties developers face in defining GUI behaviors are the result of their reactive nature. The order in which GUI code is executed depends upon the order in which it receives external inputs. Most widely used user interface programming frameworks use an event-callback model, where developers define GUI behavior by defining callbacks—sequences of low-level actions—to take in reaction to events. However, the event-callback model for user-interface development has several problems, many of which have been identified long before I started work on this dissertation. First, it is disorganized: the location and order of event-callback code often has little correspondence with the order in which it will be executed. Second, it divides GUI code in a way that requires writing interdependent code to keep the interface in a consistent state. This is because maintaining a consistent state requires referencing and modifying the same state variables across multiple different callbacks, which are often distributed throughout the code. In this dissertation, I will introduce a new framework for defining GUI behavior, called the stateconstraint framework. This framework combines constraints—which allow developers to define relationships among interface elements that are automatically maintained by the system—and state machines—which track the status of an interface. In the state-constraint framework, developers write GUI behavior by defining constraints that are enforced when the interface is in specific states. This framework allows developers to specify more nuanced constraints and allows the GUI’s appearance and behavior to vary by state. I created two tools using the state-constraint framework: a library for Web developers (ConstraintJS) and an interactive graphical language (InterState). ConstraintJS provides constraints that can be used both to control content and control display, and integrates these constraints with the three Web languages—HTML, CSS, and JavaScript. ConstraintJS is designed to take advantage of the declarative syntaxes of HTML and CSS: It allows the majority of an interactive behavior to be expressed concisely in HTML and CSS, rather than requiring the programmer to write large amounts of JavaScript. InterState introduces a visual notation and live editor to clearly represent how states and constraints combine to define GUI behavior. An evaluation of InterState showed that its computational model, visual notation, and editor were effective in allowing developers to define GUI behavior compared to conventional event-callback code. InterState also introduces extensions to the state-constraint framework to allow developers to easily re-use behaviors and primitives for authoring multi-touch gestures.

In this dissertation, we explore the problem of fault detection and fault diagnosis for systems modeled as condition systems. A condition system is a Petri net based framework of components which interact with each other and the external environment through the use of condition signals. First, a system FAULT is defined as an observed behavior which does not correspond to any expected behavior, where the expected behavior is defined through condition system models. A DETECTION is the determination that the system is not behaving as expected according to the model of the system. A DIAGNOSIS of this fault localizes the subsystem that is the source of the discrepancy between output and expected observations. We characterize faults as a behavior relaxation of model components. We then show that detection and diagnosis can be determined in a finite number of calculations. The exact solution can be computationally involved, so we also present methods to perform a rapid detection and diagnosis. We have also included a chapter on a conversion from the condition system framework into a linear-time temporal logic(LTL) framework.

L'espérance de vie a augmenté dans les dernières décennies et devrait continuer à croître dans les prochaines années. Cette augmentation entraîne de nouveaux défis concernant l'autonomie et l'indépendance des personnes âgées. Le développement d'habitats intelligents est une piste pour répondre à ces défis et permettre aux personnes de vivre plus longtemps dans un environnement sûr et confortable. Rendre un habitat intelligent consiste à y installer des capteurs, des actionneurs et un contrôleur afin de pouvoir prendre en compte le comportement de ses habitants et agir sur leur environnement, pour améliorer leur sécurité, leur santé et leur confort. La plupart de ces approches s'appuient sur la localisation en temps réel des habitants dans leur habitat. Dans cette thèse, une nouvelle approche complète permettant la localisation d'un nombre a priori inconnu d'habitants basée sur le modèle est proposée. Cette approche tire parti des paradigmes, de la théorie et des outils des Systèmes à Événements Discrets. L'utilisation des automates à états finis pour modéliser le mouvement détectable des habitants ainsi que des méthodes permettant de construire ces modèles ont été développées. A partir de ces modèles automates finis, plusieurs algorithmes permettant de localiser de manière efficace les habitants ont été définis. Enfin, plusieurs approches pour l'évaluation des performances de l'instrumentation d'un habitat intelligent pour un objectif de localisation ont été proposées. La méthode a également été totalement implémentée et mise à l'épreuve. Tout au long de cette thèse, les différentes contributions sont illustrées à l'aide de cas d'étude. / Life expectancy has continuously increased in most countries over the last decades and will probably continue to increase in the future. This leads to new challenges relative to the autonomy and the independence of elderly. The development of Smart Homes is a direction to face these challenges and to enable people to live longer in a safe and comfortable environment. Making a home smart consists in placing sensors, actuators and a controller in the house in order to take into account the behavior of their inhabitants and to act on their environment to improve their safety, health and comfort. Most of these approaches are based on the real-time indoor Location Tracking of the inhabitants. In this thesis, a whole new approach for model-based Location Tracking of an a priori unknown number of inhabitants is proposed. This approach is based on Discrete Event Systems paradigms, theory and tools. The usage of Finite Automata (FA) to model the detectable motion of the inhabitants as well as different methods to create such FA models have been developed. Based on these models, algorithms to perform efficient Location Tracking are defined. Finally, several approaches aiming at evaluating the relevance of the instrumentation of a Smart Home with the objective of Location Tracking are proposed. The approach has also been fully implemented and tested. Throughout the thesis, the different contributions are illustrated on case studies. / In den meisten Industrieländern ist die Lebenserwartung in den letzten Jahrzehnten fortlaufend gestiegen und wird höchstwahrscheinlich noch weiter steigen. Dieser Anstieg führt zu neuen Herausforderungen hinsichtlich der Autonomie und Unabhängigkeit von älteren Menschen. Die Entwicklung von intelligenten Wohnungen ist ein Weg diesen Herausforderungen zu begegnen und es den Menschen zu ermöglichen länger in einer sicheren und komfortablen Umgebung zu leben. Dazu stattet man solcheWohnungen mit Sensoren, Aktoren sowie einem Controller aus. Dies erm öglicht es, in Abhängigkeit vom Verhalten der Bewohner, dieWohnumgebung so zu beein_ussen, dass sich Sicherheit, Gesundheit und Komfort verbessern. Ansätze, die dies zum Ziel haben, basieren meistens auf Methoden, die es ermöglichen Menschen innerhalb ihrer Wohnung in Echtzeit zu lokalisieren. In dieser Dissertation wird daher ein neuer Ansatz für eine modellbasierte Lokalisierung einer a priori unbekannten Anzahl von Bewohnern vorgestellt. Dieser Ansatz fuÿt auf der Theorie, den Paradigmen und den Werkzeugen aus dem Gebiet der ereignisdiskreten Systeme. Es werden endliche Automaten eingesetzt, um die von den Sensoren erfassbaren Bewohnerbewegungen zu modellieren. Verschiedene Verfahren zur Erzeugung solcher Automaten werden gezeigt. Basierend auf diesen Modellen warden Algorithmen de_niert, mittels derer die Bewohner wirksam lokalisiert werden können. Abschlieÿend werden Methoden vorgeschlagen, die dazu dienen die Relevanz der Sensorinstrumentierung für die Lokalisierung zu bewerten. Die entwickelten Verfahren werden in der Dissertation durchgehend anhand von Fallbeispielen erläutert. Der gesamte Ansatz wurde implementiert und erprobt.

Fault isolation is the process of reasoning required to find the cause of a system failure. In a model-based approach, the available information is a model of the system and some observations. Using knowledge of how the system generally behaves, as given in the system model, together with partial observations of the events of the current situation the task is to deduce the failure causing event(s). In our setting, the observable events manifest themselves in a message log. We study post mortem fault isolation for moderately concurrent discrete event systems where the temporal order of logged messages contains little information. To carry out fault isolation one has to study the correlation between observed events and fault events of the system. In general, such study calls for exploration of the state space of the system, which is exponential in the number of system components. Since we are studying a restricted class of all possible systems we may apply aggressive specialized abstraction policies in order to allow fault isolation without ever considering the often intractably large state space of the system. In this thesis we describe a mathematical framework as well as a prototype implementation and an experimental evaluation of such abstraction techniques. The method is efficient enough to allow for not only post mortem fault isolation but also design time diagnosability analysis of the system, which can be seen as a non-trivial way of analyzing all possible observations of the system versus the corresponding fault isolation outcome. This work has been supported by VINNOVA’s Competence Center ISIS.

Life expectancy has continuously increased in most countries over the last decades and will probably continue to increase in the future. This leads to new challenges relative to the autonomy and the independence of elderly. The development of Smart Homes is a direction to face these challenges and to enable people to live longer in a safe and comfortable environment. Making a home smart consists in placing sensors, actuators and a controller in the house in order to take into account the behavior of their inhabitants and to act on their environment to improve their safety, health and comfort. Most of these approaches are based on the real-time indoor Location Tracking of the inhabitants. In this thesis, a whole new approach for model-based Location Tracking of an a priori unknown number of inhabitants is proposed. This approach is based on Discrete Event Systems paradigms, theory and tools. The usage of Finite Automata (FA) to model the detectable motion of the inhabitants as well as different methods to create such FA models have been developed. Based on these models, algorithms to perform efficient Location Tracking are defined. Finally, several approaches aiming at evaluating the relevance of the instrumentation of a Smart Home with the objective of Location Tracking are proposed. The approach has also been fully implemented and tested. Throughout the thesis, the different contributions are illustrated on case studies.

It is well known that the optimal nonblocking supervisory control problem of timed discrete event systems is NP-hard, subject in particular to state space explosion that is exponential in the number of system components. In this thesis, we propose to manage complexity by organizing the system as a Timed State Tree Structure (TSTS). TSTS are an adaptation of STS to timed Supervisory Control Theory (SCT). Based on TSTS we present an e±cient recursive symbolic algorithm that can perform nonblocking supervisory control design for systems of state size 10^12 and higher. Failure diagnosis is the process of detecting and identifying deviations of a system from its normal behavior using the information available through sensors. A method for fault diagnosis of the TSTS model is proposed. A state based diagnoser is constructed for each timed holon of TSTS. Fault diagnosis is accomplished using the state estimates provided by the timed holon diagnosers. The diagnosers may communicate among each other in order to update their state estimates. At any given time, only a subset of the diagnosers are operational, and as a result, instead of the entire model of the system, only the models of the timed holons associated with the operational diagnosers are used. It is shown that the computational complexity of constructing and storing the transition systems required for diagnosis in the proposed approach is polynomial in the number of system components, whereas in the original monolithic approach the computational complexity is exponential.

It is well known that the optimal nonblocking supervisory control problem of timed discrete event systems is NP-hard, subject in particular to state space explosion that is exponential in the number of system components. In this thesis, we propose to manage complexity by organizing the system as a Timed State Tree Structure (TSTS). TSTS are an adaptation of STS to timed Supervisory Control Theory (SCT). Based on TSTS we present an e±cient recursive symbolic algorithm that can perform nonblocking supervisory control design for systems of state size 10^12 and higher. Failure diagnosis is the process of detecting and identifying deviations of a system from its normal behavior using the information available through sensors. A method for fault diagnosis of the TSTS model is proposed. A state based diagnoser is constructed for each timed holon of TSTS. Fault diagnosis is accomplished using the state estimates provided by the timed holon diagnosers. The diagnosers may communicate among each other in order to update their state estimates. At any given time, only a subset of the diagnosers are operational, and as a result, instead of the entire model of the system, only the models of the timed holons associated with the operational diagnosers are used. It is shown that the computational complexity of constructing and storing the transition systems required for diagnosis in the proposed approach is polynomial in the number of system components, whereas in the original monolithic approach the computational complexity is exponential.

The aim of this study is to solve Fault Detection and Diagnosis (FDD) problems occurring in nonlinear dynamical systems by using model and knowledge-based FDD methods and to give a priority and a degree about faults. For this purpose, three model-based FDD approaches, called FDD by utilizing principal component analysis (PCA), system identification based FDD and inverse model based FDD are introduced. Performances of these approaches are tested on different nonlinear dynamical systems starting from simple to more complex. New fuzzy discrete event system (FDES) and fuzzy discrete event dynamical system (FDEDS) concepts are introduced and their applicability to an FDD problem is investigated. Two knowledge-based FDD methods based on FDES and FDEDS structures using a fuzzy rule-base are introduced and they are tested on nonlinear dynamical systems. New properties related to FDES and FDEDS such as fuzzy observability and diagnosibility concepts and a relation between them are illustrated. A dynamical rule-base extraction method with classification techniques and a dynamical and a static diagnoser design methods are also introduced. A nonlinear and event based extension of the Luenberger observer and its application as a diagnoser to isolate faults are illustrated. Finally, comparisons between the proposed model and knowledge-based FDD methods are made.