Circadian rhythms exist in almost all of living species, and they occupy an important role in daily biological activities of these species. This thesis deals with reduction of measurements in circadian models, and recovery of circadian phases. Two mathematical models of circadian rhythms are considered, with a 3rd order model for Neurospora, and a 7th order model for Mammals. The reduction of measurements of circadian models is shown by the proposals of observer designs to the two mathematical models of circadian rhythms. Both mathematical models contain strong nonlinearities, which make the observer design challenging. Two observer designs, reduced-order and one-sided Lipschitz, are applied to the circadian models to tackle the nonlinearities. Reduced-order observer design is based on a state transformation to make certain nonlinearities have no impact on the observer errors, and the design of one-sided Lipschitz observer is based on systems with one-sided Lipschitz nonlinearities. Both observer designs are based on the existing methods in literature. The existing method of reduced-order observer has been applied to a class of multi-output nonlinear systems. A new reduced-order observer design which extends the existing one in literature is presented in this thesis. In this new reduced-order observer method, the observer error dynamics can be designed by choosing the observer gain, unlike the existing one, of which the observer error dynamics depend on the invariant zeros under certain input-output map. The recovery of circadian phases is carried out to provide a solution to phase shifts occurred in circadian disorders. The restoration of circadian phases is performed by the synchronizations of trajectories of a controlled model with trajectories of a reference model. The reference model and the controlled model have phase differences, and both these models are based on a given 3rd order model of Neurospora circadian rhythms. The phase differences are reflected by different initial conditions, and by parameter uncertainty. The synchronizations of the two models are performed by using back-stepping method for the case of different initial conditions, and by using adaptive back-stepping method for the remaining case. Several simulation studies of the proposed observer designs and the proposed schemes of synchronizations are carried out with the results shown in this thesis.

In dieser Arbeit werden die dynamischen Strukturen und Mannigfaltigkeiten in geschlossenen chaotischen Systemen untersucht. Das Wissen um diese dynamischen Strukturen (und Mannigfaltigkeiten) ist von Bedeutung, da sie uns einen ersten Überblick über die Dynamik des Systems geben, dass heisst, mit ihrer Hilfe sind wir in der Lage, das System zu charakterisieren und eventuell sogar seine Dynamik vorherzusagen. Die Visualisierung der dynamischen Strukturen, speziell in geschlossenen chaotischen Systemen, ist ein schwieriger und oft langer Prozess. Hier werden wir die sogenannte 'Leaking-Methode' (an Beispielen einfacher mathematischer Modelle wie der Bäcker- oder der Sinus Abbildung) vorstellen, mit deren Hilfe wir die Möglichkeit haben, Teile der Mannigfaltigkeiten des chaotischen Sattels des Systems zu visualisieren. Vergleiche zwischen den gewonnenen Strukturen und Strukturen die durch chemische oder biologische Reaktionen hervorgerufen werden, werden anhand eines kinematischen Modells des Golfstroms durchgeführt. Es wird gezeigt, dass mittels der Leaking-Methode dynamische Strukturen auch in Umweltsystemen sichtbar gemacht werden können. Am Beispiel eines realistischen Modells des Mittelmeeres erweitern wir die Leaking-Methode zur sogenannten 'Exchange-Methode'. Diese erlaubt es den Transport zwischen zwei Regionen zu charakterisieren, die Transport-Routen und Austausch-Bassins sichtbar zu machen und die Austausch-Zeiten zu berechnen. Austausch-Bassins und Zeiten werden für die nördliche und südliche Region des westlichen Mittelmeeres präsentiert. Weiterhin werden Mischungseigenschaften im Erdmantel charakterisiert und die geometrischen Eigenschaften von Mannigfaltigkeiten in einem 3dimensionalen mathematischen Modell (ABC-Abbildung) untersucht. / In this thesis, dynamical structures and manifolds in closed chaotic flows will be investigated. The knowledge about the dynamical structures (and manifolds) of a system is of importance, since they provide us first information about the dynamics of the system - means, with their help we are able to characterize the flow and maybe even to forecast it`s dynamics. The visualization of such structures in closed chaotic flows is a difficult and often long-lasting process. Here, the so-called 'Leaking-method' will be introduced, in examples of simple mathematical maps as the baker- or sine-map, with which we are able to visualize subsets of the manifolds of the system`s chaotic saddle. Comparisons between the visualized manifolds and structures traced out by chemical or biological reactions superimposed on the same flow will be done in the example of a kinematic model of the Gulf Stream. It will be shown that with the help of the leaking method dynamical structures can be also visualized in environmental systems. In the example of a realistic model of the Mediterranean Sea, the leaking method will be extended to the 'exchange-method'. The exchange method allows us to characterize transport between two regions, to visualize transport routes and their exchange sets and to calculate the exchange times. Exchange times and sets will be shown and calculated for a northern and southern region in the western basin of the Mediterranean Sea. Furthermore, mixing properties in the Earth mantle will be characterized and geometrical properties of manifolds in a 3dimensional mathematical model (ABC map) will be investigated.

Systems of Systems (SoS) have received a lot of attention recently. In this thesis we will focus on SoS that are built atop the techniques of Service-Oriented Architectures and thus combine the benefits and challenges of both paradigms. For this thesis we will understand SoS as ensembles of single autonomous systems that are integrated to a larger system, the SoS. The interesting fact about these systems is that the previously isolated systems are still maintained, improved and developed on their own. Structural dynamics is an issue in SoS, as at every point in time systems can join and leave the ensemble. This and the fact that the cooperation among the constituent systems is not necessarily observable means that we will consider these systems as open systems. Of course, the system has a clear boundary at each point in time, but this can only be identified by halting the complete SoS. However, halting a system of that size is practically impossible. Often SoS are combinations of software systems and physical systems. Hence a failure in the software system can have a serious physical impact what makes an SoS of this kind easily a safety-critical system. The contribution of this thesis is a modelling approach that extends OMG's SoaML and basically relies on collaborations and roles as an abstraction layer above the components. This will allow us to describe SoS at an architectural level. We will also give a formal semantics for our modelling approach which employs hybrid graph-transformation systems. The modelling approach is accompanied by a modular verification scheme that will be able to cope with the complexity constraints implied by the SoS' structural dynamics and size. Building such autonomous systems as SoS without evolution at the architectural level --- i. e. adding and removing of components and services --- is inadequate. Therefore our approach directly supports the modelling and verification of evolution. / Systems of Systems (SoS) sind ein seit längerem bekanntes Konzept, das jedoch in letzter Zeit vermehrt Aufmerksamkeit erhielt. Das Hauptaugenmerk dieser Arbeit wird auf SoS liegen, die mit Hilfe von Techniken aus Service-Orientierten Architekturen erstellt werden. Somit vereinen die hier betrachteten SoS die Vorteile und Herausforderungen beider Paradigmen. SoS können definiert werden als Zusammenschlüsse einzelner, autonomer Systeme, die zu einem größeren System integriert werden. In diesem Zusammenhang interessant ist, dass die ehemals isolierten Systeme nach wie vor isoliert voneinander weiterentwickelt und gewartet werden. Desweiteren kommt der Strukturdynamik innerhalb des SoS eine beachtliche Bedeutung zu, da jederzeit Systeme dem SoS beitreten und es verlassen können. Zusammen mit der Tatsache, dass die Kooperationen zwischen den konstituierenden Systemen nicht immer beobachtbar sind, führt dies dazu, dass wir diese Systeme als offene Systeme bezeichnen. Wobei das System natürlich jederzeit eine klar definierte Grenze besitzt, diese aber nur durch ein Anhalten des Systems zu bestimmen ist. Dies jedoch ist, von einer praktischen Perspektive aus betrachtet, unmöglich. Häufig stellen SoS eine Kombination aus Softwaresystemen und pyhsikalischen Systemen dar mit der Folge, dass ein Fehler in der Software eine SoS schnell eine immense physikalische Wirkung entwickeln kann. Von daher fallen SoS leicht in die Klasse der sicherheitskritischen Systeme. In dieser Arbeit werden wir einen Modellierungsansatz vorstellen, der die Sprache SoaML der OMG erweitert. Die grundlegenden Konzepte dieses Ansatzes sind die Modellierung mit Kollaborationen und Rollen als Abstraktionsebene über Komponenten. Der vorgestellte Ansatz erlaubt es uns SoS auf einer architekturellen Ebene zu betrachten. Die formale Semantik unseres Modellierungsansatzes ist durch hybride Graphtransformationssysteme gegeben. Abgestimmt auf die Modellierung werden wir ebenfalls ein Verfahren zu Verifikation von SoS vorstellen, welches trotz der inhärenten Komplexität von SoS, diese zu verifizieren. Die Modellierung und Verifikation von Evolution wird von unserem Ansatz direkt unterstützt.

Thesis (MPhil)--University of Stellenbosch, 2006. / On title page: Master of Philosophy (Information and Knowledge Management). Bibliography. Also available via the Internet.

This thesis deals with the critical systems thinking (CST) and its necessity and usability within a commercial company. Critical systems thinking is defined and explained from different perspectives, first as a specific way of approaching a problem, but as a tool for problem solving as well. The thesis also details the specific skills of critical systems thinking and systems archetypes and identifies some interrelations between CST and a specific commercial company with its needs. The practical part is focused on the process of solving specific problems using critical systems thinking, it also discusses the benefits and limitations and evaluates the overall necessity of CST for a commercial company.

published_or_final_version / Computer Science / Master / Master of Philosophy

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.

Stream programming is a paradigm where a program is structured by a set of computational nodes connected by streams. Focusing on data moving between computational nodes via streams, this programming model fits well for applications that process long sequences of data. We call such applications reactive stream programs (RSPs) to distinguish them from stream programs with rather small and finite input data. In stream programming, concurrency is expressed implicitly via communication streams. This helps to reduce the complexity of parallel programming. For this reason, stream programming has gained popularity as a programming model for parallel platforms. However, it is also challenging to analyse and improve the performance without an understanding of the program's internal behaviour. This thesis targets an effi cient execution model for deploying RSPs on parallel platforms. This execution model includes a monitoring framework to understand the internal behaviour of RSPs, scheduling strategies for RSPs on uniform shared-memory platforms; and mapping techniques for deploying RSPs on heterogeneous distributed platforms. The foundation of the execution model is based on a study of the performance of RSPs in terms of throughput and latency. This study includes quantitative formulae for throughput and latency; and the identification of factors that influence these performance metrics. Based on the study of RSP performance, this thesis exploits characteristics of RSPs to derive effective scheduling strategies on uniform shared-memory platforms. Aiming to optimise both throughput and latency, these scheduling strategies are implemented in two heuristic-based schedulers. Both of them are designed to be centralised to provide load balancing for RSPs with dynamic behaviour as well as dynamic structures. The first one uses the notion of positive and negative data demands on each stream to determine the scheduling priorities. This scheduler is independent from the runtime system. The second one requires the runtime system to provide the position information for each computational node in the RSP; and uses that to decide the scheduling priorities. Our experiments show that both schedulers provides similar performance while being significantly better than a reference implementation without dynamic load balancing. Also based on the study of RSP performance, we present in this thesis two new heuristic partitioning algorithms which are used to map RSPs onto heterogeneous distributed platforms. These are Kernighan-Lin Adaptation (KLA) and Congestion Avoidance (CA), where the main objective is to optimise the throughput. This is a multi-parameter optimisation problem where existing graph partitioning algorithms are not applicable. Compared to the generic meta-heuristic Simulated Annealing algorithm, both proposed algorithms achieve equally good or better results. KLA is faster for small benchmarks while slower for large ones. In contrast, CA is always orders of magnitudes faster even for very large benchmarks.

Contexte : Les systèmes à logiciels prépondérants sont de plus en plus interopérables formant des alliances nommées « Systèmes-des-Systèmes » (SdS). Les applications des SdS peuvent aller des systèmes de gestion du trafic jusqu’aux systèmes de gestion de crises. Étant donné que les SdS supportent souvent des domaines critiques, ils doivent être fiables en traitant les disfonctionnements ou les défauts et en évitant les défaillances qui pourraient causer des dégâts et pertes importantes aux utilisateurs.Problème : Ajuster les opérations d’un SdS dépend d’une spécification précise et une attestation rigoureuse de sa consistance opérationnelle. Cependant, en plus des limitations des langages pour capturer conjointement la structure et le comportement des SdS, les prédictions de la consistance opérationnelle des SdS reposent sur leurs systèmes constitutifs qui ne sont pas totalement connus au moment de la conception. Par conséquent, les SdS ont été développés et déployés sans évaluation de leurs opérations, puisque les langages actuels ne supportent pas ce type de précision lors de l’évaluation. Objectif : Cette thèse fournit des solutions théoriques et pratiques basées sur un langage formel de description d’architectures pour supporter une évaluation précoce des opérations du SdS par rapport à la structure et le comportement du SdS à travers les simulations. Contributions : Les contributions essentielles de ce projet comprennent (i) une approche de transformation des modèles pour produire automatiquement des modèles de simulation à partir des descriptions des architectures logicielles du SdS, combinant la description structurelle et comportementale du SdS dans la même solution, (ii) une méthode d’évaluation de l’architecture logicielle du SdS pour la prédiction des opérations du SdS tout en considérant les changements inhérents qui peuvent se produire, (iii) la modélisation de l’environnement et la génération automatique des générateurs de stimulus pour soutenir la simulation des SdS, livrant des données pour nourrir tel simulation, et (iv) une méthode pour la synchronisation automatique entre l’architecture descriptive d’exécution (qui change à l’exécution par suite de l’architecture dynamique) et son architecture prescriptive d’origine basée sur des mécanismes de découverte et de récupération de modèles et une transformation de modèle à l'envers.Évaluation : Nous avons conduit des cas d’études pour évaluer nos approches en utilisant le SdS de surveillance des inondations et le SdS d’espace.Résultats : Notre approche montre une précision importante pour (i) produire des simulations des architectures logicielles des SdS sans failles et complètement opérationnelles, (ii) supporte une évaluation et une prédiction fiable des opérations du SdS à la phase de conception, (iii) génère de manière automatique des générateurs de stimuli pour soutenir et nourrir l’exécution de la simulation et (iv) maintien la synchronisation entre les versions descriptives et prescriptives de l’architecture du SdS.Conclusion : Nous avons conclu que les approches proposées font évoluer l’état de l’art de l’évaluation des architectures logicielles des SdS en offrant des solutions pour prédire l’efficacité des opérations du SdS pour maintenir une opération continue malgré les changements architecturaux, fournissant plus de confidence aux utilisateurs qui reposent dans l’avenir sur les services du SdS. / Context: Software-intensive systems have been increasingly interoperated forming alliances termed as “Systems-of-Systems” (SoS). SoS comprises a collection of systems joined to achieve a set of missions that none of the systems can individually accomplish. Each constituent system keeps its own management, goals, and resources while coordinating within the SoS and adapting to meet SoS goals. Applications of SoS range from traffic control to emergency response and crisis management. As SoS often support critical domains, such systems must be trustworthy by dealing with malfunction or defects and avoiding failures that could cause extensive damage and losses to the users.Problem: Correct SoS operations depend on a precise specification of the SoS structure and a rigorous attestation of its behaviors. However, besides limitations on languages to jointly capture SoS structure and behavior, predictions on the SoS emergent behaviors rely on constituent systems not totally known at design-time. Therefore, SoS have been developed and deployed without evaluating their operation, since current languages do not support such precision in evaluation.Objectives: This PhD project provides solutions founded on a formal architectural description language to support an early evaluation of SoS behaviors regarding its inherent SoS structure and dynamics through simulations.Contribution: The main contributions of this project comprise (i) a model transformation approach for automatically producing simulation models from SoS software architecture descriptions, combining SoS structure and behavior description in a same solution, (ii) a SoS software architecture evaluation method for SoS operation prediction considering the inherent changes that can occur, (iii) environment modeling and automatic generation of stimuli generators to sustain the SoS simulation, delivering data to feed such simulation, and (iv) a method for the automatic synchronization between the runtime descriptive architecture (changed at runtime due to dynamic architecture) and its original prescriptive architecture based on model discovery and recovery mechanisms and a backward model transformation.Evaluation: We conducted case studies to assess our approaches using Flood Monitoring SoS and Space SoS.Results: Our approaches show a high accuracy to (i) produce fault-free and operational simulations for SoS software architectures, (ii) support a reliable evaluation and prediction of SoS operation at design-time, (iii) automatically generate stimuli generators to sustain and feed the simulation execution, and (iv) maintain the synchronization between descriptive and prescriptive versions of the SoS architecture.Conclusions: We concluded that the proposed approaches advance the state of the art in SoS software architecture evaluation by offering solutions to predict the SoS operations effectiveness to maintain a continuous operation despite architectural changes, providing more trust for users that in the future shall rely on SoS services.

Systems-of-Systems (SoS) encompass diverse and independent systems that must cooperate with each other for performing a combined action that is greater than their individual capabilities. In parallel, architecture descriptions, which are the main artifact expressing software architectures, play an important role in fostering interoperability among constituents by facilitating the communication among stakeholders and supporting the inspection and analysis of the SoS from an early stage of its life cycle. The main problem addressed in this thesis is the lack of adequate architectural descriptions for SoS that are often built without an adequate care to their software architecture. Since constituent systems are, in general, not known at design-time due to the evolving nature of SoS, the architecture description must specify at design-time which coalitions among constituent systems are feasible at run-time. Moreover, as many SoS are being developed for safety-critical domains, additional measures must be placed to ensure the correctness and completeness of architecture descriptions. To address this problem, this doctoral project employs SoSADL, a formal language tailored for the description of SoS that enables one to express software architectures as dynamic associations between independent constituent systems whose interactions are mediated for accomplishing a combined action. To synthesize concrete architectures that adhere to one such description, this thesis develops a formal method, named Ark, that systematizes the steps for producing such artifacts. The method creates an intermediate formal model, named TASoS, which expresses the SoS architecture in terms of a constraint satisfaction problem that can be automatically analyzed for an initial set of properties. The feedback obtained in this analysis can be used for subsequent refinements or revisions of the architecture description. A software tool named SoSy was also developed to support the Ark method as it automates the generation of intermediate models and concrete architectures, thus concealing the use of constraint solvers during SoS design and development. The method and its accompanying tool were applied to model a SoS for urban river monitoring in which the feasibility of candidate abstract architectures is investigated. By formalizing and automating the required steps for SoS architectural synthesis, Ark contributes for adopting formal methods in the design of SoS architectures, which is a necessary step for obtaining higher reliability levels. / Sistemas-de-sistemas (SoS) englobam sistemas diversos e independentes que cooperam entre si para executar uma ação combinada que supera suas competências individuais. Em paralelo, descrições arquiteturais são artefatos que expressam arquiteturas de software, desempenhando no contexto de SoS um importante papel na promoção da interoperabilidade entre constituintes ao facilitar a comunicação entre interessados e apoiar atividades de inspeção e análise desde o início de seu ciclo de vida. O principal problema abordado nessa tese consiste na falta de descrições arquiteturais adequadas para SoS que estão sendo desenvolvidos sem um devido cuidado à sua arquitetura de software. Uma vez que os sistemas constituintes não são necessariamente conhecidos em tempo de projeto devido à natureza evolucionária dos SoS, a descrição arquitetural precisa definir em tempo de projeto quais coalisões entre sistemas constituintes são possíveis em tempo de execução. Como muitos desses sistemas são desenvolvidos para o domínio crítico de segurança, medidas adicionais precisam ser adotadas para garantir a correção e completude da descrição arquitetural. Visando tratar esse problema, esse projeto de doutorado emprega SosADL, uma linguagem formal criada especialmente para o domínio de SoS que permite expressar arquiteturas de software como associações dinâmicas entre sistemas independentes em que as interações devem ser mediadas para desempenhar uma ação conjunta. Em particular, é proposto um novo método formal, denominado Ark, para sistematizar os passos necessários na síntese de arquiteturas concretas aderentes a essa descrição. Para isso, o método cria um modelo formal intermediário, denominado TASoS, que expressa a arquitetura do SoS em termos de um problema de satisfatibilidade de restrições, possibilitando desse modo a verificação automática de um conjunto inicial de propriedades. O resultado obtido por essa análise pode ser utilizado em refinamentos e revisões subsequentes da descrição arquitetural. Uma ferramenta de apoio denominada SoSy também foi desenvolvida para automatizar a geração de modelos intermediários e arquiteturas concretas, ocultando o uso de solucionadores de restrições no projeto e desenvolvimento de SoS. O método e sua ferramenta foram aplicados em um modelo de SoS para monitoramento de rios em áreas urbanas em que a viabilidade de arquiteturas abstratas foi investigada. Ao formalizar e automatizar os passos necessários para a síntese arquitetural de SoS, é possível adotar métodos formais no projeto arquitetural de SoS, que são necessários para alcançar níveis maiores de confiabilidade.