Zuweilen wird gefördertes Erdgas als eine Brückentechnologie noch eine Weile erhalten bleiben, aber unsere Gasnetzinfrastruktur hat auch in einer Ära post-fossiler Brennstoffe eine Zukunft, um Klima-neutral erzeugtes Methan, Ammoniak oder Wasserstoff zu transportieren. Damit die Dispatcher der Zukunft, in einer sich fortwährend dynamisierenden Marktsituation, mit sich beständig wechselnden Kleinstanbietern, auch weiterhin einen sicheren Gasnetzbetrieb ermöglichen und garantieren können, werden sie auf moderne, schnelle Simulations- sowie performante Optimierungstechnologie angewiesen sein. Der Schlüssel dazu liegt in einem besseren Verständnis zur numerischen Behandlung nicht differenzierbarer Funktionen und diese Arbeit möchte einen Beitrag hierzu leisten. Wir werden stückweise differenzierbare Funktionen in sog. Abs-Normalen Form betrachten. Durch einen Prozess, der Abs-Linearisierung genannt wird, können wir stückweise lineare Approximationsmodelle erster Ordnung, mittels Techniken der algorithmischen Differentiation erzeugen. Jene Modelle können über Matrizen und Vektoren mittels gängiger Software-Bibliotheken der numerischen linearen Algebra auf Computersystemen ausgedrückt, gespeichert und behandelt werden. Über die Generalisierung der Formel von Faà di Bruno können auch Splinefunktionen höherer Ordnung generiert werden, was wiederum zu Annäherungsmodellen mit besserer Güte führt. Darauf aufbauend lassen sich gemischte Taylor-Kollokationsmethoden, darunter die mit Ordnung zwei konvergente generalisierte Trapezmethode, zur Integration von Gasnetzen, in Form von nicht glatten Algebro-Differentialgleichungssystemen, definieren. Numerische Experimente demonstrieren das Potential. Da solche implizite Integratoren auch nicht lineare und in unserem Falle zugleich auch stückweise differenzierbare Gleichungssysteme erzeugen, die es als Unterproblem zu lösen gilt, werden wir uns auch die stückweise differenzierbare, sowie die stückweise lineare Newtonmethode betrachten. / As of yet natural gas will remain as a bridging technology, but our gas grid infrastructure does have a future in a post-fossil fuel era for the transportation of carbon-free produced methane, ammonia or hydrogen. In order for future dispatchers to continue to enable and guarantee safe gas network operations in a continuously changing market situation with constantly switching micro-suppliers, they will be dependent on modern, fast simulation as well as high-performant optimization technology. The key to such a technology resides in a better understanding of the numerical treatment of non-differentiable functions and this work aims to contribute here. We will consider piecewise differentiable functions in so-called abs-normal form. Through a process called abs-linearization, we can generate piecewise linear approximation models of order one, using techniques of algorithmic differentiation. Those models can be expressed, stored and treated numerically as matrices and vectors via common software libraries of numerical linear algebra. Generalizing the Faà di Bruno's formula yields higher order spline functions, which in turn leads to even higher order approximation models. Based on this, mixed Taylor-Collocation methods, including the generalized trapezoidal method converging with an order of two, can be defined for the integration of gas networks represented in terms of non-smooth system of differential algebraic equations. Numerical experiments will demonstrate the potential. Since those implicit integrators do generate non-linear and, in our case, piecewise differentiable systems of equations as sub-problems, it will be necessary to consider the piecewise differentiable, as well as the piecewise linear Newton method in advance.

In diesem Buch schlage ich eine radikal neuartige Sicht auf den Utilitarismus vor. Meine Hauptthese ist, dass der Utilitarismus selbst keine vollständige normative Theorie ist, aus der sich per se Handlungsbewertungen ableiten ließen, sondern normativ untersättigt und neutral ist. Sein normativer Gehalt ist vollständig abhängig von angenommenen Nutzenfunktionen. Jede konsistente Menge von moralischen Regeln (Moralsystem) kann, wie ich im Anhang beweise, als ein Spezialfall des Utilitarismus interpretiert werden. Um dies zu explizieren, stelle ich utilitaristische Interpretationen verschiedener Moralpositionen vor: Zwei alltagsmoralische Regeln (das Gebot, Versprechen zu halten und das Tötungsverbot), egalitäre Positionen zu Verteilungsfragen sowie die Rawls’sche Theorie der Gerechtigkeit. Hierbei gebe ich stets korrespondierende Nutzenfunktionen an, deren Vorliegen Utilitaristen auf die interpretierten moralischen Positionen verpflichtet. Die Frage nach dem normativen Gehalt des Utilitarismus schlechthin ist somit falsch gestellt. Ein Großteil der Kritik des Utilitarismus als moralische Theorie läuft ins Leere, denn sie kritisiert einen solchen nur scheinbar eigenständigen normativen Gehalt des Utilitarismus, den sie selbst durch unterstellte Nutzenfunktionen erst erzeugt. Die Verteidigung des Utilitarismus verfehlt ebenso oft das Ziel, wenn sie zur Rettung des Utilitarismus an sich konkurrierende Nutzenfunktionen ins Feld führt, ohne die normative Neutralität des Utilitarismus generell zu thematisieren. Diese normative Neutralität macht den Utilitarismus gleichsam zur Normalform der Ethik, denn jeder moralische Disput lässt sich in einen Disput über korrespondierende Nutzenfunktionen überführen. Der Utilitarismus ist also nicht moralische Theorie, sondern vielmehr die Methode der Ethik. / In this book I suggest to look at utilitarianism in a radical new way. My key starting point is that utilitarianism in itself is not a complete normative theory from which judgements of actions could be drawn but instead that utilitarianism is normatively undersaturated and neutral. Its normative content is entirely dependent on assumed utility functions. Every consistent set of moral rules (moral system) can, as I prove in the appendix, be interpreted as a special case of utilitarianism. To explicate this, I give utilitarian interpretations of a number of different moral positions: two everyday moral rules (the rule to keep promises and the prohibition of killing), egalitarian positions on distribution, and the Rawlsian theory of justice. In each case I propose corresponding utility functions that commit utilitarians to the interpreted moral position. Thus, asking about the normative content of utilitarianism in itself is meaningless. Much of the critique of utilitarianism as a moral theory misses the point as it criticizes such an assumed normative content of utilitarianism in itself while imputing the existence of certain utility functions. Many defendants of utilitarianism fall for the same mistake, as they propose rival utility functions to rescue their assumed normative content of utilitarianism without addressing the general normative neutrality of utilitarianism. For this normative neutrality, utilitarianism can be viewed as the normal form of ethics, because every moral dispute can be translated into a dispute over corresponding utility functions. Therefore, Utilitarianism is not a moral theory, but rather the method of ethics.

No description available.

No description available.

Many control algorithms for ABS systems have been proposed in the literature since the introduction of this equipment by Bosch in 1978. In general, one can divide these control algorithms into two different types: those based on a regulation logic with wheel acceleration thresholds that are used by most commercial ABS systems; and those based on wheel slip control that are preferred in the large majority of academic algorithms. Each approach has its pros and cons [Shida 2010]. Oversimplifying, one can say that the strength of the first ones is their robustness; while that of the latter ones their short braking distances (on dry grounds) and their absence of limit cycles. At the midpoint of this industry/academy dichotomy, based on the concept of extended braking stiffness (XBS), a quite different class of ABS control strategies has been proposed by several researchers (see, e.g., [Sugai 1999] and [Ono 2003]). This concept combines the advantages from both the industrial and academic approaches. Nevertheless, since the slope of the tyre characteristic is not directly measurable, it introduces the question of real-time XBS estimation. The first part of this thesis is devoted to the study of this estimation problem and to a generalization of the proposed technique to a larger class of systems. From the technological point of view, the design of ABS control systems is highly dependent on the ABS system characteristics and actuator performance. Current ABS control algorithms on passenger cars, for instance the Bosch ABS algorithm, are based on heuristics that are deeply associated to the hydraulic nature of the actuator. An interesting observation is that they seem to work properly only in the presence of a specific delay coming from the hydraulic actuation [Gerard 2012]. For brake systems that have different delays compared to those of hydraulic actuators, like electric in-wheel motors (with a smaller delay) or pneumatic trailer brakes (with a bigger delay), they might be no longer suitable [Miller 2013]. Therefore, adapting standard ABS algorithms to other advanced actuators becomes an imperative goal in the automobile industry. This goal can be reached by the compensation of the delays induced by actuators. The second part of this thesis is focused on this issue, and to the generalization of the proposed technique to a particular class of nonlinear systems. Throughout this thesis, we employ two different linearization techniques: the linearization of the error dynamics in the construction of model-based observers [Krener 1983] and the linearization based on restricted state feedback [Brockett 1979]. The former is one of the simplest ways to build an observer for dynamical systems with output and to analyze its convergence. The main idea is to transform the original nonlinear system via a coordinate change to a special form that admits an observer with a linear error dynamics and thus the observer gains can be easily computed to ensure the observer convergence. The latter is a classical method to control nonlinear systems by converting them into a controllable linear state equation via the cancellation of their nonlinearities. It is worth mentioning that existing results for observer design by error linearization in the literature are only applied to the case of regular time scalings ([Guay 2002] and [Respondek 2004]). The thesis shows how to extend them to the case of singular time scalings. Besides, the thesis combines the classical state feedback linearization with a new method for the input delay compensation to resolve the output tracking problem for restricted feedback linearizable systems with input delays.

This thesis investigates decision-making in two-player imperfect information games against opponents whose actions can affect our rewards, and whose strategies may be based on memories of interaction, or may be changing, or both. The focus is on modelling these dynamic opponents, and using the models to learn high-reward strategies. The main contributions of this work are: 1. An approach to learn high-reward strategies in small simultaneous-move games against these opponents. This is done by using a model of the opponent learnt from sequence prediction, with (possibly discounted) rewards learnt from reinforcement learning, to lookahead using explicit tree search. Empirical results show that this gains higher average rewards per game than state-of-the-art reinforcement learning agents in three simultaneous-move games. They also show that several sequence prediction methods model these opponents effectively, supporting the idea of using them from areas such as data compression and string matching; 2. An online expectation-maximisation algorithm that infers an agent's hidden information based on its behaviour in imperfect information games; 3. An approach to learn high-reward strategies in medium-size sequential-move poker games against these opponents. This is done by using a model of the opponent learnt from sequence prediction, which needs its hidden information (inferred by the online expectation-maximisation algorithm), to train a state-of-the-art no-regret learning algorithm by simulating games between the algorithm and the model. Empirical results show that this improves the no-regret learning algorithm's rewards when playing against popular and state-of-the-art algorithms in two simplified poker games; 4. Demonstrating that several change detection methods can effectively model changing categorical distributions with experimental results comparing their accuracies to empirical distributions. These results also show that their models can be used to outperform state-of-the-art reinforcement learning agents in two simultaneous-move games. This supports the idea of modelling changing opponent strategies with change detection methods; 5. Experimental results for the self-play convergence to mixed strategy Nash equilibria of the empirical distributions of plays of sequence prediction and change detection methods. The results show that they converge faster, and in more cases for change detection, than fictitious play.

This work focuses on proposition of transfer of the expressions entered in the C pro­gramming language into DIMACS format and creation of program in programming language C++ making this transfer. This work contains a description of the C pro­gramming language and its operators. It also con­tains a description of the conjunctive normal form and a descri­ption of the DIMACS format. Following is a proposal for a program for the transfer of expression in the C programming language to the DIMACS format and description of reali­zation of program performing this transfer.

The main goal of this masther thesis is design and implementation of library for reduction of strategy profiles of strategy games in normal form. Logics of library functionality will be based on suitable heuristics founded on methods of iterative elimination of dominated strategies and FDDS. Functionality of resultant library will be demonstrated on convenient problems.

Normalformen drücken semantische Eigenschaften einer Logik durch syntaktische Restriktionen aus. Sie ermöglichen es Algorithmen, Grenzen der Ausdrucksstärke einer Logik auszunutzen. Ein Beispiel ist die Lokalität der Logik erster Stufe (FO), die impliziert, dass Graph-Eigenschaften wie Erreichbarkeit oder Zusammenhang nicht FO-definierbar sind. Gaifman-Normalformen drücken die Bedeutung einer FO-Formel als Boolesche Kombination lokaler Eigenschaften aus. Sie haben eine wichtige Rolle in Model-Checking Algorithmen für Klassen dünn besetzter Graphen, deren Laufzeit durch die Größe der auszuwertenden Formel parametrisiert ist. Es ist jedoch bekannt, dass Gaifman-Normalformen im Allgemeinen nur mit nicht-elementarem Aufwand konstruiert werden können. Dies führt zu einer enormen Parameterabhängigkeit der genannten Algorithmen. Ähnliche nicht-elementare untere Schranken sind auch für Feferman-Vaught-Zerlegungen und für die Erhaltungssätze von Lyndon, Łoś und Tarski bekannt. Diese Arbeit untersucht die Komplexität der genannten Normalformen auf Klassen von Strukturen beschränkten Grades, für welche die nicht-elementaren unteren Schranken nicht gelten. Für diese Einschränkung werden Algorithmen mit elementarer Laufzeit für die Konstruktion von Gaifman-Normalformen, Feferman-Vaught-Zerlegungen, und für die Erhaltungssätze von Lyndon, Łoś und Tarski entwickelt, die in den ersten beiden Fällen worst-case optimal sind. Wichtig hierfür sind Hanf-Normalformen. Es wird gezeigt, dass eine Erweiterung von FO durch unäre Zählquantoren genau dann Hanf-Normalformen erlaubt, wenn alle Zählquantoren ultimativ periodisch sind, und wie Hanf-Normalformen in diesen Fällen in elementarer und worst-case optimaler Zeit konstruiert werden können. Dies führt zu Model-Checking Algorithmen für solche Erweiterungen von FO sowie zu Verallgemeinerungen der Algorithmen für Feferman-Vaught-Zerlegungen und die Erhaltungssätze von Lyndon, Łoś und Tarski. / Normal forms express semantic properties of logics by means of syntactical restrictions. They allow algorithms to benefit from restrictions of the expressive power of a logic. An example is the locality of first-order logic (FO), which implies that properties like reachability or connectivity cannot be defined in FO. Gaifman's local normal form expresses the satisfaction conditions of an FO-formula by a Boolean combination of local statements. Gaifman normal form serves as a first step in fixed-parameter model-checking algorithms, parameterised by the size of the formula, on sparse graph classes. However, it is known that in general, there are non-elementary lower bounds for the costs involved in transforming a formula into Gaifman normal form. This leads to an enormous parameter-dependency of the aforementioned algorithms. Similar non-elementary lower bounds also hold for Feferman-Vaught decompositions and for the preservation theorems by Lyndon, Łoś, and Tarski. This thesis investigates the complexity of these normal forms when restricting attention to classes of structures of bounded degree, for which the non-elementary lower bounds are known to fail. Under this restriction, the thesis provides algorithms with elementary and even worst-case optimal running time for the construction of Gaifman normal form and Feferman-Vaught decompositions. For the preservation theorems, algorithmic versions with elementary running time and non-matching lower bounds are provided. Crucial for these results is the notion of Hanf normal form. It is shown that an extension of FO by unary counting quantifiers allows Hanf normal forms if, and only if, all quantifiers are ultimately periodic, and furthermore, how Hanf normal form can be computed in elementary and worst-case optimal time in these cases. This leads to model-checking algorithms for such extensions of FO and also allows generalisations of the constructions for Feferman-Vaught decompositions and preservation theorems.

Depuis l'introduction du premier système ABS par Bosch, en 1978, de nombreux algorithmes de commande pour les systèmes ABS ont été proposés dans la littérature. En général, ces algorithmes peuvent être divisés en deux catégories : ceux basés sur une logique de régulation déterminée par des seuils sur l'accélération angulaire des roues et ceux basés sur la régulation du taux de glissement. Chaque approche a ses avantages et ses inconvénients. D'une manière simplifiée, on peut dire que le point fort du premier type est sa robustesse ; tandis que ceux du deuxième type sont leur courte distance de freinage (sur les terrains secs) et leur absence de cycles limite. Au milieu de cette dichotomie industrielle/académique, en se basant sur un concept appelé extended braking stiffness (XBS), une classe complètement différente de stratégies de commande pour l'ABS a été proposée par certains chercheurs. Ce concept combine les avantages des deux approches. Néanmoins, puisque l’XBS n'est pas directement mesurable, elle introduit la question de son estimation en temps réel. La première partie de cette thèse est consacrée à l'étude de ce problème d'estimation et à une généralisation de la technique proposée à une plus grande classe de systèmes. D'un point de vue technologique, la conception des systèmes de contrôle pour l'ABS est fortement dépendante des caractéristiques physiques du système et des performances de l'actionneur. Les algorithmes de commande actuels pour l'ABS sur les véhicules, par exemple l'algorithme ABS de Bosch, sont basés sur des approches heuristiques qui sont profondément liées à la nature hydraulique de l'actionneur. Ils ne fonctionnent correctement qu'en présence d'un retard spécifique associé à la nature hydraulique de l'actionneur. Pour les systèmes de freinage qui ont un retard différent de ceux des actionneurs hydrauliques, comme les moteurs-roues électriques par exemple (un retard plus court) ou les freins pneumatiques des semi-remorques (un retard plus grand), ils ne sont plus appropriés et ont un fonctionnement déficient. Par conséquent, l'adaptation des algorithmes standards de l'ABS pour d'autres actionneurs avancés devient un objectif primordial dans l'industrie automobile. Cet objectif peut être atteint par la compensation des retards induits par les actionneurs. La deuxième partie de cette thèse se concentre sur cette question, et à la généralisation de la technique proposée à une classe particulière de systèmes non linéaires.Tout au long de cette thèse, nous utilisons deux techniques de linéarisation différentes : la linéarisation de la dynamique d'erreur dans la construction des observateurs basés sur des modèles et la linéarisation basée sur le retour d'état restreint. La première est l'une des façons les plus simples pour synthétiser un observateur pour des systèmes dynamiques avec sortie et pour analyser sa convergence. L'idée principale est de transformer le système non linéaire original via un changement de coordonnées en un système différemment formalisé, qui admette un observateur avec une dynamique d'erreur linéaire et les gains de l'observateur peuvent donc être facilement calculés pour en assurer la convergence. Cette dernière est une méthode classique pour commander des systèmes non linéaires en les convertissant en une équation d'état linéaire contrôlable via l'annulation de leurs non-linéarités. Il convient de mentionner que les résultats existants pour la synthèse des observateurs par la linéarisation de l'erreur dans la littérature ne sont appliqués que pour le cas des changements réguliers de l'échelle de temps. Cette thèse explique comment les étendre aux cas des changements singuliers de l'échelle de temps. Par ailleurs, la thèse combine la linéarisation classique par retour d'état avec une nouvelle méthode de compensation du retard de l'entrée pour résoudre le problème de suivi de la sortie pour des systèmes linéarisables par retour d'état restreint avec des retards de l'entrée. / Many control algorithms for ABS systems have been proposed in the literature since the introduction of this equipment by Bosch in 1978. In general, one can divide these control algorithms into two different types: those based on a regulation logic with wheel acceleration thresholds that are used by most commercial ABS systems; and those based on wheel slip control that are preferred in the large majority of academic algorithms. Each approach has its pros and cons [Shida 2010]. Oversimplifying, one can say that the strength of the first ones is their robustness; while that of the latter ones their short braking distances (on dry grounds) and their absence of limit cycles. At the midpoint of this industry/academy dichotomy, based on the concept of extended braking stiffness (XBS), a quite different class of ABS control strategies has been proposed by several researchers (see, e.g., [Sugai 1999] and [Ono 2003]). This concept combines the advantages from both the industrial and academic approaches. Nevertheless, since the slope of the tyre characteristic is not directly measurable, it introduces the question of real-time XBS estimation. The first part of this thesis is devoted to the study of this estimation problem and to a generalization of the proposed technique to a larger class of systems. From the technological point of view, the design of ABS control systems is highly dependent on the ABS system characteristics and actuator performance. Current ABS control algorithms on passenger cars, for instance the Bosch ABS algorithm, are based on heuristics that are deeply associated to the hydraulic nature of the actuator. An interesting observation is that they seem to work properly only in the presence of a specific delay coming from the hydraulic actuation [Gerard 2012]. For brake systems that have different delays compared to those of hydraulic actuators, like electric in-wheel motors (with a smaller delay) or pneumatic trailer brakes (with a bigger delay), they might be no longer suitable [Miller 2013]. Therefore, adapting standard ABS algorithms to other advanced actuators becomes an imperative goal in the automobile industry. This goal can be reached by the compensation of the delays induced by actuators. The second part of this thesis is focused on this issue, and to the generalization of the proposed technique to a particular class of nonlinear systems. Throughout this thesis, we employ two different linearization techniques: the linearization of the error dynamics in the construction of model-based observers [Krener 1983] and the linearization based on restricted state feedback [Brockett 1979]. The former is one of the simplest ways to build an observer for dynamical systems with output and to analyze its convergence. The main idea is to transform the original nonlinear system via a coordinate change to a special form that admits an observer with a linear error dynamics and thus the observer gains can be easily computed to ensure the observer convergence. The latter is a classical method to control nonlinear systems by converting them into a controllable linear state equation via the cancellation of their nonlinearities. It is worth mentioning that existing results for observer design by error linearization in the literature are only applied to the case of regular time scalings ([Guay 2002] and [Respondek 2004]). The thesis shows how to extend them to the case of singular time scalings. Besides, the thesis combines the classical state feedback linearization with a new method for the input delay compensation to resolve the output tracking problem for restricted feedback linearizable systems with input delays.