Cette thèse traite le développement d'un modèle mathématique d'optimisation acoustique des trajectoires de vol de deux avions commerciaux en approche sous contrainte énergétique, aérodynamique et opérationnelle. C'est un modèle analytique de contrôle optimal non-linéaire et non-convexe régi par un système d'équations différentielles ordinaires issues de la dynamique de vol et des contraintes associées. Notre contribution porte sur la modélisation mathématique des équations, l'optimisation et la programmation algorithmique d'un modèle d'optimisation non-linéaire du bruit de deux avions en approche simultanée. Les points abordés sont le développement mathématique du modèle 3D «exact» de leur dynamique de vol, la modélisation mathématique de la commande optimale de ce système dynamique, l'introduction de la consommation du carburant par les avions comme une équation différentielle avec une fonction consommation spécifique variable en fonction de l'évolution de leur dynamique, la modélisation mathématique instantanée de la fonction objectif représentant le bruit global des deux avions en approche. Sa résolution porte sur la méthode directe de programmation séquentielle quadratique avec régions de confiance sous AMPL et KNITRO. Une méthode indirecte a été appliquée sous le principe de maximum de Pontryagin suivie d’une discrétisation de type Runge-Kutta partition-née symplectique d'ordre 4 afin de démontrer la commutation entre l'approche directe et l'approche indirecte. Les résultats obtenus confirment des trajectoires optimales en descente continue, réduisant le bruit au sol ainsi que la consommation de kérosène de deux avions / This thesis develops an mathematical non-linear optimization model of flight paths of two aircraft in approach minimizing the perceived noise on the ground while energetic constraint is considered. This is an analytical model of non-linear and non-convex optimal control governed by a system of ordinary differential equations resulting from the dynamics of flight and with their associated constraints. Our contribution focuses on the mathematical modeling equations, optimization and algorithmic programming of an acoustic non-linear optimization model of two aircraft simultaneously on approach. The addressed issues are the mathematical development of the «correct» 3D model, their flight dynamics, the mathematical modeling of the optimal control of dynamic system, the consideration of fuel consumption by aircraft as a differential equation with a consumption function specific variable depending on the evolution of their dynamics, the mathematical modeling of the instantaneous objective function representing the overall noise of the two approaching aircraft. Resolution deals with the direct method of sequential quadratic programming with confidence regions while AMPL programming language and KNITRO are considered. An indirect method was applied under the Pontryagin maximum principle, followed by a Runge-Kutta symplectic partitioned discretization to demonstrate the commutation between the direct approach and indirect approach. The expected results confirm optimal trajectories reducing ground noise and fuel consumption of two aircraft

A utilização de Redes Neurais Artificias para fins de identificação e controle de sistemas dinâmicos têm recebido atenção especial de muitos pesquisadores, principalmente no que se refere a sistemas não lineares. Neste trabalho é apresentado um estudo sobre a utilização de um tipo em particular de Rede Neural Artificial, uma Perceptron Multicamadas com Atraso de Tempo, na estimação de estados da etapa fermentativa do processo de Reichstein para produção de vitamina C. A aplicação de Redes Neurais Artificiais a este processo pode ser justificada pela existência de problemas associados à esta etapa, como variáveis de estado não mensuráveis e com incertezas de medida e não linearidade do processo fermentativo, além da dificuldade em se obter um modelo convencional que contemple todas as fases do processo. É estudado também a eficácia do algoritmo de Levenberg-Marquadt, na aceleração do treinamento da Rede Neural Artificial, além de uma comparação do desempenho de estimação de estados das Redes Neurais Artificiais estudadas com o filtro estendido de Kalman, baseado em um modelo não estruturado do processo fermentativo. A análise do desempenho das Redes Neurais Artificiais estudadas é avaliada em termos de uma figura de mérito baseada no erro médio quadrático sendo feitas considerações quanto ao tipo da função de ativação e o número de unidades da camada oculta. Os dados utilizados para treinamento e avaliação da Redes Neurais Artificiais foram obtidos de um conjunto de ensaios interpolados para o intervalo de amostragem desejado. / ldentification and Control of dynamic systems using Artificial Neural Networks has been widely investigated by many researchers in the last few years, with special attention to the application of these in nonlinear systems. ls this works, a study on the utilization of a particular type of Artificial Neural Networks, a Time Delay Multi Layer Perceptron, in the state estimation of the fermentative phase of the Reichstein process of the C vitamin production. The use of Artificial Neural Networks can be justified by the presence of problems, such as uncertain and unmeasurable state variables and process non-linearity, and by the fact that a conventional model that works on all phases of the fermentative processes is very difficult to obtain. The efficiency of the Levenberg Marquadt algorithm on the acceleration of the training process is also studied. Also, a comparison is performed between the studied Artificial Neural Networks and an extended Kalman filter based on a non-structured model for this fermentative process. The analysis of lhe Artificial Neural Networks is carried out using lhe mean square errors taking into consideration lhe activation function and the number of units presents in the hidden layer. A set of batch experimental runs, interpolated to the desired time interval, is used for training and validating the Artificial Neural Networks.

Estudamos o conceito de energia na teoria física a nível histórico e a nível de ensino-aprendizagem, isto é, do ponto de vista de sua criação, representação conceitual, matemática e experimental, na constituição de seu significado na teoria científica e na linguagem comum. Como um exercício preliminar, analisamos alguns dados sobre o ensino de conceitos de física na exposição científica do IFUSP \"Ondas, Campos e Partículas\", de 1989 a 1990, e, em 1991, com o nome de \"Do Caleidoscópio ao Carrossel\", no prédio da Engenharia Mecânica (Escola Politécnica). A exposição apresenta fenômenos das teorias da física nos campos da mecânica, eletricidade e magnetismo, termodinâmica e ótica, fenômenos que implicam ações em escalas macroscópicas e a nível atômico. Descrevemos uma entrevista de 13 minutos com quatro alunos de 1o grau que visitaram a exposição com monitoramento. Durante a situação da entrevista, que chamamos de pedagógica, esses alunos constróem o conceito de energia. Essa entrevista é analisada em termos dos contextos fenomenológico e epistemológico, contidos na exposição, ainda que os monitores que acompanharam a visita não falassem em energia. Descrevemos também uma entrevista com um monitor sobre ensino e aprendizagem. Enfocamos o conceito de \"conhecimento prévio do aluno como requisito para ensino\", e analisamos usando o conceito de zona de desenvolvimento proximal (ZDP) de Vygotsky. Usamos a moldura de Vygotsky (VY 1896/1934) na análise da entrevista com os alunos, que é um exemplo de como considerar a ZDP. Ela não visa avaliação, e nem apenas coleta de dados. Propomos o desenvolvimento de entrevistas pedagógicas para já se constituir uma situação de ensino-aprendizagem, como uma interação desejável, dialógica, onde a ZDP, isto é, a capacidade do aluno \"vir a saber\", seja desenvolvida. A análise da emergência do conceito de energia no caso estudado da entrevista com alunos é feita com a perspectiva de sistemas dinâmicos, dada a natureza complexa dos fenômenos estudados. A História e Filosofia das Teorias Científicas são usadas como ferramenta heurística para identificar correlação na constituição do espaço de significação. Concluíremos que, se os monitores não enfocavam diretamente o conceito de energia e os alunos aprendiam mesmo assim, é porque a exposição é um bom contexto onde a entrevista pedagógica pode ser utilizada como instrumento de ensino, Por fim, falamos da necessidade de um treinamento para monitores, onde sua formação inclua estudos históricos e epistemológicos e uma preparação para suprir a deficiência que detetamos na exposição, isto é, a de não abordar os conceitos na sua forma matematizada. A pesquisa das condições para aprendizagem na Exposição Científica e em Entrevista se desenvolve com instrumentos próprios: um sistema de análise em vídeo foi construído para pesquisar a linguagem usada na interação entre professor e aluno. Objetivamos estabelecer condições propícias para interações dialógicas. Como resultado secundário, foi adquirida certa familiaridade em trabalhar com o vídeo como instrumento para, ao mesmo tempo, mostrar e desenvolver aquisição do conhecimento científico de conceitos de física. / We have studied the concept of energy in Physics in the historical and the Teaching-Learning contexts, i.e., from the point of view of its creation, its mathematical and experimental conceptual representation, of its scientific and ordinary meaning constitution. As a preliminary exercise, we analysed some data about the Physics concepts teaching at the \"Waves, Fields and Particles\" Science Exhibition Center located at that time, in the Engineering Building of the University of São Paulo. The content of the Exhibition was regular demonstrations of phenomena delineated by classical theories of Mechanics, Eletromagnetism, Thermodynamics and some topics in Modern Physics. An interpretation of the exhibition could be in terms of the concept of energy and its transformations, as was shown by an interview with four visiting students described here. During this interview set, which we named pedagogical, these students constructed the concept of energy. This interview is analysed in terms of phenomenological and epistemological implications in the exhibition. A monitor thinking about teaching and learning has also been situated out of an interview. This monitor considers the pupil\'s previous subject matter knowledge as a requirement for teaching. By means of the ZDP (zone of proximal development), we are warned by Vygotsky against the extreme pre-requisites, which can limit the learning. We also make use of Vygotsky\'s concept in the analysis of the interview with students. The interview described in the first part of this work is a ZDP application example. It neither aims evaluation nor just data gathering. It will be developed to be a teaching-learning instrument. We believe this is possible, for it will be an interaction where the ZDP or the pupil\'s ability to \"come to know\" is to be considered. The case study of the emergence of the concept of energy from the interview with pupils is analysed within the framework of dynamic systems given the complex nature of the considered phenomena. The interview was set out in the field of the interactions where information are exchanged between the interviewer and the group and between the peer to peer interaction. The meaning of the concept of energy in Physics was related to the context of the exhibition where the concept was implicitly present. We came to the conclusion that this science exhibition, where the pedagogical interview can be utilized as a tool for teaching, has a good context for learning, once the students showed to have learned even though the docents hadn\'t focused the concept of energy directly. Then we commented about the need of a monitor\'s training, where historical and epistemological studies should be included. This training should also account for the exhibition\'s detected deficiency in approaching the scientific concepts in their mathematical formulation. The research for the emergence of learning in the scientific exhibition center and in interviews is developed by proper tools: a video analysis system is devised to search for the most efficient language in the interaction between teacher and pupil, or in any other teaching-learning situations. Our aim is to establish propitious settings for dialogical interactions in the attempt of dealing with the Vygotsky\'s cognitive \"proximal zone of development\", which is important when we consider the \"process\" of learning a complex concept. As a parallel outcome, we got some familiarity with video recording and analysis as an instrument for both developing and showing the student\'s acquisition of scientific knowledge of physical concepts.

The aim of this thesis is to design a universal analog oscillator using transconductance amplifiers. For studying behaviour of chaotic dynamical systems can be used systems Class C. Suitable way for the purpose modeling dynamic phenomena arising in these systems is an electronic circuit that exhibits the same behavior as modeled system. After familiarization with the basic principles of synthesis of integrators systems, and studying the involvement of frequently used functional blocks were designed the concept of universal chaotic oscillator using transconductance amplifiers. The functionality of this circuit has been verified by PSpice simulation program. A typical feature of chaotic oscillator is extremely sensitivity to initial conditions. Each small change on the initial parameters can lead to major change in the shape of the attractor. The result of this thesis is a functional sample of a universal chaotic oscillator, which was verified by the dynamic behavior of the given differential equations.

Tato diplomová práce nastiňuje teoretické základy potřebné pro návrh algoritmu rekurzivní metody nejmenších čtverců a následně jeho aplikaci na experimentální data naměřená při testovacím manévru uskutečněném v roce 2001. Analyzována byla příčná dynamika jednostopého rovinného modelu vozidla. Práce také obsahuje srovnání výsledků získaných jednak rekurzivním algoritmem a dále i algoritmem Kalmanova filtru.

Práce se zabývá číslicovou simulací kytarových zesilovačů, jakož to nelineárních analogových hudebních efektů, v reálném čase. Hlavním cílem práce je návrh algoritmů, které by umožnily simulaci složitých systémů v reálném čase. Tyto algoritmy jsou prevážně založeny na automatizované DK-metodě a aproximaci nelineárních funkcí. Kvalita navržených algoritmů je stanovana pomocí poslechových testů.

Cette thèse propose une réflexion autour de l'étude des marchés financiers sous le prisme des systèmes complexes.Tout d'abord une description mathématique est proposée pour représenter le processus de prises de décision des agents dès lors où celui-ci bien que représentant les intérêts individuels d'un agent, est également influencé par l'émergence d'un comportement collectif. La méthode est particulièrement applicable lorsque le système étudié est caractérisé par une dynamique non-linéaire. Une application du modèle est proposée au travers de l'implémentation d'un marché artificiel boursier avec une approche système multi-agents. Dans cette application la dynamique du marché est décrite à la fois aux niveaux microscopiques (comportement des agents) et macroscopique (formation du prix). Le processus de décision des agents est défini à partir d'un ensemble de règles comportementales reposant sur des principes de logique floue. La dynamique de la formation du prix repose sur une description déterministe à partir des règles d'appariement d'un carnet d'ordres central tel que sur NYSE-Euronext-Paris. Il est montré que le marché artificiel boursier tel qu'implémenté est capable de répliquer plusieurs faits stylisés des marchés financiers : queue de distribution des rendements plus épaisse que celle d'une loi normale et existence de grappes de volatilité (ou volatility clustering).Par la suite, à partir de simulations numériques il est proposé d'étudier trois grandes propriétés du système : sa capacité d'auto-organisation, de résilience et sa robustesse. Dans un premier temps une méthode est introduite pour qualifier le niveau d'auto-organisation du marché. Nous verrons que la capacité d'auto-organisation du système est maximisée quand les comportements des agents sont diversifiés. Ensuite, il est proposé d'étudier la réponse du système quand celui-ci est stressé via la simulation de chocs de marché. Dans les deux analyses, afin de mettre en évidence comment la dynamique globale du système émerge à partir des interactions et des comportements des agents des résultats numériques sont systématiquement apportés puis discutés.Nos résultats montrent notamment qu'un comportement collectif grégaire apparait à la suite d'un choc, et, entraîne une incapacité temporaire du système à s'auto-organiser. Finalement, au travers des simulations numériques il peut être également remarqué que le marché artificiel boursier implémenté est plus sensible à de faibles répétitions répétées qu'à un choc plus important mais unique. / This thesis suggests reflection in studying financial markets through complex systems prism.First, an original mathematic description for describing agents' decision-making process in case of problems affecting by both individual and collective behavior is introduced. The proposed method is particularly applicable when studied system is characterized by non-linear, path dependent and self-organizing interactions. An application to financial markets is proposed by designing a multi¬agent system based on the proposed formalization.In this application, we propose to implement a computational agent-based financial market in which the system is described in both a microscopie and macroscopic levels are proposed. The agents' decision-making process is based on fuzzy logic rules and the price dynamic is purely deten-ninistic according to the basis matching rules of a central order book as in NYSE-Euronext-Paris. We show that, while putting most parameters under evolutionary control, the computational agent- based system is able to replicate several stylized facts of financial time series (distributions of stocks returns showing a heavy tau l with positive excess kurtosis and volatility clustering phenomenon).Thereafter, with numerical simulations we propose to study three system's properties: self-organization, resilience and robustness. First a method is introduced to quantify the degree of selforganization which ernerges in the system and shows that the capacity of self-organization is maximized when the agents' behaviors are heterogeneous. Secondly, we propose to study the system's response when market shock is simulated. in both cases, numerical results are presentedI and analyzed, showing how the global market behavior emerges from specific individual behavior interactions.Our results notably show that the emergence of collective herding behavior when market shock occurs leads to a temporary disruption on the system self-organization. Finaily, numerical simulations highlight that our artificial financial market can be able to absorb strong mono-shock but be lead to the rupture by low but repeated perturbations.

As tools for dynamic system modelling both conventional methods such as transfer function or state space representation and modern power flow based methods are available. The latter methods do not depend on energy domain, are able to preserve physical system structures, visualize power conversion or coupling or split, identify power losses or storage, run on conventional software and emphasize the relevance of energy as basic principle of known physical domains. Nevertheless common control structures as well as analysis and design tools may still be applied. Furthermore the generalization of power flow methods as pseudo-power flow provides with a universal tool for any dynamic modelling. The phenomenon of power flow constitutes an up to date education methodology. Thus the paper summarizes fundamentals of selected power flow oriented modelling methods, presents a Bond Graph block library for teaching power oriented modelling as compact menu-driven freeware, introduces selected examples and discusses special features.:1. Introduction 2. Fundamentals 2A. Fundamentals of BG Modelling 2.B. Fundamentals of POG Modelling 2C. Fundamentals of EMR Modelling 3. Systematization 4. Block library 4A. Simulink add-on BG Block Library 4B. Menu-Driven Customization 4C. Application Hints 5. Examples 5A. Lift a Load 5B. Solenoid 5C. Filter and Chopper 6. Special features 7. Conclusions References [1] till [25]

This thesis project is an experimental study on how to approach quantitative portfolio credit risk modelling in Venture Debt portfolios. Facing a lack of applicable default data from ArK and publicly available sets, as well as seeking to capture companies that fail to service debt obligations before defaulting per se, we present an approach to risk modeling based on trends in revenue. The main framework revolves around driving a Monte Carlo simulation with Copluas to predict future revenue scenarios across a portfolio of early-stage technology companies. Three models for a random Gaussian walk, a Linear Dynamic System and an Autoregressive Integrated Moving Average (ARIMA) time series are implemented and evaluated in terms of their portfolio Value-at-Risk influence. The model performance confirms that modeling portfolio risk in Venture Debt is challenging, especially due to lack of sufficient data and thus a heavy reliance on assumptions. However, the empirical results for Value-at-Risk and Expected Shortfall are in line with expectations. The evaluated portfolio is still in an early stage with a majority of assets not yet in their repayment period and consequently the spread of potential losses within one year is very tight. It should further be recognized that the scope in terms of explanatory variables for sales and model complexities has been narrowed and simplified for computational benefits, transparency and communicability. The main conclusion drawn is that alternative approaches to model Venture Debt risk is fully possible, and should improve in reliability and accuracy with more data feeding the model. For future research it is recommended to incorporate macroeconomic variables as well as similar company analysis to better capture macro, funding and sector conditions. Furthermore, it is suggested to extend the set of financial and operational explanatory variables for sales through machine learning or neural networks. / Detta examensarbete är en experimentell studie för kvantitativ modellering av kreditrisk i Venture Debt-portföljer. Givet en brist på tillgänlig konkurs-data från ArK samt från offentligt tillgängliga databaser i kombination med ambitionen att inkludera företag som misslyckas med skuldförpliktelser innan konkurs per se, presenterar vi en metod för riskmodellering baserad på trender i intäkter. Ramverket för modellen kretsar kring Monte Carlo-simulering med Copluas för att estimera framtida intäktsscenarier över en portfölj med tillväxtbolag inom tekniksektorn. Tre modeller för en random walk, ett linjärt dynamiskt system och ARIMA- tidsserier implementeras och utvärderas i termer av deras inflytande på portföljens Value-at- Risk. Modellens prestationer bekräftar att modellering av portföljrisk inom Venture Debt är utmanande, särskilt på grund av bristen på tillräckliga data och därmed ett stort beroende av antaganden. Dock är de empiriska resultaten för Value-at-Risk och Expected Shortfall i linje med förväntningarna. Den utvärderade portföljen är fortfarande i ett tidigt skede där en majoritet av tillgångarna fortfarande befinner sig i en amorteringsfri period och följaktligen är spridningen av potentiella förluster inom ett år mycket snäv. Det bör vidare tillkännages att omfattningen i termer av förklarande variabler för intäkter och modellkomplexitet har förenklats för beräkningsfördelar, transparens och kommunicerbarhet. Den främsta slutsatsen som dras är att alternativa metoder för att modellera risker inom Venture Debt är fullt möjliga och bör förbättras i tillförlitlighet och precision när mer data kan matas in i modellen. För framtida arbete rekommenderas det att inkorporera makroekonomiska variabler samt analys av liknande bolag för att bättre fånga makro-, finansierings- och sektorsförhållanden. Vidare föreslås det att utöka uppsättningen av finansiella och operationella förklarande variabler för intäkter genom maskininlärning eller neurala nätverk.

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