Neste mestrado propõe-se um estudo sobre o controle automático de sistemas dinâmicos para o problema de coordenação de robôs móveis. Os movimentos coordenados serão realizados em função de um líder e qualquer robô da formação pode assumir a liderança de maneira aleatória. Os robôs trocam informação através de um grafo direcionado (dígrafo) de comunicação, definido a-priori e, movimentos estáveis são gerados através de uma lei de controle descentralizada baseada nas coordenadas dos robôs. Além disso, as equações dinâmicas não lineares dos robôs são descritas na forma de espaço de estado sendo os parâmetros das matrizes dependentes da velocidade angular das rodas. Esta representação, conhecida como Quase Linear a Parâmetros Variantes (Quase-LPV), é utilizada no projeto de controle H \'INFINITO\' não linear para sistemas dinâmicos. Para garantir a estabilidade da formação quando há alternância de líder ou remoção de robôs, foi feito o controle robusto e controle tolerante a falhas para um grupo de robôs móveis com rodas (RMRs). O controle robusto é baseado em controle H \'INFINITO\' não linear via realimentação do estado e controle H \'INFINITO\' não linear via realimentação da saída. O controle tolerante a falhas é baseado em controle H \'INFINITO\' por realimentação da saída de sistemas lineares sujeitos a saltos Markovianos para garantir a estabilidade da formação quando um dos robôs é perdido durante o movimento coordenado. Resultados em simulação são apresentados para os controladores utilizados. / This dissertation proposes a study on the automatic control of dynamic systems to the problem of coordination of mobile robots. The coordinated motions are performed with the robots following a leader, and any robot of the formation can assume the leadership randomly. The robots exchange informations according to a pre-specified communication directed graph (digraph). Stable motions are generated by a decentralized control law based on the robots coordinates. In addition, the nonlinear dynamic equations of the robots are described in state-space form where the parameters matrices depend on the angular velocities of the wheels. This representation, known as Quasi-Linear Parameter Varying (Quasi-LPV), is useful for control designs based on nonlinear H \'INFINITE\' approaches. To ensure the stability formation when there is alternation of leader or one of the robots is removed, we made a robust control and fault tolerant control for a group of wheeled mobile robots (WMRs). The robust approach is based on state feedback nonlinear H \'INFINITE\' control and output feedback nonlinear H \'INFINITE\' control. The fault tolerant approach is based on output feedback H \'INFINITE\' control of Markovian jump linear systems to ensure stability of the formation when one of the robots is lost during the coordinated motion. Results in simulation are presented for the controllers used.

Este trabalho é dedicado ao estudo do erro de estimação em filtragem linear para sistemas lineares com parâmentros sujeitos a saltos markovianos a tempo discreto. Indroduzimos o conceito de alcançabilidade média para uma classe de sistemas. Construímos um conjunto de matrizes de alcançabilidade e mostramos que o conceito usual de alcan- çabilidade definido através da positividade do gramiano é caracterizado pela definição por posto completo destas matrizes. A alcançabilidade média funciona como condição necessária e suficiente para positividade do segundo momento do estado do sistema, resultado esse que auxilia na caracterização da positividade uniforme da matriz de covariância do erro de estimação. Abordamos a estabilidade de estimadores com a interpretação de que a covariância do erro permanece limitada na presença de erro de qualquer magnitude no modelo do ruído, que é uma característica relevante para aplicações. Apresentamos uma prova de que filtros markovianos são estáveis sempre que o segundo momento condicionado é positivo. Exemplos numéricos encontram-se inclusos. / This work studies linear filtering for discrete-time systems with Markov jump parameters. We introduce a notion of average reachability for these systems and present a set of matrices playing the role of reachability matrices, in the sense that their rank is full if and only if the system is average reachable. Reachability is also a sufficient condition for the second moment of the system to be positive. Uniform positiveness of the error covariance matrix is studied for general (possibly non-markovian) linear estimators, relying on the state second moment positiveness. Satbility of linear markovian estimators is also addressed, allowing to show that markovian estimators are stable whenever the system is reachable, with the interpretation that the error covariance remains bounded in the presence of error of any magnitude in the model of the noise, which is a relevant feature for applications. Numerical examples are included.

Nesta tese de doutorado são apresentados sistemas globais de estimativa baseados em modelos Markovianos aplicados na área de reabilitação robótica. Os sistemas propostos foram desenvolvidos para estimar as posições angulares dos elos de exoesqueletos para membros inferiores, desenvolvidos para reabilitação motora em pacientes que sofreram Acidente Vascular Cerebral (AVC) ou lesão medular. Filtros baseados no filtro de Kalman, um nominal e outro considerando incertezas no modelo, foram utilizados em estratégias de fusão de dados de sensores provenientes de sensores inerciais, possibilitando estimativas de posicionamentos angulares. Algoritmos genéticos são utilizados na otimização dos filtros, ajustando as matrizes de peso destes. Em oposição as modelagens tradicionais, via estimativa local, utilizando somente uma unidade inercial para cada modelo, propõe-se um sistema global de estimativa, obtendo-se a melhor informação de cada sensor combinando-os em um modelo Markoviano. Resultados experimentais com um exoesqueleto foram utilizados para comparar a abordagem Markoviana às convencionais. / In this thesis are presented global estimation systems based on Markov models applied in robotic rehabilitation area. The proposed systems have been developed to estimate the angular positions of the exoskeletons for lower limbs, designed to provide motor rehabilitation of stroke and spinal cord injured people. Filters based on the Kalman filter, one nominal and other considering uncertainties in the model, were used in sensor data fusion strategies from inertial sensors, to estimate angular positions. Genetic algorithms are used to the optimization of filters, tuning the weighting matrices. In opposition to these modelling via local estimation, using only one inertial unit, we also chose a global modelling getting the best information from each sensor, combining them in a Markov model. Experimental results with an exoskeleton were used to compare the Markovian approach to conventional.

Neste mestrado propõe-se um estudo sobre o controle automático de sistemas dinâmicos para o problema de coordenação de robôs móveis. Os movimentos coordenados serão realizados em função de um líder e qualquer robô da formação pode assumir a liderança de maneira aleatória. Os robôs trocam informação através de um grafo direcionado (dígrafo) de comunicação, definido a-priori e, movimentos estáveis são gerados através de uma lei de controle descentralizada baseada nas coordenadas dos robôs. Além disso, as equações dinâmicas não lineares dos robôs são descritas na forma de espaço de estado sendo os parâmetros das matrizes dependentes da velocidade angular das rodas. Esta representação, conhecida como Quase Linear a Parâmetros Variantes (Quase-LPV), é utilizada no projeto de controle H \'INFINITO\' não linear para sistemas dinâmicos. Para garantir a estabilidade da formação quando há alternância de líder ou remoção de robôs, foi feito o controle robusto e controle tolerante a falhas para um grupo de robôs móveis com rodas (RMRs). O controle robusto é baseado em controle H \'INFINITO\' não linear via realimentação do estado e controle H \'INFINITO\' não linear via realimentação da saída. O controle tolerante a falhas é baseado em controle H \'INFINITO\' por realimentação da saída de sistemas lineares sujeitos a saltos Markovianos para garantir a estabilidade da formação quando um dos robôs é perdido durante o movimento coordenado. Resultados em simulação são apresentados para os controladores utilizados. / This dissertation proposes a study on the automatic control of dynamic systems to the problem of coordination of mobile robots. The coordinated motions are performed with the robots following a leader, and any robot of the formation can assume the leadership randomly. The robots exchange informations according to a pre-specified communication directed graph (digraph). Stable motions are generated by a decentralized control law based on the robots coordinates. In addition, the nonlinear dynamic equations of the robots are described in state-space form where the parameters matrices depend on the angular velocities of the wheels. This representation, known as Quasi-Linear Parameter Varying (Quasi-LPV), is useful for control designs based on nonlinear H \'INFINITE\' approaches. To ensure the stability formation when there is alternation of leader or one of the robots is removed, we made a robust control and fault tolerant control for a group of wheeled mobile robots (WMRs). The robust approach is based on state feedback nonlinear H \'INFINITE\' control and output feedback nonlinear H \'INFINITE\' control. The fault tolerant approach is based on output feedback H \'INFINITE\' control of Markovian jump linear systems to ensure stability of the formation when one of the robots is lost during the coordinated motion. Results in simulation are presented for the controllers used.

Esta tese aborda o problema de regulação para sistemas lineares sujeitos a saltos Markovianos de tempo discreto com matrizes de transição incertas. Considera-se que as incertezas são limitadas em norma e os estados da cadeia de Markov podem não ser completamente observados pelo controlador. No cenário com observação completa dos estados, a solução é deduzida com base em um funcional quadrático dado em termos das probabilidades de transição incertas. Enquanto que no cenário sem observação, a solução é obtida por meio da reformulação do sistema Markoviano como um sistema determinístico, independente da cadeia de Markov. Três modelos são propostos para essa reformulação: um modelo é baseado no primeiro momento do sistema Markoviano, o segundo é obtido a partir da medida de Dirac e resulta em um sistema aumentado, e o terceiro fornece um sistema aumentado singular. Os reguladores recursivos robustos são projetados a partir de critérios de custo quadrático, dados em termos de problemas de otimização restritos. A solução é derivada da técnica de mínimos quadrados regularizados robustos e apresentada em uma estrutura matricial. A recursividade é estabelecida por equações de Riccati, que se assemelham às soluções dos reguladores clássicos, para essa classe de sistemas, quando não estão sujeitos a incertezas. / This thesis deals with regulation problem for discrete-time Markovian jump linear systems with uncertain transition matrix. The uncertainties are assumed to be normbounded type. The states of the Markov chain can not be completely observed by the controller. In the scenario with complete observation of the states, the solution is deduced based on a quadratic functional given in terms of uncertain transition probabilities. While in the scenario without observation, the solution is obtained from reformulation of the Markovian system as a deterministic system, independent of the Markov chain. Three models are proposed for the reformulation process: a model is based on the first moment of the Markovian system, the second is obtained from Dirac measure which results in an augmented system, and the third provides a singular augmented system. Recursive robust regulators are designed from quadratic cost criteria given in terms of constrained optimization problems. The solution is derived from the robust regularized least-square approach, whose framework is given in terms of a matrix structure. The recursiveness is established by Riccati equations which resemble the solutions of standard regulators for this class of systems, when they are not subject to uncertainties.

Made available in DSpace on 2016-03-15T19:25:32Z (GMT). No. of bitstreams: 1 Patricia Marilia Ricomini e Almeida.pdf: 585196 bytes, checksum: d95885c7a4db627bc6882b2064a1efeb (MD5) Previous issue date: 2006-03-09 / Fundo Mackenzie de Pesquisa / One of the most popular subjects in finance is about the search and the learning of the securities return generation process and originate with the publication of Bachelier s thesis, in 1900. In 1978, Jensen affirmed that, any strategy of business, that produces economic profits in a consistent way, discounted the risk, for a sufficient long period, observing the transaction costs, consist in evidence against market efficiency. However, occurs that empirical evidences, mainly as from 60 s decade, have verified a succession of events, that originate production of literary work in finance: conglomerate of volatility, no normality of returns, negative asymmetry, excess of kurtosis and stochastic volatility. As result of these verifications, theories arose, especially of economic nature, about the characteristic nonlinear of the data, as rational speculative bubble. This paper examines the performance of a general dynamic equity indexing strategy based on cointegration, from a market efficiency perspective, observing the different levels of risk and regimes. The identification of these regimes auto regressive in the process of generating returns in the Brazilian Market, especially in Bovespa, for the Plano Real period (January of 1995 to September of 2004), will be elaborated trough a Markov Switching Model. With this model, is possible to identify the nonlinear structure of the data and it is relation to the conditional mean and conditional variance. As result the dynamics of the data generation process, the returns can be described as function of the growth cycle ("bull markets") and decrease ("bear markets"). / Um dos mais populares assuntos em finanças trata da pesquisa e estudo do processo de geração de retornos de títulos, tendo sua origem com a publicação da tese de Bachelier, em 1900. Em 1978, Jensen afirmou que, qualquer estratégia de negócio, que produza de forma consistente ganho econômico, já descontado o risco, por um período suficientemente longo, considerando os custos de transação, constitui-se em uma evidência contra eficiência de mercado. A eficiência de mercado, portanto, pode ser traduzida para a hipótese de que o valor esperado do excesso da taxa de retorno é, na média, igual a zero, quando se leva em consideração uma medida de probabilidade que desconta o prêmio pelo risco, dado um conjunto de informações (históricas, públicas ou privadas). Todavia, ocorre que as evidências empíricas, principalmente a partir da década de sessenta, têm constatado uma série de fatos, que deram origem a uma vasta literatura em finanças: conglomerados de volatilidade, não normalidade dos retornos, assimetria negativa, excesso de curtose, volatilidade estocástica, auto- regressividade dos retornos e da volatilidade, anomalias de mercado relacionadas com a sazonalidade ou com o funcionamento dos mercados, anomalias de mercado relacionadas ao tamanho da empresa e a sua estrutura de capital, processo de reversão para o retorno médio e valores extremos. Em função dessas constatações, surgiram teorias, especialmente de natureza econômica, sobre a característica não linear dos dados, tais como: modismos, manias e pânicos e bolhas especulativas racionais. Um dos objetivos do presente estudo consiste em elaborar uma estratégia ativa baseada na construção de um Índice de Cointegração, considerando-se os diferentes níveis de riscos e de regimes auto regressivo. A identificação desses regimes no processo de geração de retornos no mercado brasileiro de ações na BOVESPA, para o período pós Plano Real (janeiro de 1995 a setembro de 2004) será elaborado através do Modelo de Regimes de Conversão de Markov. A utilização desse modelo de regimes permite identificar a estrutura não linear dos dados seja em relação à média condicional, seja em relação à variância condicional. Como resultado, a dinâmica do processo de geração poderá ser função de ciclos de crescimento persistente ( bull markets ) e de não crescimento ( bear markets ).

L’objectif de cette thèse est de conceptualiser, à partir de l’exploitation des données de remboursement de soins de l’Assurance Maladie, les différentes trajectoires de recours aux soins relatives à la prise en charge d’une pathologie chronique (asthme), et d’étudier les déterminants de ces trajectoires du point de vue du profil et du comportement subséquent du prescripteur de soins. L’étude de la relation entre le comportement prescriptif et la trajectoire de soins est appréhendée par des techniques de modélisation et d’analyses multivariées. L’objectif sous-jacent est d’évaluer, d’un point de vue médico-économique, l’impact de la typologie des prescripteurs (caractéristiques des offreurs de soins) sur les différentes trajectoires de soins suivies par les patients atteints de la pathologie définie supra. Les caractéristiques susceptibles d’identifier une typologie de prescripteur correspondent aux variables influant sur le comportement prescriptif, au sens large, du médecin (âge, sexe, durée d’exercice, type d’exercice, etc.). La question principale de la thèse est celle de l’effet régulateur de l’incitation économique, instaurée par le parcours de soins coordonnés (réforme de l’Assurance Maladie, août 2004), sur les trajectoires de soins, réellement observées, de patients atteints de pathologies chroniques. Les corollaires sont : Le déremboursement des actes hors parcours de soins coordonnés peut-il avoir un impact significatif sur la trajectoire empirique de prise en charge du patient ? Le profil du prescripteur d’actes médicaux a-t-il, toutes choses égales par ailleurs, un effet sur le respect ou non de la trajectoire de soins référentielle admise par le parcours de soins coordonnés ? Quels sont les déterminants principaux du non respect de cette trajectoire référentielle, du point de vue de l’analyse des caractéristiques des couples « médecin – patient» ? / The objective of this thesis is to conceptualize, starting from the exploitation of the refunding data of cares from the Sickness insurance, the various trajectories of cares recourses introduced by chronic diseases as asthma, and to study their determinants by analysing the profile and the subsequent behavior of the general practitioner. The study of the relation between the prescriptive behavior and the trajectory of cares is carried out by different multivariate analyses. The other objective is to evaluate, from a pharmacoeconomic point of view, the impact of the general practitioner characteristics on the various trajectories of cares followed by the patients with chronic diseases. The characteristics likely to identify a typology of practitioners correspond to the variables influencing the prescriptive behavior (age, sex, duration of exercise, type of exercise, etc). The principal question of the thesis is that of the regulating effect of the economic incentive, rested on the coordinated care pathway (reform of the Sickness insurance, August 2004), on the trajectories of cares, really observed by the chronic patients. The corollaries are: Does the no-reimbursement of some medical acts, not considered in the coordinated care pathway, have a significant impact on the empirical recourse of the patient? Does the profile of the general practitioner have an effect on the respect or not of the allowed trajectory of cares classified by the French reform? Which are the principal determinants of disregarding this referential trajectory, by notably analysing the “practitioner - patient” characteristics?

This thesis consists of four papers dealing with the futures price process. In the first paper, we propose a two-factor futures volatility model designed for the US natural gas market, but applicable to any futures market where volatility decreases with maturity and varies with the seasons. A closed form analytical expression for European call options is derived within the model and used to calibrate the model to implied market volatilities. The result is used to price swaptions and calendar spread options on the futures curve. In the second paper, a financial market is specified where the underlying asset is driven by a d-dimensional Wiener process and an M dimensional Markov process. On this market, we provide necessary and, in the time homogenous case, sufficient conditions for the futures price to possess a semi-affine term structure. Next, the case when the Markov process is unobservable is considered. We show that the pricing problem in this setting can be viewed as a filtering problem, and we present explicit solutions for futures. Finally, we present explicit solutions for options on futures both in the observable and unobservable case. The third paper is an empirical study of the SABR model, one of the latest contributions to the field of stochastic volatility models. By Monte Carlo simulation we test the accuracy of the approximation the model relies on, and we investigate the stability of the parameters involved. Further, the model is calibrated to market implied volatility, and its dynamic performance is tested. In the fourth paper, co-authored with Tomas Björk and Camilla Landén, we consider HJM type models for the term structure of futures prices, where the volatility is allowed to be an arbitrary smooth functional of the present futures price curve. Using a Lie algebraic approach we investigate when the infinite dimensional futures price process can be realized by a finite dimensional Markovian state space model, and we give general necessary and sufficient conditions, in terms of the volatility structure, for the existence of a finite dimensional realization. We study a number of concrete applications including the model developed in the first paper of this thesis. In particular, we provide necessary and sufficient conditions for when the induced spot price is a Markov process. We prove that the only HJM type futures price models with spot price dependent volatility structures, generically possessing a spot price realization, are the affine ones. These models are thus the only generic spot price models from a futures price term structure point of view. / Diss. Stockholm : Handelshögskolan, 2004

Estimating the state of a system from noisy measurements is a problem which arises in a variety of scientific and industrial areas which include signal processing, communications, statistics and econometrics. Recursive filtering is one way to achieve this by incorporating noisy observations as they become available with prior knowledge of the system model. Bayesian methods provide a general framework for dynamic state estimation problems. The central idea behind this recursive Bayesian estimation is computing the probability density function of the state vector of the system conditioned on the measurements. However, the optimal solution to this problem is often intractable because it requires high-dimensional integration. Although we can use the Kalman lter in the case of a linear state space model with Gaussian noise, this method is not optimum for a non-linear and non-Gaussian system model. There are many new methods of filtering for the general case. The main emphasis of this thesis is on one such recently developed filter, the particle lter [2,3,6]. In this thesis, a detailed introduction to particle filters is provided as well as some guidelines for the efficient implementation of the particle lter. The application of particle lters to various communication channels like detection of symbols over the channels, capacity calculation of the channel are discussed.

The problem under consideration in the thesis is a two level atom in a photonic crystal and a pumping laser. The photonic crystal provides an environment for the atom, that modifies the decay of the exited state, especially if the atom frequency is close to the band gap. The population inversion is investigated als well as the emission spectrum. The dynamics is analysed in the context of open quantum systems. Due to the multiple reflections in the photonic crystal, the system has a finite memory that inhibits the Markovian approximation. In the Heisenberg picture the equations of motion for the system variables form a infinite hierarchy of integro-differential equations. To get a closed system, approximations like a weak coupling approximation are needed. The thesis starts with a simple photonic crystal that is amenable to analytic calculations: a one-dimensional photonic crystal, that consists of alternating layers. The Bloch modes inside and the vacuum modes outside a finite crystal are linked with a transformation matrix that is interpreted as a transfer matrix. Formulas for the band structure, the reflection from a semi-infinite crystal, and the local density of states in absorbing crystals are found; defect modes and negative refraction are discussed. The quantum optics section of the work starts with the discussion of three problems, that are related to the full resonance fluorescence problem: a pure dephasing model, the driven atom and resonance fluorescence in free space. In the lowest order of the system-environment coupling, the one-time expectation values for the full problem are calculated analytically and the stationary states are discussed for certain cases. For the calculation of the two time correlation functions and spectra, the additional problem of correlations between the two times appears. In the Markovian case, the quantum regression theorem is valid. In the general case, the fluctuation dissipation theorem can be used instead. The two-time correlation functions are calculated by the two different methods. Within the chosen approximations, both methods deliver the same result. Several plots show the dependence of the spectrum on the parameters. Some examples for squeezing spectra are shown with different approximations. A projection operator method is used to establish two kinds of Markovian expansion with and without time convolution. The lowest order is identical with the lowest order of system environment coupling, but higher orders give different results. / Die Arbeit befasst sich mit der Emission eines 2-Niveau-Atoms in einem photonischen Kristall mit einem treibenden Laser. Der photonische Kristall stellt für das Atom eine Umgebung dar, die seinen Zerfall verändert, insbesondere wenn die Übergangsfrequenz des Atoms nahe an der Bandkante ist. Es werden sowohl die Besetzungen als auch das Emissionsspektrum untersucht. Die Dynamik wird im Kontext offener Quantensysteme analysiert. Durch die vielfachen Reflexionen im photonischen Kristall hat das System ein endliches Gedächtnis, das die Markov-Näherung verhindert. Im Heisenberg-Bild stellen die Bewegungsgleichungen für die Systemvariablen eineunendliche Hierachie von Integro-Differentialgleichungen dar. Um ein geschlossenes System zu erhalten, sind Näherungen wie eine schwache Kopplung nötig. Zunächst wird ein einfacher photonischer Kristall betrachtet.: Der eindimensionale photonische Kristall, der aus wechselnden Lagen besteht. Die Blochmoden innerhalb und die Vakuummoden außerhalb des endlichen photonischen Kristalls sind durch eine Transformationsmatrix, die als Transfermatrix interpretiert werden kann, miteinander verbunden. Einfache Formeln für die Bandstruktur, Reflexion eines halb-unendlichen Kristalls, die lokale Zustandsdichte im absorbierenden Kristall werden gefunden; außerdem werden Defektmoden und negative Brechung diskutiert. Im quantenoptischen Teil der Arbeit werden zu Anfang drei Probleme diskutiert, die im Zusammenhang zum Problem der Resonanzfluoreszenz stehen und die analytisch berechnet werden können: Ein Dephasierungsmodell, das getriebenen Atom und Resonanzfluoreszenz im freien Raum. In der niedrigsten Ordnung der System-Bad-Kopplung werden die Erwartungswerte analytisch berechnet und die stationären Zustände werden für bestimmte Fälle diskutiert. Bei der Berechnung der Zweizeitkorrelationsfunktion und der Spektren taucht das zusätzliche Problem der Korrelationen zwischen den beiden Zeiten auf. Im Markov-Fall gilt das Quantenregressionstheorem. Im allgemeinen Fall kann stattdessen das Fluktuations-Dissipations-Theorem benutzt werden. Die Korrelationsfunktionen werden mit zwei verschiedenen Methoden berechnet. Innerhalb der gewählten Näherungen liefern beide Methoden dasselbe Resultat. Einige Plots zeigen die Abhängigkeit des Spektrums von den verschiedenen Parametern. Mehrere Beispiele für Squeezing-Spektren werden mit den verschiedenen Näherungen gezeigt. Eine Projektions-Operator-Methode wird benutzt, um zwei Arten einer Markov-Entwicklung zu implementieren, mit und ohne Faltungsintegral. Die niedrigste Ordnung ist identisch mit der niedrigsten Ordnung der System-Bad-Kopplung, wohingegen höhere Ordnungen andere Resultate ergeben.