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.

Wir betrachten die stochastische Differentialgleichung mit Gedächtnis (SDDE) mit Gedächtnislänge r dX(t) = b(X(u);u in [t-r,t])dt + sigma(X(u);u in [t-r,t])dB(t) mit eindeutiger schwacher Lösung. Dabei ist B eine Brownsche Bewegung, b and sigma sind stetige, lokal beschränkte Funktionen mit Definitionsbereich C[-r,0], und X(u);u in [t-r,t] bezeichnet das Segment der Werte von X(u) für Zeitpunkte u im Intervall [t,t-r]. Unser Ziel ist eine Folge von diskreten Zeitreihen Xh höherer Ordung zu konstruieren, so dass mit h gegen 0 die Zeitreihen Xh schwach gegen die Lösung X der stochastischen Differentialgleichung mit Gedächtnis konvergieren. Desweiteren werden wir Bedingungen angeben, unter denen eine gegeben Folge von Zeitreihen Xh höherer Ordung schwach gegen die Lösung X einer stochastischen Differentialgleichung mit Gedächtnis konvergiert. Als ein Beispiel werden wir den schwachen Grenzwert einer Folge von diskreten GARCH-Prozessen höherer Ordnung ermitteln. Dieser Grenzwert wird sich als schwache Lösung einer stochastischen Differentialgleichung mit Gedächtnis herausstellen. / Consider the stochastic delay differential equation (SDDE) with length of memory r dX(t) = b(X(u);u in [t-r,t])dt + sigma(X(u);u in [t-r,t])dB(t), which has a unique weak solution. Here B is a Brownian motion, b and sigma are continuous, locally bounded functions defined on the space C[-r,0], and X(u);u in [t-r,t] denotes the segment of the values of X(u) for time points u in the interval [t,t-r]. Our aim is to construct a sequence of discrete time series Xh of higher order, such that Xh converges weakly to the solution X of the stochastic differential delay equation as h tends to zero. On the other hand we shall establish under which conditions time series Xh of higher order converge weakly to a weak solution X of a stochastic differential delay equation. As an illustration we shall derive a weak limit of a sequence of GARCH processes of higher order. This limit tends out to be the weak solution of a stochastic differential delay equation.

A utilização de sistemas semi-ativos no controle de movimento e vibração vem crescendo muito nos últimos anos, e está se firmando como a opção mais econômica em muitas aplicações. Os sistemas de controle semi-ativos baseados em fluidos magneto-reológicos (MR) já são empregados no controle de vibrações desde máquinas de lavar a grandes pontes suspensas, e até mesmo no controle de vibração de edifícios sujeitos a abalos sísmicos. No controle de movimento, eles têm sido aplicados em aparelhos de fisioterapia, próteses de joelho humano e embreagens. No setor automobilístico, os sistemas semi-ativos são empregados em sistemas de controle da suspensão e sistemas anti-rolagem, e também no controle de sistemas de torque e tração. Visto a crescente importância dos sistemas de controle semi-ativo, este trabalho aborda este assunto dividindo-o em duas partes: a primeira, apresentada no volume 1, trata do projeto de atuadores magneto-reológicos e do seu modelamento dinâmico voltado para projetos de controle; e a segunda parte, apresentada no volume 2, trata de projeto de controladores para sistemas semi-ativos, mais especificamente voltados para o controle de suspensão veicular semi-ativa, buscando a melhoria do desempenho em conforto, segurança e dirigibilidade do veículo. Na primeira parte, a maior contribuição deste trabalho está em preencher uma lacuna na literatura no que diz respeito a uma técnica sistemática de projeto de atuadores magneto-reológicos e da forma mais adequada de sua representação dinâmica para projetos de controle, que é feita a partir de dados experimentais. Na segunda parte deste trabalho buscou-se desenvolver um sistema de controle economicamente viável para veículos utilitários (caminhonetes principalmente). Estes são os veículos que mais carecem de sistemas de suspensão capazes de atender a uma grande variedade de situações (variação de pista, variação de carga), e cujo mercado exige uma relação custo/benefício melhor que aquela dos mercados de carros de luxo, onde estes sistemas são empregados atualmente. Como resultados mais importantes deste trabalho têmse: uma proposição para o uso da lei de controle LQG/LTR em sistemas não estritamente próprios; um modelo de um veículo utilitário completo com sete graus de liberdade e capaz de representar as situações mais importantes do comportamento dinâmico deste tipo de veículo; o desenvolvimento de uma estratégia de controle robusto baseado na técnica LQG/LTR, adequada para trabalhar com atuadores semi-ativos, e que utiliza sensores de custo compatível com a aplicação. O sistema de controle proposto foi capaz de melhorar o desempenho em conforto e segurança, evitando situações de perda de aderência dos pneus e comportamentos dinâmicos indesejáveis destes veículos, que foi verificado experimentalmente e através de simulações em computador. / The application of semi-active systems to motion and vibration control has significantly grown during the last years, and it is becoming an economically viable option for several applications. Semi-active systems based on magneto-rheological (MR) fluids were applied to vibration control ranging from washing machines to suspended bridges, and also in vibration control of buildings under seismic tremors. Regarding the movement control, they have been used in gym apparati, human knee prosthesis and clutches. More specifically in the automotive industry, semi-active systems have been applied in suspension and anti-roll systems, and also in torque and traction control systems. This work treats this subject dividing it into two parts: the first one, presented in volume 1, deals with the design of semi-active actuators based on magneto-rheological fluids and dynamic modeling; and the second one, presented in volume 2, deals with the design of semi-active control for vehicular suspension systems. The control main objective is the performance improvement in comfort, safety and handling features of a vehicle. In the first part, the main contribution of this work is to fulfill a literature gap regarding a systematic procedure for design of magneto-rheological actuators and to find a better representation for the dynamic behavior regarding the control system development, which is done based on experimental data analysis. The second part of this work leaded with the development of a vehicular suspension system for utility vehicles (for SUVs, and mainly for light trucks), which need suspension systems able to face a great number of situations (road variation, load variation, etc.), and which present stability problems due to its high gravity center height. Important results of this work are: the development of a robust control strategy based on LQG/LTR techniques for non-strictly proper systems, the development of a dynamic model for light trucks and SUVs with seven degrees of freedom; the development of a robust control strategy based on the LQG/LTR synthesis, suit to work with semi-active actuators, and using sensors with costs compatible to the application. The proposed control system was able to improve the performance of comfort and safety, avoiding the loss of adherence between tires and the ground and other undesirable dynamic behaviors of these vehicles, that was verified experimentally and through computer simulations.

In telecommunications, distributed cooperative communications refer to techniques which allow different users in a wireless network to share or combine their information in order to increase diversity gain or power gain. Unlike conventional point-to-point communications maximizing the performance of the individual link, distributed cooperative communications enable multiple users to collaborate with each other to achieve an overall improvement in performance, e.g., improved range and data rates. The first part of this dissertation focuses the problem of jointly decoding binary messages from a single distant transmitter to a cooperative receive cluster. The outage probability of distributed reception with binary hard decision exchanges is compared with the outage probability of ideal receive beamforming with unquantized observation exchanges. Low- dimensional analysis and numerical results show, via two simple but surprisingly good approximations, that the outage probability performance of distributed reception with hard decision exchanges is well-predicted by the SNR of ideal receive beamforming after subtracting a hard decision penalty of slightly less than 2 dB. These results, developed in non-asymptotic regimes, are consistent with prior asymptotic results (for a large number of nodes and low per-node SNR) on hard decisions in binary communication systems. We next consider the problem of estimating and tracking channels in a distributed transmission system with multiple transmitters and multiple receivers. In order to track and predict the effective channel between each transmit node and each receive node to facilitate coherent transmission, a linear time-invariant state- space model is developed and is shown to be observable but nonstabilizable. To quantify the steady-state performance of a Kalman filter channel tracker, two methods are developed to efficiently compute the steady-state prediction covariance. An asymptotic analysis is also presented for the homogenous oscillator case for systems with a large number of transmit and receive nodes with closed-form results for all of the elements in the asymptotic prediction covariance as a function of the carrier frequency, oscillator parameters, and channel measurement period. Numeric results confirm the analysis and demonstrate the effect of the oscillator parameters on the ability of the distributed transmission system to achieve coherent transmission. In recent years, the development of efficient radio frequency (RF) radiation wireless power transfer (WPT) systems has become an active research area, motivated by the widespread use of low-power devices that can be charged wirelessly. In this dissertation, we next consider a time division multiple access scenario where a wireless access point transmits to a group of users which harvest the energy and then use this energy to transmit back to the access point. Past approaches have found the optimal time allocation to maximize sum throughput under the assumption that the users must use all of their harvested power in each block of the "harvest-then-transmit" protocol. This dissertation considers optimal time and energy allocation to maximize the sum throughput for the case when the nodes can save energy for later blocks. To maximize the sum throughput over a finite horizon, the initial optimization problem is separated into two sub-problems and finally can be formulated into a standard box- constrained optimization problem, which can be solved efficiently. A tight upper bound is derived by relaxing the energy harvesting causality. A disadvantage of RF-radiation based WPT is that path loss effects can significantly reduce the amount of power received by energy harvesting devices. To overcome this problem, recent investigations have considered the use of distributed transmit beamforming (DTB) in wireless communication systems where two or more individual transmit nodes pool their antenna resources to emulate a virtual antenna array. In order to take the advantages of the DTB in the WPT, in this dissertation, we study the optimization of the feedback rate to maximize the energy efficiency in the WPT system. Since periodic feedback improves the beamforming gain but requires the receivers to expend energy, there is a fundamental tradeoff between the feedback period and the efficiency of the WPT system. We develop a new model to combine WPT and DTB and explicitly account for independent oscillator dynamics and the cost of feedback energy from the receive nodes. We then formulate a "Normalized Weighted Mean Energy Harvesting Rate" (NWMEHR) maximization problem to select the feedback period to maximize the weighted averaged amount of net energy harvested by the receive nodes per unit of time as a function of the oscillator parameters. We develop an explicit method to numerically calculate the globally optimal feedback period.

The present research study is comprised of two main parts. The first part aims at the development of a systematic system-theoretic framework that allows the derivation of optimal chemotherapy protocols for HIV patients. The proposed framework is conceptually aligned with a notion of continuous-time model predictive control of nonlinear dynamical systems, and results in an optimal way to control viral replication, while maintaining low antiretroviral drug toxicity levels. This study is particularly important because it naturally integrates powerful system-theoretic techniques into a clinically challenging problem with worldwide implications, namely the one of developing chemotherapy patterns for HIV patients that are effective and do not induce adverse side-effects. The second part introduces a new digital controller design methodology for nonlinear (bio)chemical processes, that reflects contemporary necessities in the practical implementation of advanced process control strategies via digital computer-based algorithms. The proposed methodology relies on the derivation of an accurate sampled-data representation of the process, and the subsequent formulation and solution to a nonlinear digital controller synthesis problem. In particular, for the latter two distinct approaches are followed that are both based on the methodological principles of Lyapunov design and rely on a short-horizon model-based prediction and optimization of the rate of“energy dissipation" of the system, as it is realized through the time derivative of an appropriately selected Lyapunov function. First, the Lyapunov function is computed by solving the discrete Lyapunov matrix equation. In the second approach however, it is computed by solving a Zubov-like functional equation based on the system's drift vector field. Finally, two examples of a chemical and a biological reactor that both exhibit nonlinear behavior illustrate the main features of the proposed digital controller design method.

Este trabalho apresenta um estudo da discretização de controladores ressonantes aplicados a fontes ininterruptas de energia (UPSs, do termo em inglês, Uninterruptible Power Suppllies). Primeiramente, diferentes métodos de discretização serão considerados na obtenção de um modelo em tempo discreto da UPS. Além disso, estes métodos serão comparados do ponto de vista frequencial para a definição da formulação do controlador ressonante a ser utilizado. Então, uma metodologia de projeto robusto do controlador ressonante em tempo discreto é proposta a partir de uma representação em espaço de estados do sistema em malha fechada e os parâmetros do controlador são obtidos através da solução de um problema de otimização convexa sujeito a restrições na forma de Desigualdades Matriciais Lineares (do inglês, Linear Matrix Inequalities - LMIs). A estratégia proposta foi validada por meio de resultados de simulação e experimentais obtidos com um inversor comercial de 3,5 kVA considerando os critérios estabelecidos na norma IEC 62040-3. Nestas condições, demonstrara-se um desempenho melhor do que os obtidos com a discretização do controlador projetado em tempo contínuo, sobretudo quando consideradas frequências de amostragem menores. / This work presents a study about discrete-time resonant controllers applied to uninterruptible power supplies (UPSs). First, different discretization methods are considered to obtain an equivalent UPS discrete-time model. Moreover, these methods are compared in the frequency domain in order to define the resonant controller structure to be employed. Then, a robust design methodology to the discrete-time resonant controller is proposed using a state-space representation of the closed-loop system and the controller parameters are obtained by solving a convex optimization problem subject to constraints in the form of Linear Matrix Inequalities (LMIs). The proposed strategy was validated by means of simulation and experimental results obtained with a 3.5 kVA commercial inverter taking into account the IEC 62040-3 norm requirements. In this conditions, a better performance was achieved than those obtained through discretization of a continuous-time controller, especially when considering smaller sampling frequencies.

Esta dissertação de mestrado aborda o problema de regulação robusta recursiva para sistemas lineares discretos sujeitos a incertezas paramétricas. Um novo funcional quadrático, baseado na combinação de função penalidade e função custo do tipo jogos, é projetado para lidar com este problema. Uma característica interessante desta abordagem é que a recursividade pode ser realizada sem a necessidade do ajuste de parâmetros auxiliares. Bastante útil para aplicações online. A solução proposta é baseada numa equação recursiva de Riccati. Também, a convergência e a estabilidade do regulador para o sistema linear incerto invariante no tempo são garantidas. / This dissertation deals with robust recursive regulators for discrete-time systems subject to parametric uncertainties. A new quadratic functional based on the combination of penalty functions and game theory is proposed to solve this class of problems. An important issue of this approach is that the recursiveness can be performed without the need of adjusting auxiliary parameters. It is useful for online applications. The solution proposed is based on Riccati equation which guarantees the convergence and stability of the time-invariant system.

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.

Esta dissertação de mestrado aborda o problema de regulação robusta recursiva para sistemas lineares discretos sujeitos a incertezas paramétricas. Um novo funcional quadrático, baseado na combinação de função penalidade e função custo do tipo jogos, é projetado para lidar com este problema. Uma característica interessante desta abordagem é que a recursividade pode ser realizada sem a necessidade do ajuste de parâmetros auxiliares. Bastante útil para aplicações online. A solução proposta é baseada numa equação recursiva de Riccati. Também, a convergência e a estabilidade do regulador para o sistema linear incerto invariante no tempo são garantidas. / This dissertation deals with robust recursive regulators for discrete-time systems subject to parametric uncertainties. A new quadratic functional based on the combination of penalty functions and game theory is proposed to solve this class of problems. An important issue of this approach is that the recursiveness can be performed without the need of adjusting auxiliary parameters. It is useful for online applications. The solution proposed is based on Riccati equation which guarantees the convergence and stability of the time-invariant system.

Most of the past research on the problem of deadlock avoidance for complex resource allocation systems (RAS) has acknowledged the fact that the computation of the maximally permissive (optimal) deadlock avoidance policy (DAP) possesses super-polynomial complexity for most RAS classes, and therefore, it has resorted to solutions that trade off maximal permissiveness for computational tractability. In this work, we distinguish between the off-line and the on-line computation that is required for the effective implementation of the maximally permissive DAP, and we seek to develop representations of this policy that will require minimal on-line computation. The particular representation that we adopt is that of a compact classifier that will effect the underlying dichotomy of the reachable state space into safe and unsafe subspaces. Through a series of reductions of the derived classification problem, we are also able to attain extensive reductions in the computational complexity of the off-line task of the construction of the sought classifier. In a first study of the aforementioned problem, we restrict our attention to a particular RAS class that is motivated by an ongoing project called Gadara. This particular RAS class accepts the separation of the safe and unsafe subspaces of its instantiations through a set of linear inequalities. We propose design procedures that will construct a classifier employing the minimum possible number of linear inequalities, and we formally establish their "completeness", i.e., their ability to provide an effective classifier for every instance of the considered RAS class. We also offer heuristics that, if necessary, can alleviate the computational effort that is necessary for the construction of the sought classifier. We extend the aforementioned results to encompass more general RAS classes, where the sought dichotomy might not be represented by a set of linear inequalities. To this end, we propose new parametric and non-parametric classification schemes for this more complex case, and establish formally their completeness. We also provide effective and computationally efficient procedures for the synthesis of the sought classifiers. A bottleneck in the developments described above is defined by the fact that they presuppose the availability of the enumerations of the RAS safe and unsafe subspaces. To address this obstacle, we propose a novel approach for the deployment of the maximally permissive DAP for RAS, that is based on the identification and the efficient storage of a critical subset of states of the underlying RAS state space. In particular, the proposed algorithm provides those critical states, while avoiding the complete enumeration of the RAS state space. Furthermore, we extend the existing theory on maximally permissive deadlock avoidance, so that it can handle RAS with reader/writer (R/W) locks. A key challenge that is posed by this new RAS class stems from the fact that the underlying state space is not necessarily finite. We effectively address this obstacle by taking advantage of special structure that exists in the set of unsafe states and enables a finite representation of this set through its minimal elements. Finally, we would like to mention that numerical experimentation demonstrates the efficacy of the proposed approaches, and establishes their ability to support the deployment of maximally permissive DAP for RAS with very large structure and state spaces. To the best of our knowledge, these experiments also establish the ability of the proposed methodology to effectively compute tractable implementations of the maximally permissive DAP for problem instances significantly beyond the capacity of any other approach currently available in the literature. Moreover, this is the first work to address the RAS with R/W locks.