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.

Data distribution management (DDM) is a mechanism to interconnect data producers and data consumers in a distributed application. Data producers provide useful data to consumers in the form of messages. For each message produced, DDM determines the set of data consumers interested in receiving the message and delivers it to those consumers. We are particularly interested in DDM techniques for parallel and distributed discrete event simulations. Thus far, researchers have treated synchronization of events (i.e. time management) and DDM independent of each other. This research focuses on how to realize time managed DDM mechanisms. The main reason for time-managed DDM is to ensure that changes in the routing of messages from producers to consumers occur in a correct sequence. Also time managed DDM avoids non-determinism in the federation execution, which may result in non-repeatable executions. An optimistic approach to time managed DDM is proposed where one allows DDM events to be processed out of time stamp order, but a detection and recovery procedure is used to recover from such errors. These mechanisms are tailored to the semantics of the DDM operations to ensure an efficient realization. A correctness proof is presented to verify the algorithm correctly synchronizes DDM events. We have developed a fully distributed implementation of the algorithm within the framework of the Georgia Tech Federated Simulation Development Kit (FDK) software. A performance evaluation of the synchronized DDM mechanism has been completed in a loosely coupled distributed system consisting of a network of workstations connected over a local area network (LAN). We compare time-managed versus unsynchronized DDM for two applications that exercise different mobility patterns: one based on a military simulation and a second utilizing a synthetic workload. The experiments and analysis illustrate that synchronized DDM performance depends on several factors: the simulations model (e.g. lookahead), applications mobility patterns and the network hardware (e.g. size of network buffers). Under certain mobility patterns, time-managed DDM is as efficient as unsynchronized DDM. There are also mobility patterns where time-managed DDM overheads become significant, and we show how they can be reduced.

This Thesis is concerned with the approximation of high order controllers or the controller reduction problem. We firstly consider approximating high-order controllers by low order controllers based on the closed-loop system approximation. By approximating the closed-loop system transfer function, we derive a new parametrized double-sided frequency weighted model reduction problem. The formulas for the input and output weights are derived using three closed-loop system configurations: (i) by placing a controller in cascade with the plant, (ii) by placing a controller in the feedback path, and (iii) by using the linear fractional transformation (LFT) representation. One of the weights will be a function of a free parameter which can be varied in the resultant frequency weighted model reduction problem. We show that by using standard frequency weighted model reduction techniques, the approximation error can be easily reduced by varying the free parameter to give more accurate low order controllers. A method for choosing the free parameter to get optimal results is being suggested. A number of practical examples are used to show the effectiveness of the proposed controller reduction method. We have then considered the relationships between the closed-loop system con gurations which can be expressed using a classical control block diagram or a modern control block diagram (LFT). Formulas are derived to convert a closed-loop system represented by a classical control block diagram to a closed-loop system represented by a modern control block diagram and vice versa.

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xvi, 209 p.; also includes graphics. Includes bibliographical references (p. 202-209). Available online via OhioLINK's ETD Center

The escape of trajectories is a ubiquitous phenomenon in open dynamical systems and stochastic processes. If escape occurs repetitively for a statistical ensemble of trajectories, the population of remaining trajectories often undergoes an exponential decay characterised by the so-called escape rate. Its inverse defines the lifetime of the decaying state, which represents an intrinsic property of the system. This paradigm is fundamental to nucleation theory and reaction-rate theory in chemistry, physics, and biology.<p><p>In many circumstances, escape is activated by the presence of noise, which may be of internal or external origin. This is the case for thermally activated escape over a potential energy barrier and, more generally, for noise-induced escape in continuous-time or discrete-time dynamics. <p><p>In the weak-noise limit, the escape rate is often observed to decrease exponentially with the inverse of the noise amplitude, a behaviour which is given by the van't Hoff-Arrhenius law of chemical kinetics. In particular, the two important quantities to determine in this case are the exponential dependence (the ``activation energy') and its prefactor.<p><p>The purpose of the present thesis is to develop an analytical method to determine these two quantities. We consider in particular one-dimensional continuous and discrete-time systems perturbed by Gaussian white noise and we focus on the escape from the basin of attraction of an attracting fixed point.<p><p>In both classes of systems, using path-integral methods, a formula is deduced for the noise-induced escape rate from the attracting fixed point across an unstable fixed point, which forms the boundary of the basin of attraction. The calculation starts from the trace formula for the eigenvalues of the operator ruling the time evolution of the probability density in noisy maps. The escape rate is determined by the loop formed by two heteroclinic orbits connecting back and forth the two fixed points in a two-dimensional auxiliary deterministic dynamical system. The escape rate is obtained, including the expression of the prefactor to van't Hoff-Arrhenius exponential factor./L'échappement des trajectoires est un phénomène omniprésent dans les systèmes dynamiques ouverts et les processus stochastiques. Si l'échappement se produit de façon répétitive pour un ensemble statistique de trajectoires, la population des trajectoires restantes subit souvent une décroissance exponentielle caractérisée par le taux d'échappement. L'inverse du taux d'échappement définit alors la durée de vie de l'état transitoire associé, ce qui représente une propriété intrinsèque du système. Ce paradigme est fondamental pour la théorie de la nucléation et, de manière générale, pour la théorie des taux de transitions en chimie, en physique et en biologie.<p><p>Dans de nombreux cas, l'échappement est induit par la présence de bruit, qui peut être d'origine interne ou externe. Ceci concerne en particulier l'échappement activé thermiquement à travers une barrière d'énergie potentielle, et plus généralement, l'échappement dû au bruit dans les systèmes dynamiques à temps continu ou à temps discret.<p><p>Dans la limite de faible bruit, on observe souvent une décroissance exponentielle du taux d'échappement en fonction de l'inverse de l'amplitude du bruit, un comportement qui est régi par la loi de van't Hoff-Arrhenius de la cinétique chimique. En particulier, les deux quantités importantes de cette loi sont le coefficient de la dépendance exponentielle (c'est-à-dire ``l'énergie d'activation') et son préfacteur.<p><p>L'objectif de cette thèse est de développer une théorie analytique pour déterminer ces deux quantités. La théorie que nous présentons concerne les systèmes unidimensionnels à temps continu ou discret perturbés par un bruit blanc gaussien et nous considérons le problème de l'échappement du bassin d'attraction d'un point fixe attractif. Pour s'échapper, les trajectoires du système bruité initialement contenues dans ce bassin d'attraction doivent alors traverser un point fixe instable qui forme la limite du bassin.<p><p>Dans le présent travail, et pour les deux types de systèmes, une formule est dérivée pour le taux d'échappement du point fixe attractif en utilisant des méthodes d'intégrales de chemin. Le calcul utilise la formule de trace pour les valeurs propres de l'opérateur gouvernant l'évolution temporelle de la densité de probabilité dans le système bruité. Le taux d'échappement est déterminé en considérant la boucle formée par deux orbites hétéroclines liant dans les deux sens les deux points fixes dans un système dynamique auxiliaire symplectique et bidimensionnel. On obtient alors le taux d'échappement, comprenant l'expression du préfacteur de l'exponentielle de la loi de van't Hoff-Arrhenius. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Este trabalho aborda o problema de controle ótimo por modos deslizantes via função penalidade para sistemas de tempo discreto. Para resolver este problema será desenvolvido uma estrutura matricial alternativa baseada no problema de mínimos quadrados ponderados e funções penalidade. A partir desta nova formulação é possível obter a lei de controle ótimo por modos deslizantes, as equações de Riccati e a matriz do ganho de realimentação através desta estrutura matricial alternativa. A motivação para propormos essa nova abordagem é mostrar que é possível obter uma solução alternativa para o problema clássico de controle ótimo por modos deslizantes. / This work introduces a penalty function approach to deal with the optimal sliding mode control problem for discrete-time systems. To solve this problem an alternative array structure based on the problem of weighted least squares penalty function will be developed. Using this alternative matrix structure, the optimal sliding mode control law of, the matrix Riccati equations and feedback gain were obtained. The motivation of this new approach is to show that it is possible to obtain an alternative solution to the classic problem of optimal sliding mode control.

Esta tese apresenta novos algoritmos que resolvem problemas de estimativas filtrada, suavizadora e preditora para sistemas singulares no tempo discreto usando apenas argumentos determinísticos. Cada capítulo aborda inicialmente as estimativas para o sistema nominal e em seguida, as versões robustas para o sistema com incertezas limitadas. Os resultados encontrados podem ser aplicados tanto em sistemas invariantes como variantes no tempo discreto, utilizando a mesma estrutura do filtro de Kalman. Nos últimos anos, uma quantidade significativa de trabalhos envolvendo estimativas singulares foi publicada enfocando apenas a estimativa filtrada sob a justificativa de que a estimativa preditora era de significativa complexidade quando modelada pelo método dos mínimos quadrados. Por este motivo, poucos trabalhos, como NIKOUKHAH et al. (1992) e ZHANG et al. (1998), deduziram a estimativa preditora. Este último artigo apresentou também um algoritmo para a estimativa suavizadora, mas usando o modelo de inovação ARMA. No entanto, até onde foi possível identificar, nenhum trabalho até agora resolveu o problema de estimativa robusta, considerando incertezas nos parâmetros, para sistemas singulares. Para a dedução das estimativas singulares robustas, esta tese tomou como base SAYED (2001), que deduz o filtro de Kalman robusto com incertezas limitadas utilizando uma abordagem determinística, o chamado filtro BDU. Os filtros robustos para sistemas singulares apresentados nesta tese, são mais abrangentes que os apresentados em SAYED (2001). Quando particularizados para o espaço de estados sem incertezas, todos os filtros se assemelham ao filtro de Kalman. / New algorithms to optimal recursive filtering, smoothed and prediction for general time-invariant or time-variant descriptor systems are proposed in this thesis. The estimation problem is addressed as an optimal deterministic trajectory fitting. This problem is solved using exclusively deterministic arguments for systems with or without uncertainties. Kalman type recursive algorithms for robust filtered, predicted and smoothed estimations are derived. In the last years, many papers have paid attention to the estimation problems of linear singular systems. Unfortunately, all those works were concentrated only on the study of filtering problems, for nominal systems. The predicted and smoothed filters are more involved and were considered only by few works : NIKOUKHAH et al. (1992) and ZHANG et al. (1998) had proposed a unified approach for filtering, prediction and smoothing problems which were derived by using the projection formula and were calculated based on the ARMA innovation model, but they had not considered the uncertainties. In this thesis its applied for descriptor systems a robust procedure for usual state space systems developed by SAYED (2001), called BDU filter. It is obtained a robust descriptor Kalman type recursions for filtered, predicted and smoothed estimates. Considering the nominal state space, all descriptor filters developed in this work collapse to the Kalman filter.

Este trabalho aborda o problema de controle ótimo por modos deslizantes via função penalidade para sistemas de tempo discreto. Para resolver este problema será desenvolvido uma estrutura matricial alternativa baseada no problema de mínimos quadrados ponderados e funções penalidade. A partir desta nova formulação é possível obter a lei de controle ótimo por modos deslizantes, as equações de Riccati e a matriz do ganho de realimentação através desta estrutura matricial alternativa. A motivação para propormos essa nova abordagem é mostrar que é possível obter uma solução alternativa para o problema clássico de controle ótimo por modos deslizantes. / This work introduces a penalty function approach to deal with the optimal sliding mode control problem for discrete-time systems. To solve this problem an alternative array structure based on the problem of weighted least squares penalty function will be developed. Using this alternative matrix structure, the optimal sliding mode control law of, the matrix Riccati equations and feedback gain were obtained. The motivation of this new approach is to show that it is possible to obtain an alternative solution to the classic problem of optimal sliding mode control.