Doctor of Philosophy / Electrical and Computer Engineering / Balasubramaniam Natarajan / A cyber-physical system (CPS) typically consists of networked computational elements that control physical processes. As an integral part of CPS, the widespread deployment of communicable sensors makes the task of monitoring and control quite challenging especially from the viewpoint of scalability and complexity. This research investigates two unique aspects of overcoming such barriers, making a CPS more robust against data explosion and network vulnerabilities. First, the correlated characteristics of high-resolution sensor data are exploited to significantly reduce the fused data volume. Specifically, spatial, temporal and spatiotemporal compressed sensing approaches are applied to sample the measurements in compressed form. Such aggregation can directly be used in centralized static state estimation even for a nonlinear system. This approach results in a remarkable reduction in communication overhead as well as memory/storage requirement. Secondly, an agent based architecture is proposed, where the communicable sensors (identified as agents) also perform local information processing. Based on the local and underdetermined observation space, each agent can monitor only a specific subset of global CPS states, necessitating neighborhood information exchange. In this framework, we propose an agent based static state estimation encompassing local consensus and least square solution. Necessary bounds for the consensus weights are obtained through the maximum eigenvalue based convergence analysis and are verified for a radial power distribution network. The agent based formulation is also applied for a linear dynamical system and the consensus approach is found to exhibit better and more robust performance compared to a diffusion filter. The agent based Kalman consensus filter (AKCF) is further investigated, when the agents can choose between measurements and/or consensus, allowing the economic allocation of sensing and communication tasks as well as the temporary omission of faulty agents. The filter stability is guaranteed by deriving necessary consensus bounds through Lyapunov stability analysis. The states dynamically estimated from AKCF can be used for state-feedback control in a model predictive fashion. The effect of lossy communication is investigated and critical bounds on the link failure rate and the degree of consensus that ensure stability of the agent based control are derived and verified via simulations.

abstract: In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems - in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) - whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers - machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers. We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2016

Orientador: Fábio Roberto Chavarette / Resumo: São diversos os equipamentos de engenharia que apresentam vibrações mecânicas, e estas podem ser observadas em forma de acelerações, deslocamentos e velocidade. Os primeiros estudos envolvendo vibrações foram direcionados aos fenômenos naturais e modelagem matemática de sistemas vibrantes, então, começou a aplicação desses estudos em equipamentos de engenharia. Vibrações mecânicas, na maioria dos sistemas dinâmicos, são consideradas como algo indesejado e podem ser danosos. Porém, existem situações que são utilizadas para melhorar o funcionamento e desempenho de máquinas. São diversas as causas de vibrações em sistemas de engenharia, neste trabalho, destaca-se as vibrações causadas por impacto. Quando componentes destes sistemas impactam entre si, causando ruídos de curta duração, são caracterizados como sistemas tipo vibro - impacto. Podem ser citados diversos equipamentos com essas características, como rolos compactadores de solo, martelos de impacto, perfuratrizes de solo, etc. Neste trabalho, demonstra-se o comportamento dinâmico de um sistema vibro – impactante. Para análise deste sistema, foram desenvolvidos códigos computacionais, através do software Octave. No diagrama de estabilidade de Lyapunov, verificou-se que, pontualmente o sistema se apresenta de forma estável. A partir da variação da frequência de excitação, foi observado através dos históricos no tempo, espectros de frequência, mapas de Poincaré e planos de fase, um comportamento periódico e estável, com sit... (Resumo completo, clicar acesso eletrônico abaixo) / Mestre

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-06T12:39:52Z No. of bitstreams: 1 viniciuscampistabrum.pdf: 846002 bytes, checksum: 5ac93812c3739c70741f6052b77b22c8 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-06-06T14:06:19Z (GMT) No. of bitstreams: 1 viniciuscampistabrum.pdf: 846002 bytes, checksum: 5ac93812c3739c70741f6052b77b22c8 (MD5) / Made available in DSpace on 2017-06-06T14:06:19Z (GMT). No. of bitstreams: 1 viniciuscampistabrum.pdf: 846002 bytes, checksum: 5ac93812c3739c70741f6052b77b22c8 (MD5) Previous issue date: 2015-08-28 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Análise de agrupamento é uma tarefa descritiva e não-supervisionada de mineração de dados que utiliza amostras não-rotuladas com o objetivo de encontrar grupos naturais, isto é, grupos de amostras fortemente relacionadas de forma que as amostras que per-tençam a um mesmo grupo sejam mais similares entre si do que amostras em qualquer outro grupo. Avaliação ou validação é considerada uma tarefa essencial dentro da análise de agrupamento. Essa tarefa apresenta técnicas que podem ser divididas em dois tipos: técnicas não-supervisionadas ou de validação interna e técnicas supervisionadas ou de va-lidação externa. Trabalhos recentes introduziram uma abordagem de validação interna que busca avaliar e melhorar a estabilidade do algoritmo de agrupamento por meio de identificação e remoção de amostras que são consideradas prejudiciais e, portanto, de-veriam ser estudadas isoladamente. Por meio de experimentos foi identificado que essa abordagem apresenta características indesejáveis que podem resultar em remoção de todo um grupo e ainda não garante melhoria de estabilidade. Considerando essas questões, neste trabalho foi desenvolvida uma abordagem mais ampla utilizando algoritmo genético para análise de agrupamento e estabilidade de dados. Essa abordagem busca garantir melhoria de estabilidade, reduzir o número de amostras para remoção e permitir que o usuário controle o processo de análise de estabilidade, o que resulta em maior aplicabi-lidade e confiabilidade para tal processo. A abordagem proposta foi avaliada utilizando diferentes algoritmos de agrupamento e diferentes bases de dados, sendo que uma base de dados genotípicos também foi utilizada com o intuito de aquisição e validação de conhe-cimento. Os resultados mostram que a abordagem proposta é capaz de garantir melhoria de estabilidade e também é capaz de reduzir o número de amostras para remoção. Os resultados também sugerem a utilização da abordagem como uma ferramenta promissora para aquisição e validação de conhecimento em estudos de associação ampla do genoma (GWAS). Este trabalho apresenta uma abordagem que contribui para aquisição e valida-ção de conhecimento por meio de análise de agrupamento e estabilidade de dados. / Clustering analysis is a descriptive and unsupervised data mining task, which uses non-labeled samples in order to find natural groups, i.e. groups of closely related samples such that samples within the same cluster are more similar than samples within the other clusters. Evaluation and validation are considered essential tasks within the clustering analysis. These tasks present techniques that can be divided into two kinds: unsuper-vised or internal validation techniques and supervised or external validation techniques. Recent works introduced an internal clustering validation approach to evaluate and im-prove the clustering algorithm stability through identifying and removing samples that are considered harmful and therefore they should be studied separately. Through experi-mentation, it was identified that this approach has two undesirable characteristics, it can remove an entire cluster from dataset and still decrease clustering stability. Taking into account these issues, in this work a broader approach was developed using genetic algo-rithm for clustering and data stability analysis. This approach aims to increase stability, to reduce the number of samples for removal and to allow the user control the stability analysis process, which gives greater applicability and reliability for such process. This approach was evaluated using different kinds of clustering algorithm and datasets. A genotype dataset was also used in order to knowledge acquisition and validation. The results show the approach proposed in this work is able to increase stability, and it is also able to reduce the number of samples for removal. The results also suggest the use of this approach as a promising tool for knowledge acquisition and validation on genome-wide association studies (GWAS). This work presents an approach that contributes for knowledge acquisition and validation through clustering and data stability analysis.

Magister Scientiae - MSc / Efficient numerical approaches for parameter dependent problems have been an inter- esting subject to numerical analysts and engineers over the past decades. This is due to the prominent role that these problems play in modeling many real life situations in applied sciences. Often, the choice and the e ciency of the approaches depend on the nature of the problem to solve. In this work, we consider the general linear first-order singularly perturbed Volterra integro-differential equations (SPVIDEs). These singularly perturbed problems (SPPs) are governed by integro-differential equations in which the derivative term is multiplied by a small parameter, known as "perturbation parameter". It is known that when this perturbation parameter approaches zero, the solution undergoes fast transitions across narrow regions of the domain (termed boundary or interior layer) thus affecting the convergence of the standard numerical methods. Therefore one often seeks for numerical approaches which preserve stability for all the values of the perturbation parameter, that is "numerical methods. This work seeks to investigate some "numerical methods that have been used to solve SPVIDEs. It also proposes alternative ones. The various numerical methods are composed of a fitted finite difference scheme used along with suitably chosen interpolating quadrature rules. For each method investigated or designed, we analyse its stability and convergence. Finally, numerical computations are carried out on some test examples to con rm the robustness and competitiveness of the proposed methods.

Alors qu'il est bien connu que le phénomène d'instabilité de Faraday est une manifestation d'ondes de gravité capillaire, son comportement lorsque les effets capillaires et gravitationnels disparaissent reste inexploré théoriquement et expérimentalement. Une étude expérimentale et théorique détaillée est réalisée pour comprendre la physique de ce phénomène dans une petite cavité rectangulaire où la proximité des murs entraîne des contraintes considérables sur les parois latérales. Un couple de liquides binaires est utilisé avec une faible tension interfaciale pour une interface presque plate. Le contrôle thermique de ce système de fluide est utilisé pour diminuer la force capillaire et d’étudier ainsi les instabilités de Faraday dans les fluides miscibles où la tension interfaciale s’annule. Afin de prendre en compte les effets gravitationnels, l'expérience a été réalisée dans des campagnes de vols paraboliques. Pour l'approche théorique, une analyse de stabilité linéaire est effectuée à l'aide d'équations de Navier-Stokes dans un système de fluide visqueux incompressible et newtonien. Ceci est réalisé grâce à une méthode de Fourier-Floquet résultant en un problème aux valeurs propres. Les comparaisons montrent des différences non négligeables. Les équations sont ensuite résolues en incluant des effets d'amortissement visqueux pour compenser les contraintes des parois latérales. Les fluides binaires ont fourni une option commode pourchanger le coefficient de tension interfaciale en augmentant la température jusqu’à la température critique, ce qui a permis de passer d’un système de fluides non miscibles à celui des fluides miscibles tout en restant au-dessous de la température d’ébullition. Le taux d'amortissement visqueux linéaire est mesuré expérimentalement. La correction des calculs théoriques en prenant en compte le taux d'amortissement visqueux a permis une amélioration nette des résultats et donc de mieux comprendre la prédiction de l'amplitude critique expérimentale pour les modes sous-harmonique et harmonique. / While it is well known that the phenomenon of Faraday instability is a manifestation of vibrational acceleration, its behaviour when both the capillary and gravitational effects vanish, remains unexplored theoretically and experimentally. A detailed experimental and theoretical study is performed to understand the physics of this phenomenon in small rectangular geometry where the proximity of wall results in considerable sidewall stresses. A novel binary liquids system is utilized with low interfacial tension for a near flat interface. Thermal control of fluid system is utilized for achieving reduction in capillary force with study of miscible fluids where interfacial tension reduces to almost zero. In order to discriminate between gravity and capillarity effects, experiments were performed in parabolic flight campaigns. . For the theoretical approach a linear stability analysis is performed through Navier-Stokes equations in a Newtonian incompressible viscous fluid system. This is achieved through a Fourier Floquet method resulting into an eigenvalue problem. Equations are solved by including viscous damping effects for compensating sidewall stresses. Experimentally binary fluids provided a convenient option of changing the coefficient of interfacial tension by temperature control and going through immiscible to miscible system without change of liquid charge. Viscous damping rate is determined experimentally by measuring the linear damping rate. The correction in the theoretical calculations with the viscous damping rate helped in achieving a better understanding of the prediction of the experimental critical amplitude for sub-harmonic and harmonic modes.

Studying the coupling between buoyancy-driven instabilities and chemical reactions is not only relevant to fundamental research, but has also recently gained increased interest because of its relevance to CO$_2$ sequestration in subsurface geological zones. This technique aims to limit the emissions of CO$_2$ to the atmosphere, with a view to mitigating climate change. When injected in e.g. a saline aquifer, CO$_2$ dissolves into the brine occupying the geological formation, thereby increasing the density of the aqueous phase. This increase of density upon dissolution leads to a denser fluid boundary layer rich in CO$_2$ on top of less dense fluid in the gravity field, which drives dissolution-driven convection. This process, also called convective dissolution, accelerates the transport of dissolved CO$_2$ to the host phase and thus improves the safety of CO$_2$ sequestration. The same kind of instability can develop in other contexts involving the dissolution of a phase A into a host phase, such as solid dissolution or transfer between partially miscible liquids. In this context, the goal of our thesis is to understand how chemical reactions coupled to dissolution-driven convection affect the dynamics of the dissolving species A in the host solution. To do so, we introduce a general reaction of the type A + B $rightarrow$ C where A, B and C affect the density of the aqueous solution. We theoretically analyze the influence of the relative physical properties of A, B and C on the convective dynamics. Our theoretical analysis uses a reaction-diffusion-convection model for the evolution of solute concentration in a host fluid solvent occupying a porous medium. First, we quantify the characteristic growth rate of the perturbations by using a linear stability analysis. Thereby we show that a chemical reaction can either accelerate or slow down the development of convection, depending on how it modifies the density profile that develops in the reactive solution. In addition, new dynamics are made possible by differential diffusion effects. Then, by analyzing the full nonlinear dynamics with the help of direct numerical simulations, we calculate the dissolution flux into the host phase. In particular, the dissolution flux can be amplified when convection develops earlier, as CO$_2$ is then transported faster away from the interface. Finally, we compare these theoretical and numerical predictions with results of laboratory experiments and discuss the possible implications of this study for CO$_2$ sequestration. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Ce travail de thèse traite de l’analyse de la stabilité et la stabilisation des systèmes non-linéaires représentés par des modèles T-S. L’objectif est de réduire le conservatisme des conditions de stabilité, obtenue par la méthode directe de Lyapunov, et écrites, dans la mesure du possible, sous forme de LMIs. Dans ce cadre, deux contributions principales ont été apportées. Tout d’abord, nous avons proposé de nouvelles conditions de synthèse non-quadratique de lois de commande, strictement LMIs et sans restriction d’ordre, pour les modèles T-S via des FLICs. En effet, dans ce contexte, les résultats de la littérature ne sont valables que pour les modèles T-S d’ordre inférieur ou égal à 2. Afin de lever cette restriction, les conditions ont été obtenues grâce à la démonstration d’une propriété de dualité. Ensuite, peu de travaux traitant de la spécification des performances en boucle fermée, de nouvelles conditions LMIs (quadratiques et non-quadratiques) ont été proposées via le concept de D-stabilité. Dans un premier temps, la synthèse de lois de commande PDC et non-PDC D-stabilisantes a été proposée pour les modèles T-S nominaux. Ensuite, ces résultats ont été étendus au cas des modèles T-S incertains. De plus, nous avons mis en évidence, au travers d’un exemple de D-stabilisation en attitude d’un modèle de drone quadrirotor, que les modèles T-S incertains pouvaient être avantageusement considérés lorsque les non-linéarités d’un modèle non-linéaire dépendent à la fois de l’état et de l’entrée. / This work deals with the stability analysis and the stabilisation of nonlinear systems represented by T-S models.The goal is to reduce the conservatism of the stability conditions, obtained through the direct Lyapunov methodand written, when it is possible, as LMIs. In this framework, two main contributions has been proposed. First ofall, we have proposed some new conditions based on FLICs, strictly LMIs and without any order restrictions, forthe non-quadratic design of control laws devoted to stabilize T-S models. Indeed, in this non-quadratic context,the existing works are only available for 2nd order T-S models. In order to unlock this restriction, the proposed conditions have been obtained based on the proof of a dual property. Then, starting from the fact that few worksdeals with the closed-loop performances specification, some new LMI conditions (quadratic and non-quadratic)have been proposed via the D-stability concept. As a first step, D-stabilizing PDC and non-PDC controller designhas been considered for nominal T-S models. Then, these results have been extended to uncertain T-S models.Moreover, it has been highlighted, from an example of the attitude D-stabilization of a quadrotor model, that wecan make use of uncertain T-S models to cope with nonlinear models involving nonlinearities depending on bothstate and input variables.

Philosophiae Doctor - PhD / In this thesis, we consider some nonlinear differential models that govern unsteady magneto-hydrodynamic convective flow and mass transfer of viscous, incompressible,electrically conducting fluid past a porous plate with/without heat sources. The study focusses on the effect of a combination of a number of physical parameters (e.g., chemical reaction, suction, radiation, soret effect,thermophoresis and radiation absorption) which play vital role in these models.Non dimensionalization of these models gives us sets of differential equations. Reliable solutions of such differential equations can-not be obtained by standard numerical techniques. We therefore resorted to the use of the singular perturbation approaches. To proceed, each of these model problems is discretized in time by using a suitable time-stepping method and then by using a fitted operator finite difference method in spatial direction. The combined methods are then analyzed for stability and convergence. Aiming to study the robustness of the proposed numerical schemes with respect to change in the values of the key parame- ters, we present extensive numerical simulations for each of these models. Finally, we confirm theoretical results through a set of specificc numerical experiments.

Afin de satisfaire les besoins futurs en énergie et de réduire l’impact environnemental, l’application de l’énergie renouvelable propre a été récemment reconsidérée. Dans ce contexte, un intérêt croissant pour le système d’alimentation isolé a été mesuré.Le besoin de topologies de faible puissance alimentées par un générateur photovoltaïque, évitant l’utilisation de transformateur, accentue l’étude de systèmes d’alimentation autonomes de basse tension. D’où la nécessité d’étudier les stratégiesde contrôle associées garantissant la stabilité, la fiabilité et l’efficacité.À mesure que les systèmes d’alimentation autonome deviennent plus complexes, les non-linéarités jouent un rôle de plus en plus important dans le comportement du système. La modélisation doit refléter avec précision la dynamique des composants et du système. En outre, les outils d’analyse des systèmes dynamiques devraient être fiable, même dans différents régimes de fonctionnement, fournissant des prédictions précises du comportement de ces derniers. Ce travail est consacré à l’étude d’un système photovoltaïque autonome. La structure proposée se compose d’un panneau photovoltaïque, d’un hacheur et d’une charge connectée en cascade via un bus continu. Les efforts de recherche se concentrent sur le processus de modélisation et l’analyse de stabilité du système. Une implémentation avec une description complète du modèle est ainsi détaillée est validé epar des résultats de simulation. Après avoir donné l’état de l’art, le manuscrit est divisé en quatre parties. Ces parties sont dédiées à la modélisation d’une installation photovoltaïque, à l’amélioration de la simulation numérique, et à l’étude de dynamique de ce système sous contrôles numériques.La thèse présente un aperçu des modèles de générateurs photovoltaïques. Ensuite,un modèle électrique modifié du panneau photovoltaïque est proposé. Nous avons également détaillé le processus de modélisation de l’installation photovoltaïque.Un solveur amélioré de modèle Differential-Algebraic Equations (DAEs) est ensuite développé. Une dixième approche de modélisation est aussi présentée. Nous avons également décrit le système photovoltaïque par un modèle discret simplifié. Ensuite, l’analyse de stabilité du système étudié est détaillée. En outre, nous avons étudié le comportement chaotique qui apparaît dans l’installation photovoltaïque basée sur le hacheur à deux cellules. Le but de la dernière partie est de montrer comment stabiliser l’orbite chaotique du système. Enfin, pour atteindre cet objectif, la commande par retour d’état retardé Time-Delayed Feedback Control (TDFC) est appliquée. / In order to satisfy future energy requirement and reduce environmental impact, application of clean renewable energy, have been reconsidered recently. In this context, a growing interest in isolated power system has been observed. The need of low power topologies fed by photovoltaic array avoiding the use oftransformer open the study of small-scale stand-alone power system. Hence, theneed to study the associated control design strategies ensuring stability, reliability and high efficiency.As systems become more complex, nonlinearities play an increasingly importantrole in stand-alone power system behaviour. Modeling must accurately reflect component and system dynamics. In addition, analysis tools should continue to workreliably, even under various system conditions, providing accurate predictions of systems behaviour.This work is devoted to the study of a stand-alone photovoltaic power system.The proposed structure consists on photovoltaic array, a dc-dc buck converter, anda load connected in cascade through a dc bus. The research efforts focus on themodeling process and stability analysis, which leads to an implementation with acomprehensive description validated through simulation results.After giving the state-of-the-art in second chapter, the manuscript is divided into four chapters. These parts are dedicated to photovoltaic plant modeling, the numeric simulation improvements and dynamic investigation of the photovoltaic system under digital controls.The thesis presents an overview of the photovoltaic generator models. Then, amodified photovoltaic array model is proposed. We also detailed the photovoltaic plant modeling process. An improved Differential-Algebraic Equations (DAEs)solver is then investigated. We also described the photovoltaic system by a simplified discrete model. Then, the dynamic stability analysis is detailled. In addition,we have studied the chaotic behaviour that appears in the photovoltaic plant basedon the two-cell dc-dc buck converter.The aim of the last part is to show, using control theory and numerical simulation,how to apply a method to stabilize the chaotic orbit. Finally, to accomplish this aim, a time-delayed feedback controller is used.