Nous étudions la commandabilité du système de contrôle décrivant le procédé de roulement, sans glissement ni pivotement, de deux variétés riemanniennes n-dimensionnelles, l'une sur l'autre. Ce modèle est étroitement associé aux concepts de développement et d'holonomie des variétés, et il se généralise au cas de deux variétés affines. Les contributions principales sont celles données dans quatre articles, attachés à la fin de la thèse.Le premier d'entre eux «Rolling manifolds and Controllability : the 3D case»traite le cas où les deux variétés sont 3-dimensionelles. Nous donnons alors, la liste des cas possibles pour lesquelles le système n'est pas commandable.Dans le deuxième papier «Rolling manifolds on space forms», l'une des deux variétés est supposée être de courbure constante. On peut alors réduire l'étude de commandabilité à l'étude du groupe d'holonomie d'une certaine connexion vectorielle et on démontre, par exemple, que si la variété à courbure constante est une sphère n-dimensionelle et si ce groupe de l'holonomie n'agit pas transitivement, alors l'autre variété est en fait isométrique à la sphère.Le troisième article «A Characterization of Isometries between Riemannian Manifolds by using Development along Geodesic Triangles» décrit, en utilisant le procédé de roulement (ou développement) le long des lacets, une version alternative du théorème de Cartan-Ambrose-Hicks, qui caractérise, entre autres, les isométries riemanniennes. Plus précisément, on prouve que si on part d'une certaine orientation initiale, et si on ne roule que le long des lacets basés au point initial (associé à cette orientation), alors les deux variétés sont isométriques si (et seulement si) les chemins tracés par le procédé de roulement sur l'autre variété, sont tous des lacets.Finalement, le quatrième article «Rolling Manifolds without Spinning» étudie le procédé de roulement et sa commandabilité dans le cas où l'on ne peut pas pivoter. On caractérise alors les structures de toutes les orbites possibles en termes des groupes d'holonomie des variétés en question. On montre aussi qu'il n'existe aucune structure de fibré principal sur l'espace d'état tel que la distribution associée à ce modèle devienne une distribution principale, ce qui est à comparer notamment aux résultats du deuxième article.Par ailleurs, dans la troisième partie de cette thèse, nous construisons soigneusement le modèle de roulement dans le cadre plus général des variétés affines, ainsi que dans celui des variétés riemanniennes de dimensiondifférente. / We study the controllability of the control system describing the rolling motion, without slipping nor spinning, of two n-dimensional Riemannian manifolds, one against the other.This model is closely related to the concepts of development and holonomy of the manifolds, and it generalizes to the case of affine manifolds.The main contributions are those given in four articles attached to the the thesis.First of them "Rolling manifolds and Controllability: the 3D case"deal with the case where the two manifolds are 3-dimensional. We give the listof all the possible cases for which the system is not controllable.In the second paper "Rolling manifolds on space forms"one of the manifolds is assumed to have constant curvature.We can then reduce the study of controllability to the study of the holonomy groupof a certain vector bundle connection and we show, for example, thatif the manifold with the constant curvature is an n-sphere and ifthis holonomy group does not act transitively,then the other manifold is in fact isometric to the sphere.The third paper "A Characterization of Isometries between Riemannian Manifolds by using Development along Geodesic Triangles"describes, by using the rolling motion (or development) along the loops,an alternative version of the Cartan-Ambrose-Hicks Theorem,which characterizes, among others, the Riemannian isometries.More precisely, we prove that if one starts from a certain initial orientation,and if one only rolls along loops based at the initial point (associated to this orientation),then the two manifolds are isometric if (and only if) the pathstraced by the rolling motion on the other manifolds, are all loops.Finally, the fourth paper "Rolling Manifolds without Spinning"studies the rolling motion, and its controllability, when slipping is allowed.We characterize the structure of all the possible orbits in terms of the holonomy groupsof the manifolds in question. It is also shown that there does not exist anyprincipal bundle structure such that the related distribution becomes a principal distribution,a fact that is to be compared especially to the results of the second article.Furthermore, in the third chapter of the thesis, we construct carefully the rolling modelin the more general framework of affine manifolds, as well as that of Riemannian manifolds,of possibly different dimensions.

The effects of winds and/or waves on ship motions, forces, moments, maneuverability and controllability are investigated with URANS computations. The air/water flow computations employ a semi-coupled approach in which water is not affected by air, but air is computed assuming the free surface as a moving immersed boundary. The exact potential solution of waves/wind problem is modified introducing a logarithmic blending in air, and imposed as boundary and initial conditions. The turbulent air flows over 2D water waves are studied to investigate the effects of waves on incoming wind flow. Ship airwake computations are performed with different wind speeds and directions for static drift and dynamic PMM in calm water, pitch and heave in regular waves, and 6DOF motions in irregular waves simulating hurricane CAMILLE. Ship airwake analyses show that the vortical structures evolve due to ship motions and affect the ship dynamics significantly. Strong hurricane head and following winds affect up to 28% the resistance and 7% the motions. Beam winds have most significant effects causing considerable roll motion and drift forces, affecting the controllability of the ship. A harmonic wave group single run seakeeping procedure is developed, validated and compared with regular wave and transient wave group procedures. The regular wave procedure requires multiple runs, whereas single run procedures obtain the RAOs for a range of frequencies at a fixed speed, assuming linear ship response. The transient wave group procedure provides continuous RAOs, while the harmonic wave group procedure obtains discrete transfer functions, but without focusing. Verification and validation studies are performed for transient wave group procedure. Validation is achieved at the average interval of 9.54 (%D). Comparisons of the procedures show that harmonic wave group is the most efficient, saving 75.8% on the computational cost compared to regular wave procedure. Error values from all procedures are similar at 4 (%D). Harmonic wave group procedure is validated for a wide range of Froude numbers, with satisfactory results. Deterministic wave groups are used for three sisters rogue waves modeling. A 6DOF ship simulation is demonstrated which shows total loss of controllability with extreme ship motions, accelerations and structural loads.

Fuzzy set is a generalization of the classical set. A classical set is distinguished from another by a sharp boundary at some threshold value and therefore, they are also known as crisp set. In fuzzy theory, sharp boundary and crisp set are replaced by partial truth and fuzzy sets. The idea of partial truth facilitates information description especially those communicated through natural language whose transition between descriptive terms are not abrupt discontinuities. Instead, the transition is a smooth change over a range corresponding to the degree of fulfillment each intermediate elements has according to the operating definition of the concept. The shape of a fuzzy set is defined by its membership function. This, by far, has been the common extent of concern regarding the membership function. Different applications may use the membership function to describe different variables such as speed, position, temperature, dirtiness, traffic conditions etc. But the underlying application of fuzzy sets remains the same: to describe information whose membership function, created in an initial setting, preserve the same size and shape throughout its entire application. In other word, fuzzy sets are utilized as if they are static entities. Nothing has been said about how an initially defined membership function can develop over time with respect to a system. The current research proposes a new framework that concerns the evolution of membership functions. We introduce the concept of membership function propagation as a dynamic description of uncertainty. Given a dynamical system with a set of uncertain initial states which can be represented by membership functions, the membership function propagation describes how these membership functions evolve over time with respect to the system. The evolution produces a set of propagated membership functions that have different size and shape from their predecessors. They represent the uncertainty associated with the states of the system at a given time. This new description also confers new definitions for two important concepts in control theory, namely controllability and observability. These two concepts are re-introduced in a fuzzy sense, based on the concept of membership function propagation. By assuming convexity of the fuzzy set, criterions for controllability and observability can be derived. These criterions are illustrated by MATLAB and SIMULINK simulations of an inverted pendulum and a 2 degree of freedom mechanical manipulator.

Networked systems have attracted great interests from the control society during the last decade. Several issues rising from the recent research are addressed in this dissertation. Connectedness is one of the important conditions that enable distributed coordination in a networked system. Nonetheless, it has been assumed in most implementations, especially in continuous-time applications, until recently. A nonlinear weighting strategy is proposed in this dissertation to solve the connectedness preserving problem. Both rendezvous and formation problem are addressed in the context of homogeneous network. Controllability of heterogeneous networks is another issue which has been long omitted. This dissertation contributes a graph theoretical interpretation of controllability. Distributed sensor networks make up another important class of networked systems. A novel estimation strategy is proposed in this dissertation. The observability problem is raised in the context of our proposed distributed estimation strategy, and a graph theoretical interpretation is derived as well. The contributions of this dissertation are as follows: It solves the connectedness preserving problem for networked systems. Based on that, a formation process is proposed. For heterogeneous networks, the leader-follower structure is studied and sufficient and necessary conditions are presented for the system to be controllable. A novel estimation strategy is proposed for distributed sensor networks, which could improve the performance. The observability problem is studied for this estimation strategy and a necessary condition is obtained. This work is among the first ones that provide graph theoretical interpretations of the controllability and observability issues.

In this thesis, we develop a feedback-invariant theory of local controllability for affine distributions. We begin by developing an unexplored notion in control theory that we call proper small-time local controllability (PSTLC). The notion of PSTLC is developed for an abstraction of the well-known notion of a control-affine system, which we call an affine system. Associated to every affine system is an affine distribution, an adaptation of the notion of a distribution. Roughly speaking, an affine distribution is PSTLC if the local behaviour of every affine system that locally approximates the affine distribution is locally controllable in the standard sense. We prove that, under a regularity condition, the PSTLC property can be characterized by studying control-affine systems. The main object that we use to study PSTLC is a cone of high-order tangent vectors, or variations, and these are defined using the vector fields of the affine system. To better understand these variations, we study how they depend on the jets of the vector fields by studying the Taylor expansion of a composition of flows. Some connections are made between labeled rooted trees and the coefficients appearing in the Taylor expansion of a composition of flows. Also, a relation between variations and the formal Campbell-Baker-Hausdorff formula is established. After deriving some algebraic properties of variations, we define a variational cone for an affine system and relate it to the local controllability problem. We then study the notion of neutralizable variations and give a method for constructing subspaces of variations. Finally, using the tools developed to study variations, we consider two important classes of systems: driftless and homogeneous systems. For both classes, we are able to characterize the PSTLC property. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2010-01-11 20:11:45.466

This thesis describes a new concept, applicable to high-power current-sourced conversion (CSC), where a controllable firing-angle shift is introduced between series and parallel converters to enable independent active and reactive power control. The firing-shift concept solves a difficult problem, by giving thyristor based CSCs the control flexibility of pulse-width modulated (PWM) converters, but without a loss in efficiency or rating. Several configurations are developed, based on the firing-shift concept, and provide flexible, efficient solutions for both very high power HVDC transmission, and very high current industrial processes. HVDC transmission configurations are first developed for 4-quadrant high-pulse operation, based on the series connected multi-level current reinjection (MLCR) topology. Independent reactive power control between two ends of an HVDC link are proven under firing-shift control, with high-pulse operation, and without on-load tap changing (OLTC) transformers. This is followed by application of firing-shift control to a bi-directional back-to-back HVDC link connecting two weak systems to highlight the added dc voltage control flexibility of the concept. The fault recovery capability of an MLCR based ultra-HVDC (UHVDC) long distance transmis-sion scheme is also proven under firing-shift control. The scheme responds favourably to both ac disturbances and hard dc faults, without the risk of commutation failures and instability experienced during fault recovery of line-commutated conversion. The two-quadrant capability of very high current rectification is also proven with configurations based on phase-shifted 12-pulse and MLCR parallel CSCs. The elimination of the electro-mechanical OLTC/satruable reactor voltage control, the high-current CSC’s biggest shortcoming, greatly improves controllability and with firing-shift control, ensures high power-factor for all load conditions. This reduces the reactive power demands on the transmission system, which results in more efficient power delivery

Orientador: Waldemar Donizete Bastos / Banca: Andrea Cristina Prokopczyk Arita / Banca: Juliana Conceição Precioso Pereira / Banca: Carlos Alberto Raposo da Cunha / Banca: Valéria Neves Domingos Cavalcanti / Resumo: Neste trabalho estudamos o problema de controlabilidade exata na fronteira para um sistema de equações de onda acopladas em paralelo, em domínios suave por partes do plano, sob ação de controle do tipo Neuman. Utilizando o método empregado por D. L. Russell em [33] obtemos controlabilidade em tempo suficientemente grande para dados iniciais de energia finita e controle de quadrado integrável. A fim de obter tempo de controle próximo a valores ótimos, procedemos como em [21]: estendemos a solução do problema de Cauchy para tempo complexo e provamos que o operador solução associado ao problema de Cauchy é compacto e depende analiticamente do tempo num setor adequado do plano complexo. Utilizando decaimento local de energia, analiticidade e compacidade do operador solução obtemos o resultado desejado. / Abstract: In this work we study the problem of exact controllability on the boundary for a system of wave equations coupled in parallel, in piecewise smooth domains of the plane, under the action of control of Neuman type. Using the method employed by D. L. Russell in [33] we obtain controllability in time sufficiently large for initial data of finite energy and square integrable control. In order to obtain control time close to optimal values, we proceed as in [21]: we extend the solution of the Cauchy problem to complex time and we prove that the solution operator associated with the Cauchy problem is compact and depends analytically of the time in an appropriate sector of the complex plane. Using local decay of energy, analyticity and compactness of the solution operator we obtain the desired result. / Doutor

A geração de testes para circuitos combinacionais com fan-outs recovergentes é um problema NP-completo. Com o rápido crescimento da complexidade dos circuitos fabricados, a geração de testes passou a ser um sério problema para a indústria de circuitos integrados. Muitos algoritmos de ATPG (Automatic Test Pattern Generation) baseados no algoritmo D, usam heurísticas para guiar o processo de tomada de decisão na propagação n e na justificação das constantes de forma a aumentar sua eficiencia. Existem heurísticas baseadas em medidas funcionais, estruturais e probabilísticas. Estas medidas são normalmente referidas como observabilidade e controlabilidade que fazem parte de um conceito mais geral, a testabilidade. As medidas que o algoritmo utiliza podem ser calculadas apenas uma vez, durante uma etapa de pré-processamento (medidas de testabilidade estáticas - STM's), ou dinamicamente, recalculando estas medidas durante o processamento sempre que elas forem necessárias (medidas de testabilidade dinâmicas — DTM's). Para alguns circuitos, o use de medidas dinâmicas ao invés de medidas estáticas diminui o número de backtrackings pcir vetor gerado. Apesar disto, o tempo total de CPU por vetor aumenta. Assim, as DTM's só devem ser utilizadas quando as STM's não apresentam uma boa performance. Isto pode ser feito utilizando-se as medidas estáticas ate um certo número de backtrackings. Se o padrão de teste não for encontrado, então medidas dinâmicas são utilizadas. Entretanto, a necessário ainda buscar formas de melhorar o processo dinâmico, diminuindo o custo computacional. A proposta original do calculo das DTM's apresenta algumas técnicas, baseadas em selective tracing, com o objetivo de reduzir o custo computacional. Este trabalho analisa o use combinado de heurísticas e propõe técnicas alternativas, na forma das heurísticas de recalculo parcial e recalculo de linhas não free, que visam minimizar o overhead do calculo das DTM's. E proposta ainda a técnica de Pré-implicação que transfere a complexidade do algoritmo para a memória. Isto é feito através de um preprocessamento que armazena informações necessárias para a geração de todos os vetores de teste. De outra forma estas informações teriam de ser calculadas na geração de cada um destes vetores. A implementação do algoritmo D com as várias heurísticas permitiu a realização de um experimento pratico. Isto possibilitou a análise quantitativa da performance do algoritmo D para vários tipos de circuitos e demonstrou a eficiência de uma das heurísticas propostas neste trabalho. / The test generation for combinational circuits that contain reconvergence is a NP-complete problem. With the rapid increase in the complexity of the fabricated circuits, the generation of test patterns poses a serious problem to the IC industry. A number of existing ATPG algorithms based on the D algorithm use heuristics to guide the decision process in the D-propagation and justification to improve the efficiency. The heuristics used by ATPG algorithm are based on structural, functional and probabilistics measures. These measures are commonly referred to as line controllability and observability and they are combined under the , more general notion of testability. The measures used by ATPG algorithms can be computed only once, during a preprocessing stage (static testability measures - STM's) or can be calculated dinamically, updating the testability measures during the test generation process (dymanic testability measures - DTM's). For some circuits, replacing STM's by DTM's decreases the average number of backtrackings per generated vector. Despite these decrease, the total CPU time per generated vector is greater when using DTM's instead of STM's. So, DTM's only must be used if the STM's don't present a good performance. This can be done by STM's until a certain number of backtrackings. If a test pattern has still not been found, then DTM's are used. Therefore, it is yet necessary to search for ways to improve the dynamic process and decrease the CPU time requirements. In the original approach some techniques for reducing the computational overhead of DTM's based on the well-know technique of selective path tracing are presented. In this work, the combined use of heuristics are analised and alternative techniques — the heuristics of partial recalculus and not free lines recalculus — are proposed. These alternative techniques were developed in order to minimize the overhead of the DTM's calculus. It is yet proposed the pre-implication technique which transfers to memory the algorithm complexity. It includes a preprocessing stage which storages all necesary informations to the generation of all test vectors. So, these informations don't need be computed in the generation of each test vector. The implementation of the D-Algorithm with diferent heuristics has possibilited a practical experiment. It was possible to analise the performance of the D-Algorithm on diferent circuit types and to demonstrate the efficiency of one of the proposed heuristics.

Este trabalho apresenta a formulação de um problema de otimização topológica para o posicionamento ótimo de atuadores baseado na teoria de controle. A estrutura é composta por dois materiais: um material passivo elástico e um material ativo piezelétrico, ambos lineares. Pretende-se obter um sistema de controle no qual todos os estados sejam controláveis. O processo de otimização topológica busca a distribuição de material piezelétrico que maximize o menor autovalor do Gramiano de controlabilidade garantindo, assim, sua não singularidade e, consequentemente, que o sistema seja completamente controlável. Programação linear sequencial (SLP) é utilizada para a solução do problema de otimização e as sensibilidades para o modelo de elementos finitos são deduzidas para a função objetivo e restrições. Análises modais das topologias ótimas são utilizadas para a definição de um controlador LQR e as respostas das estruturas controladas submetidas à uma carga impulsiva são analisadas. / This work presents a topology optimization formulation for the actuator placement based on the control theory. The structure is composed by two materials: a passive elastic material and an active piezoelectric material, both linear. The aim is to obtain a control system which all states are controllable. The topology optimization process searches the piezoelectric material distribution which maximizes the smallest eigenvalue of the controllability Gramian ensuring its non-singularity and, therefore, the system is completely controllable. Sequential linear programming (SLP) is used to solve the optimization problem. The sensitivities for the finite element model were derived for the objective function and constraints. Modal analysis from the optimal topologies were employed in an LQR controller and the responses for the controlled structures submitted to an impulsive load are analyzed.

L’objet de cette thèse est l’étude de certains problèmes liés à l’ingénierie des bioprocédés, en particulier l’analyse du comportement et de la culture optimale des microalgues et la connexion de plusieurs bioréacteurs. Trois problèmes sont proposés et analysés. Le première est basé sur une étude récente dans laquelle les auteurs modifient le modèle classique du Monod en incorporant l’incidence de la lumière sur la dynamique à travers le rôle de la croissance de la biomasse. L’idée est d’étudier un problème plus général de l’optimisation non linéaire qui considère maximisation de la biomasse moyenne de microalgues en fonction du temps, pour des intervalles de temps différents. La difficulté mathématique qui se pose est lié à la discontinuité des intervalles de temps qui rend la fonction à optimiser non différentiable. Ce manque de régularité comprend la formulation d’un problème d’optimisation non-lisse. Dans le deuxième problème, un modèle réduit du réservoir microalgues avec nitrification est analysé, en supposant que les microalgues peuvent se développer à partir de la consommation de nitrate et d’ammonium, de préférence par l’ammonium. La limitation de la lumière par l’auto-ombrage est également inclus dans le taux de croissance du microalgues comme inhibition non compétitive. En réduisant le système en utilisant la théorie des systèmes asymptotiquement autonomes, il peut être considéré comme une perturbation d’un système de deux espèces en compétition pour un substrat. Par conséquent, nous utilisons un résultat de systèmes perturbés non-évanescentes pour obtenir un théorème de stabilité pour la coexistence.Le dernier problème est lié aux systèmes compartimentés. Il est prouvé que pour une grande classe de systèmes entrées-sorties positifs de dimension finie, représentant transport et diffusion de soluté entre des compartiments mobiles et immobiles, il existe des représentations MINC (multiple interacting continua) et MRMT (multi-rate mass transfer) algébriquement équivalentes. En outre, des méthodes explicites sont donnés pour construire ces représentations équivalentes, où la contrôlabilité des systèmes joue un rôle important. / The purpose of this thesis is to study some problems that arise from bioprocess engineering, in particular the behaviour analysis and optimal cultivation of microalgae and the connection of multiple bioreactors. The thesis consists of three problems. The first is based on a recent study in which the authors extend the classical Monod model incorporating light incidence on the dynamics through the role of biomass growth. The idea is to study a more general problem of nonlinear optimization which considers maximization average biomass of microalgae versus time, for different time intervals. The mathematical difficulty that arises is related to that discontinuity of the time intervals which causes non differentiability in some domain points. This lack of regularity involves the formulation of a non-smooth optimization problem. In the second problem, a reduced mathematical model of a microalgal pond with nitrification is analyzed, assuming that microalgae can grow either by ammonium consumption or by nitrate consuming, with preference for ammonium. Light limitation by self-shading is also included in the growth rate of microalgae as a noncompetitive inhibition.It is feasible to reduce the system using the theory of asymptotically autonomous systems and the limiting system obtained can be considered as a perturbation of a system of two species competing for a substrate. So, we use a result of non-vanishing perturbated systems to obtain a strong stability theorem for equilibrium coexistence. The last problem is related to compartmental systems. It is proved that for a large class of finite dimensional input-output positive systems that represent networks of transport and diffusion of solute in mobile and immobile compartments, there exist MINC (multiple interacting continua) and MRMT (multirate mass transfer) algebraically equivalent representations. Moreover, we provide explicit methods to construct these representations, where controllability property is playing a crucial role.