Viscoelastic fluids, or Non-Newtonian fluids, are those that do not have a linear algebraic relation between the velocity field and the stresses arising in the media. Such fluids exhibit properties of both solids and liquids, and therefore cannot be modeled with methods of elasticity or Newtonian fluid mechanics. The popular models of viscoelasticity differ from each other only by the differential equation that describes the constitutive law for the fluid. Also, the media can have several relaxation modes, such as fluid mixes. This means that the stresses are determined as the sum of the stresses for each individual relaxation mode, which are described by corresponding differential equations evolving independently. The question of controllability of the equations that describe the evolution of viscoelastic fluids is largely open. The presence of the non-algebraic constitutive relation makes the analysis unfeasible in general setup. The presence of several relaxation modes makes the problem even more complicated. Another issue is the necessity of controlling the stresses, since they are not determined by the momentary velocity field, thus they need to be included as the controlled states. In this work we are concentrating on the controllability of the stresses arising in the viscoelastic fluid that has its motion constrained to be of the shearing type. This restriction allows us to concentrate on the stresses only and assign the shearing rate to be the control. We consider only the Upper Convected Maxwell fluid which has several relaxation modes present. The results demonstrate that contrary to the one relaxation mode case the normal stresses cannot be driven arbitrary close to the exponentially decaying regime, unless the shearing stresses satisfy certain requirements, while the shear stresses remain exactly controllable. / Ph. D.

In this thesis we study the methods for motion planning for nonholonomic systems. These systems are characterized by nonholonomic constraints on their generalized velocities. The motion planning problem with constraints on the velocities is transformed into a control problem having fewer control inputs than the degrees of freedom. The main focus of the thesis is on the study of motion planning and design of the feedback control laws for an autonomous underwater vehicle: a nonholonomic system. The nonlinear controllability issues for the system are also studied. For the design of feedback controllers, the system is transformed into chained and power forms. The methods of transforming a nonholonomic system into these forms are discussed. The work presented in this thesis is a step towards the initial study concerning the applicability of kinematic-based control on underwater vehicles. / Master of Science

<p>The CANDU-900 reactor design is an improvement on the current CANDU-6 reactor in the areas of economics, safety of operation and fuel cycle flexibility. As power grids start to rely more heavily on nuclear, it will be imperative for future nuclear generating station designs to be able to adjust their output to suit the fluctuating demands of the grid. Additionally, the need to reduce global nuclear waste has motivated research into mixed oxide fuel with the goal of maximizing spent fuel repository capacity and reducing decay heat via transmutation of transuranic actinides. The objective of this thesis is to provide insight into the load following capabilities of the CANDU-900 reactor design for a transuranic mixed oxide (TRUMOX) fueled core.</p> <p>The three-dimensional fuel management code, RFSP-IST, was used to simulate a reactor operating history for week long load following operations in a generic CANDU-900 reactor. Daily refuelling operations as well as reactivity device movements supplementary to RFSP were performed using the RECORD RRS emulator program. Core snapshots were taken at periodic intervals using the SIMULATE module to observe and track various reactor parameters. Average liquid zone controller fills as well as core reactivity and channel power values were used to determine the controllability of the reactor for various load following depths.</p> <p>The results of the load following simulations show that TRUMOX fuel has superior load following capabilities to that of conventional NU fuel for practical operational scenarios in a CANDU-900 reactor. Load following operations could be performed for TRUMOX fuel down to 85% full power in a safe and controllable manner using only the liquid zone controllers to account for the xenon transient reactivity as compared to NU which could only be done down to 90% full power. For load following simulations that both fuel types were capable of performing in a controllable manner, the TRUMOX fuelled core maintained on average a larger safety margin between the average liquid zone controller fills and the established safety limits.</p> / Master of Applied Science (MASc)

Cette thèse a pour objet l'étude de la contrôlabilité à zéro de systèmes d'équations aux dérivées partielles paraboliques, que l'on rencontre en physique, chimie ou en biologie. En chimie ou en biologie, ces systèmes modélisent l'évolution au cours du temps d'une concentration chimique ou de la densité d'une population (de bactéries, de cellules). Le but de la contrôlabilité à zéro est d'amener la solution du système à l'état nul à un temps donné T, en agissant sur le système à l'aide d'un contrôle. Nous recherchons donc un contrôle, de norme minimale, tel que la solution associée y vérifie y(T)=O dans le domaine Omega considéré. Les problèmes de contrôlabilité à zéro considérés dans cette thèse sont de trois types. Dans un premier temps, nous nous intéressons à la contrôlabilité à zéro avec un nombre fini de contraintes sur la dérivée normale de l'état, pour l'équation de la chaleur semi-linéaire. Puis, nous analysons la contrôlabilité simultanée à zéro avec contrainte sur le contrôle, pour un système linéaire de deux équations paraboliques couplées. Notre dernière étude concerne la contrôlabilité à zéro d'un système non linéaire de deux équations paraboliques couplées. Nous abordons ces problèmes de contrôlabilité principalement à l'aide d'inégalités de Carleman. En effet, l'étude des problèmes de contrôlabilité à zéro, et plus généralement de contrôlabilité exacte, peut se ramener à l'établissement d'inégalités d'observabilité pour le problème adjoint, conséquences d'inégalités de Carleman. Nous construisons le contrôle optimal en utilisant la méthode variationnelle et nous le caractérisons par un système d'optimalité / This thesis is devoted to the study of the null controllability of systems of parabolic partial differential equations, which we meet in physics, chemistry or in biology. In chemistry or in biology, the se systems model the evolution in time of a chemical concentration or the density of a population (of bacteria, cells). The aim of nu Il controllability is to lead the solution of the system to zero in a given time T, by acting on the system with a control. Thus we are looking for a control, of minimal norm, such as the associated solution y satisfies y(T)=O in the domain Omega under concern. We consider three types of null controllability problems in this thesis. At first, we are interested in the null controllability with afinite number of constraints on the normal derivative of the state, for the serni-Iinear heat equation. Then, we analyze the simultaneous null controllability with constraint on the control, for a linear system of two coupled parabolic equations. Our last study deals with the null controllability ofa non linear system oftwo coupled parabolic equations. We approach these controllability problems mainly by means of Carleman's inequalities. Indeed, the study of null controllability problems, and more generally exact controllability problems, is equivalent to obtain observability inequalities for the adjoint problem, consequences of Carleman's inequalities. We build the optimal controlusing the variationnal method and we characterize it by an optimality system

Purpose The thesis purpose is to contribute with understanding about managers’ opinions about how to handle deviations caused by unit interdependence. Methodology Qualitative data has been gathered to this exploratory study by semi-structured interviews with 14 managers within the R&amp;D, purchasing and production units at Scania, Södertälje. The result has been interpreted and analyzed by dividing the managers in five smaller groups.  Result from analyzing empirical findings It is found in the analysis that the largest part of the managers in this study seem not to believe it is worth striving for excellence through procedural justice. Reoccurring similarities in opinion between managers is that visualization, dialogue, clear responsibility and less tolerance towards deviations are needed for handling and preventing deviations. Differences in opinion are primarily related to how costs occurred from deviations should be allocated and the purpose with such reallocation. Most managers express a strong concern about undesired behavior developed by a control system where a causing unit always should take the effect from a deviation. However, all managers state that costs occurred from deviations due to interdependence with a external supplier should be invoiced to the supplier.  Conclusion The concern about undesired behavior that may be developed by the way of handling and preventing deviation is strongly mediated by the managers. Instead of handling deviations by justly reallocating effects according to the controllability principle it is perceived as more important to extend the areas of responsibility and increase consciousness between interdependent units through improved dialogue and cross-functional transparency. One should therefore not seek equitable allocation of impacts and cost of devices in dealing with anomalies of this type.

VIEIRA, F. B. Controlabilidade de algumas EDPs não lineares, e, densidade e espectro de subvariedades mínimas em espaço forma. 2017. 89 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017. / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-04-19T13:15:27Z No. of bitstreams: 1 2016_tese_fbvieira.pdf: 681898 bytes, checksum: d123b89ff8ddaa52a643807b847421b5 (MD5) / Rejected by Rocilda Sales (rocilda@ufc.br), reason: Para o aluno. Alterar a data e incluir a conclusão, tanto no sumário como no final do texto. Conclusão é capítulo portanto numerado. Rocilda on 2017-04-19T14:54:37Z (GMT) / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-04-19T16:23:39Z No. of bitstreams: 1 2016_tese_fbvieira.pdf: 683722 bytes, checksum: 8e8575ca8d8e8496b31047d5bc8c68c0 (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2017-04-24T11:15:25Z (GMT) No. of bitstreams: 1 2016_tese_fbvieira.pdf: 683722 bytes, checksum: 8e8575ca8d8e8496b31047d5bc8c68c0 (MD5) / Made available in DSpace on 2017-04-24T11:15:25Z (GMT). No. of bitstreams: 1 2016_tese_fbvieira.pdf: 683722 bytes, checksum: 8e8575ca8d8e8496b31047d5bc8c68c0 (MD5) Previous issue date: 2017-05-24 / In the first part of this thesis we deal with the 3D Navier-Stokes and Boussinesq systems in a cube. We prove some results concerning the global approximate controllability by means of boundary controls which act in some part of the boundary. They are generalizations and variants of some previous results by Guerrero, Imanuvilov and Puel. Still in the first part of this Thesis, we prove the internal and boundary local null controllability of a 1D parabolic PDE with nonlinear diffusion. Here, the main tools are Liusternik’s inverse function Theorem and appropriate Carleman estimates. In the second part of this Thesis, we consider M m minimal properly immersed submanifolds in a complete ambient space N n suitably close to a space form N n k of curvature −k ≤ 0. We are interested in the relation between the density function Θ(r) of M m and the spectrum of the Laplace-Beltrami operator. In particular, we prove that if Θ(r) has subexponential growth (when k < 0) or sub-polynomial growth (k = 0) along a sequence, then the spectrum of M m is the same as that of the space form N m k . Notably, the result applies to Anderson’s (smooth) solutions of Plateau’s roblem at infinity on the hyperbolic space H n , independently of their boundary regularity. We also give a simple condition on the second fundamental form that ensures M to have finite density. In particular, we show that minimal submanifolds of H n with finite total curvature have finite density. / Na primeira parte desta tese tratamos dos sistemas 3D de Navier-Stokes e Boussinesq em um cubo. Nós provamos alguns resultados sobre a controlabilidade aproximada global por meio de controles de bordo que agem em uma parte da fronteira. Estes reultados são generalizações e variações de alguns resultados anteriores de Guerrero, Imanuvilov e Puel. Ainda na primeira parte da tese, nós provamos a controlabilidade nula local interna e de bordo de uma EDP parabólica 1D com difusão não linear. Aqui, as ferramentas principais são o teorema da função inversa de Liusternik e desigualdades de Carleman adequadas. Na segunda parte desta tese, consideramos M m subvariedades mínimas propriamente imersas em um espaço ambiente completo N n adequadamente próximo a um espaço forma N n k de curvatura −k ≤ 0. Estamos interessados na relação entre a função densidade Θ(r) de M m e o espectro do operador Laplace-Beltrami. Em particular, provamos que se Θ(r) temum crescimento subexponencial (quando k < 0) ou bubpolinomial (k = 0) ao longo de uma sequência, então o espectro de M m é o mesmo do espaço forma N m k . Notavelmente, o resultado se aplica a soluções Anderson (suaves) do problema de Plateau no infinito sobre o espaço hiperbólico H n , independentemente da regularidade dos seus bordos. Nós também fornecemos uma condição simples sobre a segunda forma fundamental que garante que M tem densidade finita. Em particular, mostramos que subvariedades mínimas de H n com curvatura total finita te densidade finita.

Made available in DSpace on 2015-05-15T11:46:05Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 674722 bytes, checksum: eb17d5816a0fce98d1def5be593711f1 (MD5) Previous issue date: 2011-09-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / We have as main issue in this work the Hierarchical Control, which consists in a leader-followers system. We studied in special the heat equation approximate controllability under Stackelberg-Nash&#146;s strategy, which is directed in controlling every system from local controls choices with the minimum possible costs. / Temos como principal tema neste trabalho o Controle Hierárquico, que consiste em um sistema de líder e seguidores. Estudamos em especial a controlabilidade aproximada da equação do Calor sob a estratégia de Stackelberg-Nash, estratégia esta direcionada em controlar todo sistema a partir de escolhas de controles locais com o mínimo de custos possíveis.

Cette thèse étudie les propriétés de contrôle par migration d’équations aux dérivées partielles modélisant la dynamique d’une population structurée en âge. Les équations de populations considérées seront essentiellement celles décrites par Lotka et McKendrick, en tenant compte ou non de la diffusion spatiale des individus, ainsi que leur pendant non-linéaire décrit par les équations de Gurtin et MacCamy. La première partie étudie les propriétés de contrôlabilité interne des équations linéaires de Lotka et McKendrick (sans diffusion), lorsque le contrôle n’agit que pour les jeunes individus formant la population. La contrôlabilité à zéro ainsi que la contrôlabilité vers les solutions stationnaires du système considéré est démontrée, en utilisant les propriétés du semi-groupe associé à l’opérateur de population originellement étudié par Song (contrôleur supposé responsable de la radicalisation de la politique de l’enfant unique en Chine). En outre, la conservation au cours du temps de la positivité de la densité de population contrôlée est étudiée. Les deux parties suivantes établissent respectivement des propriétés de contrôle à zéro et de contrôle en temps optimal pour l’équation de Lotka et McKendrick, lorsque le déplacement spatial des individus est considéré (ici, le contrôle agit pour tous les âges mais seulement dans une certaine zone du milieu considéré). Les méthodes employées relèvent d’une adaptation de celles originellement développées pour le contrôle d’équations paraboliques, notamment la méthode de Lebeau et Robbiano (pour l’étude du contrôle à zéro de l’équation de la chaleur), ainsi que leur généralisation développée par Wang pour l’étude du contrôle en temps optimal de l’équation de la chaleur. Une dernière partie étudie les propriétés de contrôlabilité des équations non-linéaires de Gurtin et MacCamy (sans diffusion), lorsque le contrôle est voué à n’agir que pour une certaine tranche d’âge d’individus. L’utilisation de principes de comparaison en dynamique de populations permet notamment d’obtenir le contrôle à zéro des équations considérées. / This work is devoted to study the controllability properties of some infinite dimensional systems modeling an age structured population dynamics. The considered equations are essentially those described by Lotka and McKendrick, with or without spatial diffusion, and their nonlinear versions described by the Gurtin and MacCamy equations. The first part of this thesis aims to study the controllability properties of the linear Lotka and McKendrick system (without diffusion), in the case when the control acts for the very young individuals. The null controllability and the controllability towards the stationnary solutions of the considered system are established, using a semigroup approach. In addition, the nonnegativity of the controlled population dynamics is studied. The next two parts are respectively devoted to establish a null controllability result and a time optimal control result for the Lotka McKendrick equation with spatial diffusion (here, the control acts for every ages but only on a subdomain of the considered spatial domain). The methods employed are those originally devoted to study the internal controllability properties of the heat equation. A last part studies the controllability properties of the Gurtin and MacCamy nonlinear equations (without diffuion), when the control acts only in an arbitrary age range. In this case, the use of comparison principles in age structured population dynamics ensures the null controllability of the considered equations.

Estudamos sistemas lineares em grupos de Lie introduzido por Ayala e Tirao em [3]. Esta nova classe de sistemas de controle é obtido através de uma generalização aos grupos de Lie de campos de vetores lineares em espaços vetoriais. Eles extendem não somente a classe bem conhecida de sistemas lineares em \'R POT. n\' mas também sistemas invariantes em grupos de Lie e os avanços recentes mostram que eles aparecem como modelos para ampla classe de sistemas de controle proveniente de diversas áreas de ciência e engenharia. Focamos nossa atenção em normalizador, que tem tido um papel fundamental em formulação de sistemas lineares em grupos de Lie, e lidamos com curvas integrais de seus campos vetoriais. Finalmente mostramos que sob certas hipóteses sistemas lineares em grupos de Lie possuem a propriedade de controlabilidade local a partir de identidade do grupo / We study linear control systems on Lie groups introduced by Ayala and Tirao in [3]. This new class of control systems is obtained through a generalization to Lie groups of linear vector fields on vector spaces. They extend not only well-known class of linear control systems on \'R POT. n\' but also invariant systems on Lie groups and recent achievements show that they appear as models for a wide class of control systems coming from several areas of science and engineering. We focus our attention on the notion of normalizer which has been played a key role for formulation of linear systems on Lie groups and then deal with integral curves of its vector fields. Finally we show that under certain assumptions linear systems on Lie groups have local controllability property from the group identity

Este trabalho estuda a observabilidade e controlabilidade para uma classe de sistema dinâmico markoviano com saltos nos parâmetros, e uma coleção de matrizes de observabilidade e controlabilidade associadas. São explorados alguns resultados de invariância, bem como certas propriedades envolvendo essas matrizes. Uma dessas propriedades, relacionada com a coleção de matrizes de observabilidade é conhecida na literatura desta classe de sistemas, mas não há uma prova disponível. Esses resultados de invariancia foram estendidos para o estudo da controlabilidade e sua respectiva coleção de matrizes associada, obtendo assim uma propriedade análoga ao caso da observabilidade. Os resultados obtidos são importantes para validar outros resultados existentes que se baseiam na propriedade referida / This work studies observability and controlability of a class of Markov systems with jumping parameters, and associated set of observability and controlability matrices. We explore some invariance results regarding the state trajectory and certain properties involving those matrices. One of these properties, related with the collection of observability matrices, is employed in the literature of this class of systems, but there is no available proof. The invariance results are extended similarly to the context of controlability leading to a property that is analogous to the observability case. The obtained results are important to validate other existing results that rely on that property