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Thematische Bibliographien / Optimization Calculus of Variations and Optimal Control / Dissertationen

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Dissertationen zum Thema „Optimization Calculus of Variations and Optimal Control“

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Veröffentlicht am 28. Juli 2024

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1

Dymkou, Siarhei. "Approximations for some classes of optimal control problems with state constraints and repetitive control systems." Thesis, University of Ballarat, 2005. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/69220.

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This report presents the investigation on the research work "Approximations for some classes of optimal control problems with state constraints and repetitive control systems". This report mainly gives the theoretical part of the research which is based on the numerical methods that are developed. It is conjectured that the corresponding algorithms will be realized as computer programs after which they can be used in practical work.<br>Master of Information Technology

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2

Anderson, James David. "Dynamical system decomposition and analysis using convex optimization." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:624001be-28d5-4837-a7d8-2222e270e658.

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This thesis is concerned with investigating new methods for the analysis of large-scale dynamical systems using convex optimization. The proposed methodology is based on composite Lyapunov theory and is computationally implemented using polynomial programming techniques. The main result of this work is the development of a system decomposition framework that makes it possible to analyze systems that are of such a scale that traditional methods cannot cope with. We begin by addressing the problem of model invalidation. A barrier certificate method for invalidating models in the presence of unce

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3

Pearson, John W. "Fast iterative solvers for PDE-constrained optimization problems." Thesis, University of Oxford, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581405.

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In this thesis, we develop preconditioned iterative methods for the solution of matrix systems arising from PDE-constrained optimization problems. In order to do this, we exploit saddle point theory, as this is the form of the matrix systems we wish to solve. We utilize well-known results on saddle point systems to motivate preconditioners based on effective approximations of the (1,1)-block and Schur complement of the matrices involved. These preconditioners are used in conjunction with suitable iterative solvers, which include MINRES, non-standard Conjugate Gradients, GMRES and BiCG. The sol

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4

Taha, Haithem Ezzat Mohammed. "Mechanics of Flapping Flight: Analytical Formulations of Unsteady Aerodynamics, Kinematic Optimization, Flight Dynamics and Control." Diss., Virginia Tech, 2013. http://hdl.handle.net/10919/24428.

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A flapping-wing micro-air-vehicle (FWMAV) represents a complex multi-disciplinary system whose analysis invokes the frontiers of the aerospace engineering disciplines. From the aerodynamic point of view, a nonlinear, unsteady flow is created by the flapping motion. In addition, non-conventional contributors, such as the leading edge vortex, to the aerodynamic loads become dominant in flight. On the other hand, the flight dynamics of a FWMAV constitutes a nonlinear, non-autonomous dynamical system. Furthermore, the stringent weight and size constraints that are always imposed on FWMAVs invoke d

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5

Chaturapruek, Sorathan. "A Mathematical Framework for Unmanned Aerial Vehicle Obstacle Avoidance." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/60.

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The obstacle avoidance navigation problem for Unmanned Aerial Vehicles (UAVs) is a very challenging problem. It lies at the intersection of many fields such as probability, differential geometry, optimal control, and robotics. We build a mathematical framework to solve this problem for quadrotors using both a theoretical approach through a Hamiltonian system and a machine learning approach that learns from human sub-experts' multiple demonstrations in obstacle avoidance. Prior research on the machine learning approach uses an algorithm that does not incorporate geometry. We have developed tool

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6

Luria, Gianvittorio. "Constrained Calculus of Variations and Geometric Optimal Control Theory." Doctoral thesis, Università degli studi di Trento, 2010. https://hdl.handle.net/11572/368036.

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The present work provides a geometric approach to the calculus of variations in the presence of non-holonomic constraints. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The usual classification of the evolutions into normal and abnormal ones is also discussed, showing the existence of a universal algorithm assigning to every admissible curve a corresponding abnormality index, defined in terms of a suitable linear map. A gauge-invariant formulation of the variational problem, based on

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7

Luria, Gianvittorio. "Constrained Calculus of Variations and Geometric Optimal Control Theory." Doctoral thesis, University of Trento, 2010. http://eprints-phd.biblio.unitn.it/170/1/Constrained_Calculus_of_Variations_and_Geometric_Optimal_Control_Theory.pdf.

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The present work provides a geometric approach to the calculus of variations in the presence of non-holonomic constraints. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The usual classification of the evolutions into normal and abnormal ones is also discussed, showing the existence of a universal algorithm assigning to every admissible curve a corresponding abnormality index, defined in terms of a suitable linear map. A gauge-invariant formulation of the variational problem, based on

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8

Pooseh, Shakoor. "Computational methods in the fractional calculus of variations and optimal control." Doctoral thesis, Universidade de Aveiro, 2013. http://hdl.handle.net/10773/11510.

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Doutoramento em Matemática<br>The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional problems, numerical techniques are developed. Here, we mainly investigate the approximation of fractional operators by means of series of integer-order derivatives and generalized finite differences. We give upper bounds for the error of proposed approximations and study their effi

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Gouveia, Paulo D. F. "Computação de simetrias variacionais e optimização da resistência aerodinâmica newtoniana." Doctoral thesis, Universidade de Aveiro, 2008. http://hdl.handle.net/10198/1571.

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Neste trabalho exploram-se alguns dos actuais recursos de computação científica no contexto da optimização estática e dinâmica. Começa-se por propor um conjunto de procedimentos computacionais algébricos que permitem automatizar todo o processo de obtenção de simetrias e leis de conservação, quer no contexto clássico do cálculo das variações, quer no contexto mais abrangente do controlo óptimo. A utilidade do package de funções desenvolvido é demonstrada com a identificação de novas leis de conservação para alguns problemas do controlo óptimo conhecidos na literatura. Estabelece-se depois uma

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10

Chen, Chuei Yee. "Quasiminimality and coercivity in the calculus of variations." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:d6daadfd-92fb-4fa6-9d5b-fd8403955079.

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11

Pitcher, Ashley Brooke. "Mathematical modelling and optimal control of constrained systems." Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:044a26ab-99dc-4b34-b4a3-04e5c0d61ba0.

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This thesis is concerned with mathematical modelling and optimal control of constrained systems. Each of the systems under consideration is a system that can be controlled by one of the variables, and this control is subject to constraints. First, we consider middle-distance running where a runner's horizontal propulsive force is the control which is constrained to be within a given range. Middle-distance running is typically a strategy-intensive race as slipstreaming effects come into play since speeds are still relatively fast and runners can leave their starting lane. We formulate a two-run

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12

Santos, Simão Pedro Silva. "Calculus of variations of Herglotz type." Doctoral thesis, Universidade de Aveiro, 2017. http://hdl.handle.net/10773/22503.

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Doutoramento em Matemática<br>We consider several problems based on Herglotz’s generalized variational problem. We dedicate two chapters to extensions on Herglotz’s generalized variational problem to higher-order and first-order problems with time delay, using a variational approach. In the last four chapters, we rewrite Herglotz's type problems in the optimal control form and use an optimal control approach. We prove generalized higher- order Euler-Lagrange equations, first without and then with time delay; higher-order natural boundary conditions; Noether's first theorem for the first-order

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Bedford, Stephen James. "Calculus of variations and its application to liquid crystals." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:a2004679-5644-485c-bd35-544448f53f6a.

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The thesis concerns the mathematical study of the calculus of variations and its application to liquid crystals. In the first chapter we examine vectorial problems in the calculus of variations with an additional pointwise constraint so that any admissible function <strong>n</strong> ε W<sup>1,1</sup>(ΩM), and M is a manifold of suitable regularity. We formulate necessary and sufficient conditions for any given state <strong>n</strong> to be a strong or weak local minimiser of I. This is achieved using a nearest point projection mapping in order to use the more classical results which apply in

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Hopper, Christopher Peter. "On the regularity of holonomically constrained minimisers in the calculus of variations." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:d8bde7a2-7dae-44d2-919d-48b9f2543789.

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This thesis concerns the regularity of holonomic minimisers of variational integrals in the context of direct methods in the calculus of variations. Specifically, we consider Sobolev mappings from a bounded domain into a connected compact Riemannian manifold without boundary, to which such mappings are said to be holonomically constrained. For a general class of strictly quasiconvex integral functionals, we give a direct proof of local C<sup>1,α</sup>-Hölder continuity, for some 0 < α < 1, of holonomic minimisers off a relatively closed 'singular set' of Lebesgue measure zero. Cru

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Blagouchine, Iaroslav. "Modélisation et analyse de la parole : Contrôle d’un robot parlant via un modèle interne optimal basé sur les réseaux de neurones artificiels. Outils statistiques en analyse de la parole." Thesis, Aix-Marseille 2, 2010. http://www.theses.fr/2010AIX26666.

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Cette thèse de doctorat traite les aspects de la modélisation et de l'analyse de la parole, regroupés sous le chapeau commun de la qualité. Le premier aspect est représenté par le développement d'un modèle interne de contrôle de la production de la parole ; le deuxième, par le développement des outils pour son analyse. Un modèle interne optimal sous contraintes est proposé pour le contrôle d'un robot parlant, basé sur l'hypothèse du point d'équilibre (EPH, modèle-lambda). Ce modèle interne se repose sur le principe suivant : les mouvements du robot sont produits de telle façon que la longueur

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Buerger, Johannes Albert. "Fast model predictive control." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:6e296415-f02c-4bc2-b171-3bee80fc081a.

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This thesis develops efficient optimization methods for Model Predictive Control (MPC) to enable its application to constrained systems with fast and uncertain dynamics. The key contribution is an active set method which exploits the parametric nature of the sequential optimization problem and is obtained from a dynamic programming formulation of the MPC problem. This method is first applied to the nominal linear MPC problem and is successively extended to linear systems with additive uncertainty and input constraints or state/input constraints. The thesis discusses both offline (projection-ba

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Forclaz, A. "Variational methods in materials science." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249532.

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Three problems are being investigated in this thesis. The first two relate to the modelling and analysis of martensitic phase transitions, while the third is concerned with some mathematical tools used in this setting. After a short introduction (Chapter 1) and overviews of the calculus of variations and martensitic phase transformations (Chapter 2), the research part of this thesis is divided into three chapters. We show in Chapter 3 that for the two wells $\mathrm{SO}(3)U$ and $\mathrm{SO}(3)V$ to be rank-one connected, where the $3\times 3$ symmetric positive definite $U$ and $V$ have the s

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18

Khalil, Nathalie. "Conditions d'optimalité pour des problèmes en contrôle optimal et applications." Thesis, Brest, 2017. http://www.theses.fr/2017BRES0095/document.

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Le projet de cette thèse est double. Le premier concerne l’extension des résultats précédents sur les conditions nécessaires d’optimalité pour des problèmes avec contraintes d’état, dans le cadre du contrôle optimal ainsi que dans le cadre de calcul des variations. Le deuxième objectif consiste à travailler sur deux nouveaux aspects de recherche : dériver des résultats de viabilité pour une classe de systèmes de contrôle avec des contraintes d’état dans lesquels les conditions dites ‘standard inward pointing conditions’ sont violées; et établir les conditions nécessaires d’optimalité pour des

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19

Paião, Ana Pedro Lemos. "Introduction to optimal control theory and its application to diabetes." Master's thesis, Universidade de Aveiro, 2015. http://hdl.handle.net/10773/16806.

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Mestrado em Matemática e Aplicações<br>O Cálculo das Variações e o Controlo Ótimo são dois ramos da Matemática que estão muito interligados entre si e também com outras áreas. Como exemplo, podemos citar a Geometria, a Física, a Mecânica, a Economia, a Biologia, bem como a Medicina. Nesta tese estudamos vários tipos de problemas variacionais e de Controlo Ótimo, estabelecendo a ligação entre alguns destes. Fazemos uma breve introdução sobre a Diabetes Mellitus, uma vez que estudamos um modelo matemático que traduz a interação entre a glicose e a insulina no sangue por forma a otimizar o

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20

Koné, Mamadou Ibrahima. "Contrôle optimal et calcul des variations en présence de retard sur l'état." Thesis, Paris 1, 2016. http://www.theses.fr/2016PA01E063/document.

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L'objectif de cette thèse est de contribuer à l'optimisation de problèmes dynamiques en présence de retard. Le point de vue qui nous intéressera est celui de Pontryagin qui dans son ouvrage publié en 1962 a donné les conditions nécessaires d'existence de solutions pour ce type de problème. Warga dans son ouvrage publié en 1972 a fait un catalogue des solutions possible, Li et al. ont étudié le cas de contrôle périodique. Notre méthode de démonstration est directement inspirée de la démonstration de P. Michel du cas des systèmes gouvernés par des équations différentielles ordinaires. La princip

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Cahill, Nathan D. "Constructing and solving variational image registration problems." Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:ed43a6f4-216f-45b5-88c5-2baaba1e684a.

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Nonrigid image registration has received much attention in the medical imaging and computer vision research communities, because it enables a wide variety of applications. Feature tracking, segmentation, classification, temporal image differencing, tumour growth estimation, and pharmacokinetic modeling are examples of the many tasks that are enhanced by the use of aligned imagery. Over the years, the medical imaging and computer vision communties have developed and refined image registration techniques in parallel, often based on similar assumptions or underlying paradigms. This thesis focuses

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Koumatos, Konstantinos. "The formation of microstructure in shape-memory alloys." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:1089932b-d36e-4414-b128-6f7bcfe9cdf3.

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The application of techniques from nonlinear analysis to materials science has seen great developments in the recent years and it has really been a driving force for substantial mathematical research in the area of partial differential equations and the multi-dimensional calculus of variations. This thesis has been motivated by two recent and remarkable experimental observations of H. Seiner in shape-memory alloys which we attempt to interpret mathematically. Much of the work is original and has given rise to deep problems in the calculus of variations. Firstly, we study the formation of non-c

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Hudson, Thomas. "Stability and regularity of defects in crystalline solids." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:48ab1e44-f81a-4de0-b380-6fb0411bf1a9.

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This thesis is devoted to the mathematical analysis of models describing the energy of defects in crystalline solids via variational methods. The first part of this work studies a discrete model describing the energy of a point defect in a one dimensional chain of atoms. We derive an expansion of the ground state energy using Gamma-convergence, following previous work on similar models [BDMG99,BC07,SSZ11]. The main novelty here is an explicit characterisation of the first order limit as the solution of a variational problem in an infinite lattice. Analysing this variational problem, we prove a

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Helmers, Michael. "Kinks in a model for two-phase lipid bilayer membranes." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:15343985-1b1c-4123-838d-8e157e837db1.

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In the spontaneous curvature model for two-phase lipid bilayer membranes the shape of vesicles is governed by a combination of an elastic bending energy and an interface energy that penalises the size of phase boundaries. Each lipid phase induces a preferred curvature to the membrane surface, and these curvatures as well as phase boundaries may lead to the development of kinks. In a rotationally symmetric setting we introduce a family of energies for smooth surfaces and phase fields for the lipid components and study convergence to a sharp-interface limit, which depends on the choice of the be

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25

Trey, Baptiste. "Existence et régularité des formes optimales pour des problèmes d'optimisation spectrale Free boundary regularity for a multiphase shape optimization problem. Communications in Partial Dfferential Equations Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form Existence and regularity of optimal shapes for elliptic operators with drift. Calculus of Variations and Partial Differential Equations." Thesis, Université Grenoble Alpes, 2020. http://www.theses.fr/2020GRALM019.

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Dans cette thèse, on étudie l'existence et la régularité des formes optimales pour certains problèmes d'optimisation spectrale qui font intervenir un opérateur elliptique avec condition de Dirichlet.On s'intéresse d'abord au problème de la minimisation de la valeur propre principale d'un opérateur avec un terme de transport borné.Que le terme de transport soit fixé ou non, ce problème admet une solution parmi les quasi-ouverts, et si le terme de transport est en outre le gradient d'une fonction Lipschitzienne, alors les solutions sont des ouverts localement de classe C^{1,alpha} en dehors de p

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Bourdin, Loïc. "Contributions au calcul des variations et au principe du maximum de Pontryagin en calculs time scale et fractionnaire." Thesis, Pau, 2013. http://www.theses.fr/2013PAUU3009/document.

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Cette thèse est une contribution au calcul des variations et à la théorie du contrôle optimal dans les cadres discret, plus généralement time scale, et fractionnaire. Ces deux domaines ont récemment connu un développement considérable dû pour l’un à son application en informatique et pour l’autre à son essor dans des problèmes physiques de diffusion anormale. Que ce soit dans le cadre time scale ou dans le cadre fractionnaire, nos objectifs sont de : a) développer un calcul des variations et étendre quelques résultats classiques (voir plus bas); b) établir un principe du maximum de Pontryagin

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Angoshtari, Bahman. "Stochastic modeling and methods for portfolio management in cointegrated markets." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:1ae9236c-4bf0-4d9b-a694-f08e1b8713c0.

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In this thesis we study the utility maximization problem for assets whose prices are cointegrated, which arises from the investment practice of convergence trading and its special forms, pairs trading and spread trading. The major theme in the first two chapters of the thesis, is to investigate the assumption of market-neutrality of the optimal convergence trading strategies, which is a ubiquitous assumption taken by practitioners and academics alike. This assumption lacks a theoretical justification and, to the best of our knowledge, the only relevant study is Liu and Timmermann (2013) which

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Henao, Manrique Duvan Alberto. "Variational modelling of cavitation and fracture in nonlinear elasticity." Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:82b6fdc7-4b66-4853-86ad-7fa4488a32ea.

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Motivated by experiments on titanium alloys of Petrinic et al. (2006), which show the formation of cracks through the growth and coalescence of voids in ductile fracture, we consider the problem of formulating a variational model in nonlinear elasticity compatible both with cavitation and the appearance of discontinuities across two-dimensional surfaces. As in the model for cavitation of Müller and Spector (1995) we address this problem, which is connected to the sequential weak continuity of the determinant of the deformation gradient in spaces of functions having low regularity, by means of

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Chá, Sílvia Alexandra Carrapato. "Problemas convexos e não-convexos do cálculo das variações." Doctoral thesis, Universidade de Évora, 2014. http://hdl.handle.net/10174/17929.

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Nas aplicações do Cálculo das Variações, Controlo Óptimo & Inclusões Diferenciais, muitos problemas importantes da vida real são vectoriais não-convexos e sujeitos a restrições pontuais. O teorema clássico da convexidade de Liapunov é uma ferramenta crucial para resolver problemas vectoriais não-convexos envolvendo integrais simples. No entanto, a possibilidade da extensão deste teorema para lidar com restrições pontuais manteve-se um problema em aberto durante duas décadas, no caso mais realista usando controlos vectoriais variáveis. Nesta tese apresentamos condições necessárias e condições s

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"Optimal control of hereditary differential system." Chinese University of Hong Kong, 1985. http://library.cuhk.edu.hk/record=b5885549.

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31

Galindro, Aníbal André Pereira. "A mathematical model for unemployment: optimal control with real data from Portugal." Master's thesis, 2017. http://hdl.handle.net/10773/25136.

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During this thesis we study the Calculus of Variations and Optimal Control theory while we present a few examples. After a brief overview of the Portuguese employment market reality we propose a simple Optimal Control model for unemployment and we compare it with previous studies. Despite its inherent simpleness, we claim that the model is more realistic and useful than the ones available in the literature. A case study with real data from Portugal (2004- 2016) supports our claim<br>Ao longo desta tese, estudamos a teoria do Cálculo das Variações e do Controlo Óptimo enquanto formulamos

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Luo, Biyong. "Shooting method based algorithms for solving control problems associated with second order hyperbolic PDEs." 2001. http://wwwlib.umi.com/cr/yorku/fullcit?pNQ66358.

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Thesis (Ph. D.)--York University, 2001. Graduate Programme in Mathematics.<br>Typescript. Includes bibliographical references (leaves 114-119). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ66358.

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(5930081), Ashutosh Nayak. "DYNAMIC LOAD SCHEDULING FOR ENERGY EFFICIENCY IN A MICROGRID." Thesis, 2019.

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Growing concerns over global warming and increasing fuel costs have pushed the traditional fuel-based centralized electrical grid to the forefront of mounting public pressure. These concerns will only intensify in the future, owing to the growth in electricity demand. Such growths require increased generation of electricity to meet the demand, and this means more carbon footprint from the electrical grid. To meet the growing demand economically by using clean sources of energy, the electrical grid needs significant structural and operational changes to cope with various challenges. Microgrids

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