<p>This dissertation studies the optimal control of two different dynamic systems with learning: (i) diagnostic service systems, and (ii) green incentive policy design. In both cases, analytical models have been developed to improve our understanding of the system, and managerial insights are gained on its optimal management.</p><p>We first consider a diagnostic service system in a queueing framework, where the service is in the form of sequential hypothesis testing. The agent should dynamically weigh the benefit of performing an additional test on the current task to improve the accuracy of her judgment against the incurred delay cost for the accumulated workload. We analyze the accuracy/congestion tradeoff in this setting and fully characterize the structure of the optimal policy. Further, we allow for admission control (dismissing tasks from the queue without processing) in the system, and derive its implications on the structure of the optimal policy and system's performance.</p><p>We then study Feed-in-Tariff (FIT) policies, which are incentive mechanisms by governments to promote renewable energy technologies. We focus on two key network externalities that govern the evolution of a new technology in the market over time: (i) technological learning, and (ii) social learning. By developing an intertemporal model that captures these dynamics, we investigate how lawmakers should leverage on such effects to make FIT policies more efficient. We contrast our findings against the current practice of FIT-implementing jurisdictions, and also determine how the FIT regimes should depend on specific technology and market characteristics.</p> / Dissertation

Une approche fondamentale pour la résolution de problémes de contrôle optimal est basée sur le principe de programmation dynamique. Ce principe conduit aux équations d'Hamilton-Jacobi, qui peuvent être résolues numériquement par des méthodes classiques comme la méthode des différences finies, les méthodes semi-lagrangiennes, ou les schémas antidiffusifs. À cause de la discrétisation de l'espace d'état, la dimension des problèmes de contrôle pouvant être abordés par ces méthodes classiques est souvent limitée à 3 ou 4. Ce phénomène est appellé malédiction de la dimension. Cette thèse porte sur les méthodes numériques max-plus en contôle optimal deterministe et ses analyses de convergence. Nous étudions et developpons des méthodes numériques destinées à attenuer la malédiction de la dimension, pour lesquelles nous obtenons des estimations théoriques de complexité. Les preuves reposent sur des résultats de théorie de Perron-Frobenius non linéaire. En particulier, nous étudions les propriétés de contraction des opérateurs monotones et non expansifs, pour différentes métriques de Finsler sur un cône (métrique de Thompson, métrique projective d'Hilbert). Nous donnons par ailleurs une généralisation du "coefficient d'ergodicité de Dobrushin" à des opérateurs de Markov sur un cône général. Nous appliquons ces résultats aux systèmes de consensus ainsi qu'aux équations de Riccati généralisées apparaissant en contrôle stochastique.

Digital inpainting is the technique of filling in the missing regions of an image or a video using information from surrounding area. This technique has found widespread use in applications such as restoration, error recovery, multimedia editing, and video privacy protection. This dissertation addresses three significant challenges associated with the existing and emerging inpainting algorithms and applications. The three key areas of impact are 1) Structure completion for image inpainting algorithms, 2) Fast and efficient object based video inpainting framework and 3) Perceptual evaluation of large area image inpainting algorithms. One of the main approach of existing image inpainting algorithms in completing the missing information is to follow a two stage process. A structure completion step, to complete the boundaries of regions in the hole area, followed by texture completion process using advanced texture synthesis methods. While the texture synthesis stage is important, it can be argued that structure completion aspect is a vital component in improving the perceptual image inpainting quality. To this end, we introduce a global structure completion algorithm for completion of missing boundaries using symmetry as the key feature. While existing methods for symmetry completion require a-priori information, our method takes a non-parametric approach by utilizing the invariant nature of curvature to complete missing boundaries. Turning our attention from image to video inpainting, we readily observe that existing video inpainting techniques have evolved as an extension of image inpainting techniques. As a result, they suffer from various shortcoming including, among others, inability to handle large missing spatio-temporal regions, significantly slow execution time making it impractical for interactive use and presence of temporal and spatial artifacts. To address these major challenges, we propose a fundamentally different method based on object based framework for improving the performance of video inpainting algorithms. We introduce a modular inpainting scheme in which we first segment the video into constituent objects by using acquired background models followed by inpainting of static background regions and dynamic foreground regions. For static background region inpainting, we use a simple background replacement and occasional image inpainting. To inpaint dynamic moving foreground regions, we introduce a novel sliding-window based dissimilarity measure in a dynamic programming framework. This technique can effectively inpaint large regions of occlusions, inpaint objects that are completely missing for several frames, change in size and pose and has minimal blurring and motion artifacts. Finally we direct our focus on experimental studies related to perceptual quality evaluation of large area image inpainting algorithms. The perceptual quality of large area inpainting technique is inherently a subjective process and yet no previous research has been carried out by taking the subjective nature of the Human Visual System (HVS). We perform subjective experiments using eye-tracking device involving 24 subjects to analyze the effect of inpainting on human gaze. We experimentally show that the presence of inpainting artifacts directly impacts the gaze of an unbiased observer and this in effect has a direct bearing on the subjective rating of the observer. Specifically, we show that the gaze energy in the hole regions of an inpainted image show marked deviations from normal behavior when the inpainting artifacts are readily apparent.

RFID has been characterized as a “disruptive technology” that has the potential to revolutionize numerous key sectors. A key advantage of passive RFID applications is the ability to wirelessly transmit automatic identification and related information using very little power. This paper presents an experimental investigation to inform the optimal configuration for programming passive ultra-high frequency (UHF) RFID media in dynamic applications. Dynamic programming solutions must be designed around the tag’s functionality, the physical programming configuration and environment. In this investigation, we present a methodology to determine an optimal configuration to maximize the systems programming efficiency for dynamic applications.

The minimum set cover problem is, without question, among the most ubiquitous and well-studied problems in computer science. Its theoretical hardness has been fully characterized--logarithmic approximability has been established, and no sublogarithmic approximation exists unless P=NP. However, the gap between real-world instances and the theoretical worst case is often immense--many covering problems of practical relevance admit much better approximations, or even solvability in polynomial time. Simple combinatorial or geometric structure can often be exploited to obtain improved algorithms on a problem-by-problem basis, but there is no general method of determining the extent to which this is possible. In this thesis, we aim to shed light on the relationship between the structure and the hardness of covering problems. We discuss several measures of structural complexity of set cover instances and prove new algorithmic and hardness results linking the approximability of a set cover problem to its underlying structure. In particular, we provide: - An APX-hardness proof for a wide family of problems that encode a simple covering problem known as Special-3SC. - A class of polynomial dynamic programming algorithms for a group of weighted geometric set cover problems having simple structure. - A simplified quasi-uniform sampling algorithm that yields improved approximations for weighted covering problems having low cell complexity or geometric union complexity. - Applications of the above to various capacitated covering problems via linear programming strengthening and rounding. In total, we obtain new results for dozens of covering problems exhibiting geometric or combinatorial structure. We tabulate these problems and classify them according to their approximability.

Thesis (Ph. D.)--University of Canterbury, 2006. / Typescript (photocopy). Includes bibliographical references (p. 459-469). Also available via the World Wide Web.

Resumo: Este trabalho propõe uma nova metodologia para extração de rodovias utilizando imagens aéreas digitais. A inovação baseia-se no algoritmo de Programação dinâmica (PD), que nesta metodologia realiza o processo de otimização no espaço objeto, e não no espaço imagem como as metodologias tradicionais de extração de rodovias por PD. A feição rodovia é extraída no espaço objeto, o qual implica um rigoroso modelo matemático, que é necessário para estabelecer os pontos entre o espaço imagem e objeto. Necessita-se que o operador forneça alguns pontos sementes no espaço imagem para descrever grosseiramente a rodovia, e estes pontos devem ser transformados para o espaço objeto para inicialização do processo de otimização por PD. Esta metodologia pode operar em diferentes modos (modo mono e estéreo), e com diversos tipos de imagens, incluindo imagens multisensores. Este trabalho apresenta detalhes da metodologia mono e estéreo e também os experimentos realizados e os resultados obtidos. / Abstract: This work proposes a novel road extraction methodology from digital images. The innovation is based on the dynamic programming (DP) algorithm to carry out the optimisation process in the object space, instead of doing it in the image space such as the DP traditional methodologies. Road features are traced in the object space, which implies that a rigorous mathematical model is necessary to be established between image and object space points. It is required that the operator measures a few seed points in the image space to describe sparsely and coarsely the roads, which must be transformed into the object space to make possible the initialisation of the DP optimisation process. Although the methodology can operate in different modes (mono-plotting or stereoplotting), and with several image types, including multisensor images, this work presents details of our single and stereo image methodology, along with the experimental results. / Orientador: João Fernando Custódio da Silva / Coorientador: Aluir Porfírio Dal Poz / Banca: Júlio Kiyoshi Hasegawa / Banca: Messias Meneguette Júnior / Doutor

Face à une concurrence féroce par suite de la modélisation économique, les entreprises doivent bien gérer leurs chaînes logistiques afin de réduire leurs coûts d’exploitation tout en améliorant leurs services au client. Un enjeu majeur de cette gestion et la gestion efficace des stocks multi-échelons. Dans cette thèse, nous étudions des systèmes de stocks multi-échelons avec des coûts de passation de commande à chaque stock. En raison de l’existence des coûts de passation de commande, l’optimisation d’un tel système devient très compliquée. Récemment, l’approche de service garanti (GSA) a été utilisée pour déterminer les stocks de sécurité pour les systèmes de stocks multi-échelons, mais sans coûts fixes de passation de commande. Nous généralisons la GSA pour optimiser la politique de stockage (R, Q) d’un système de stocks multi-échelons avec la demande suivant un processus de Poisson et coûts fixes de passation de commande à chaque stock. Nous considérons trois types de systèmes de stocks multi-échelons, et pour chaque type, nous d'abord établissons un modèle mathématique pour le problème d’optimisation. Ensuite, le modèle est résolu par une procédure itérative fondée sur deux algorithmes de programmation dynamique (DP). Un algorithme DP est utilisé pour résoudre le sous-problème de détermination de quantités de commande et l'autre est utilisé pour résoudre le sous-problème de détermination de points de recommande du modèle. Les résultats numériques démontrent l'efficacité des algorithmes et de la procédure / With the increasing complexity of supply chains led by economic globalization, integrated supply chain management has become an important strategy utilized by the firms to reduce the overall cost while meeting the customer service. This change has made academic researchers and industrial practitioners pay more and more attention to multi-echelon inventory management over the last two decades. In this thesis, we study multi-echelon inventory systems with fixed order costs at each stock. Because of the existence of fixed order costs, the optimization of such system becomes very complicated. Recently, Guaranteed Service Approach (GSA) was used to set safety stock for multi-echelon inventory systems, but without fixed order costs. We extend the GSA to optimize (R, Q) inventory policies for multi-echelon inventory systems with Poisson demand and fixed order costs. Our objective is to find optimal (R, Q) policy for such a system so that its total cost is minimized while achieving a service level to customer. Three types of multi-echelon inventory systems, serial systems, assembly systems and two-level distribution systems are considered. For each type, we first establish a mathematical model for the optimization problem. Then, the model is solved by an iterative procedure based on two dynamic programming (DP) algorithms. One DP algorithm is used to solve the order size decision subproblem and the other is used to solve the reorder point decision subproblem of the model. Numerical experiments demonstrate the efficiency of the algorithms and the procedure

>Magister Scientiae - MSc / Bank asset management mainly involves profit maximization through invest- ment in loans giving high returns on loans, investment in securities for reducing risk and providing liquidity needs. In particular, commercial banks grant loans to creditors who pay high interest rates and are not likely to default on their loans. Furthermore, the banks purchase securities with high returns and low risk. In addition, the banks attempt to lower risk by diversifying their asset portfolio. The main categories of assets held by banks are loans, treasuries (bonds issued by the national treasury), reserves and intangible assets. In this mini-thesis, we solve an optimal asset allocation problem in banking under the mean-variance frame work. The dynamics of the different assets are modelled as geometric Brownian motions, and our optimization problem is of the mean- variance type. We assume the Basel II regulations on banking supervision. In this contribution, the bank funds are invested into loans and treasuries with the main objective being to obtain an optimal return on the bank asset port- folio given a certain risk level. There are two main approaches to portfolio optimization, which are the so called martingale method and Hamilton Jacobi Bellman method. We shall follow the latter. As is common in portfolio op- timization problems, we obtain an explicit solution for the value function in the Hamilton Jacobi Bellman equation. Our approach to the portfolio prob- lem is similar to the presentation in the paper [Hojgaard, B., Vigna, E., 2007. Mean-variance portfolio selection and efficient frontier for defined contribution pension schemes. ISSN 1399-2503. On-line version ISSN 1601-7811]. We pro- vide much more detail and we make the application to banking. We illustrate our findings by way of numerical simulations.

Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro / Neste trabalho apresentamos as etapas para a utilização do método da Programação Dinâmica, ou Princípio de Otimização de Bellman, para aplicações de controle ótimo. Investigamos a noção de funções de controle de Lyapunov (FCL) e sua relação com a estabilidade de sistemas autônomos com controle. Uma função de controle de Lyapunov deverá satisfazer a equação de Hamilton-Jacobi-Bellman (H-J-B). Usando esse fato, se uma função de controle de Lyapunov é conhecida, será então possível determinar a lei de realimentação ótima; isto é, a lei de controle que torna o sistema globalmente assintóticamente controlável a um estado de equilíbrio. Como aplicação, apresentamos uma modelagem matemática adequada a um problema de controle ótimo de certos sistemas biológicos. Este trabalho conta também com um breve histórico sobre o desenvolvimento da Teoria de Controle de forma a ilustrar a importância, o progresso e a aplicação das técnicas de controle em diferentes áreas ao longo do tempo. / This dissertation presents the steps for using the method of Dynamic Programming or Bellman Optimization Principle for optimal control applications. We investigate the notion of control-Lyapunov functions (CLF) and its relation to the stability of autonomous systems with control. A control-Lyapunov function must satisfy the Hamilton-Jacobi- Bellman equation (H-J-B). Using this fact, if a control-Lyapunov function is known, it is possible to determine the optimal feedback law, in other words, the control law which makes the system globally asymptotically controllable at an equilibrium state. As an application, we present a mathematical model suitable for an optimal control problem of certain biological systems. This dissertation also presents a brief historic about the development of the Control Theory in a way of illustrate the importance and the progress of the control techniques, specially where it can be applied, according to the diverse areas and different times that this techniques were discovered and used.