Cette thèse est consacrée à l’étude de la linéarisation géométrique locale des systèmes complètement intégrables dans la catégorie C1. Le sujet est la conjecture de linéarisation géométrique proposée (et établie dans le cadre analytique) par Nguyen Tien Zung. Nous commençons par les systèmes linéaires, puis introduisons la normalisation dans la catégorie formelle. Nous montrons qu’un système intégrable peut être décomposé en une partie hyperbolique et une partie elliptique. Nous établissons une bonne forme normale de Poincaré-Dulac pour les champs de vecteurs et discutons sa relation avec la linéarisation géométrique. Nous montrons que les systèmes intégrables faiblement hyperboliques sont géométriquement linéarisables en utilisant les outils de Chaperon. Nous étudions les systèmes intégrables sur les espaces de petite dimension : si celle-ci n’est pas plus grande que 4, alors la plupart des cas sont géométriquement linéarisables ; en particulier, la linéarisation géométrique est possible pour les systèmes intégrables de type de foyer-foyer. Enfin, nous généralisons la démonstration en grande dimension et proposons une condition sur les variétés fortement invariantes, sous laquelle nous linéarisons géométriquement les systèmes. Nous parvenons également à normaliser une action de R × T à plusieurs foyers en nous référant aux idées de Zung. / This thesis is devoted to the local geometric linearization of completely integrable systems in the C1 category. The subject is the geometric linearization conjecture proposed (and proved in the analytic case) by Nguyen Tien Zung. We start from linear systems and introduce normalization in the formal category. Wes how that an integrable system can be decomposed into a hyperbolic part and an elliptic part. We establish a good Poincaré-Dulac normal form for the vector fields and discuss its relation with geometric linearization. We prove that weakly hyperbolic integrable systems are geometrically linearizable byusing Chaperon’s tools. We then study integrable systems on small dimensional spaces: if the dimension is no more than 4, then most cases are geometrically linearizable; in particular,geometric linearization works for integrable system of focus-focus type. Finally, we generalize the proof to high dimensions and propose a condition about strongly invariant manifolds, under which we linearize the systems in the geometric sense. We also manage to normalize an R × T-action of several focuses by referring to the ideas of Zung.

This diploma thesis deals with application optimization method in circular economy branch. The introduction is focused on explaining main features of the issue and its benefits for economy and environment. Afterwards are mentioned some obstacles, which are preventing transition from current waste management. Mathematical apparatus, which is used in practical section, is described in the thesis. Core of the thesis is mathematical optimization model, which is implemented in the GAMS software, and generator of input data is made in VBA. The model includes all of significant waste management options with respect to economic and enviromental aspect, including transport. Functionality is then demostrated on a small task. Key thesis result is application of the model on real data concerning Czech Republic. In conclusion an analysis of computation difficulty, given the scale of the task, is accomplished.

Táto diplomová práca sa zaoberá návrhom a konštrukciou elektromagnetickej, polohovacej platformy, pre testovanie nelineárnych riadiacich a identifikačných algoritmov. Platforma je založená na tvarovaní magnetického poľa v každom bode pomocou troch elektromagnetov a polohuje oceľovú guličku po dotykovom paneli ktorý sníma polohu tejto guličky. Platforma má slúžiť hlavne pre demonštráciu rôznych nelineárnych riadiacich algoritmov vo výukovom prostredí. Tri príklady takýchto algoritmov sú ukázané a overené v rámci tejto diplomovej práce.

This diploma thesis is focused on designing and specifying a linear quadratic regulator for longitudinal and lateral motion of the aircraft. The regulator is designed for a linear system obtained from a linearization of our nonlinear dynamic dynamic model of aircraft around the basic reference state (trimmed state-and-level ight). To nd a complete description of this reference state, some optimality problem has to be solved and the solution of this problem is called a trimmed state.

The thesis focuses on implementation of a hot runner controller for injection molds for plastic materials with a maximum number of 56 regulated zones. The first part of the thesis deals with already existing and used solutions of the given subject. The following part of the thesis describes the principles of temperature measurement by means of thermoelectric sensors, including their linearization as well as communication protocols MODBUS, EUROMAP 17. The identification of a regulated system ( heating zone) has been carried out before the hardware design. The development process is divided into some parts : system conception, hardware design, software development. The controller consists of measuring modules designed to collect data and handle power controllers for management of performance of heating elements. The necessary calculation power is integrated into the controllling computer. All parts of a hot runner controller are implemented taking into account the costs.

This research is concerned with the development of algorithmic approaches for solving problems that arise in the design and analysis of telecommunication networks, location-allocation distribution contexts, and intelligent transportation networks. Specifically, the corresponding problems addressed in these areas are a local access and transport area (LATA) network design problem, the discrete equal-capacity p-median problem (PMED), and the estimation of dynamic origin-destination path ows or trip tables in a general network. For the LATA network problem, we develop a model and apply the Reformulation-Linearization Technique (RLT) to construct various enhanced tightened versions of the proposed model. We also design efficient Lagrangian dual schemes for solving the linear programming relaxation of the various enhanced models, and construct an effective heuristic procedure for deriving good quality solutions in this process. Extensive computational results are provided to demonstrate the progressive tightness resulting from the enhanced formulations and their effect on providing good quality feasible solutions. The results indicate that the proposed procedures typically yield solutions having an optimality gap of less than 2% with respect to the derived lower bound, within a reasonable effort that involves the solution of a single linear program. For the discrete equal-capacity p-median problem, we develop various valid inequalities, a separation routine for generating cutting planes via specific members of such inequalities, as well as an enhanced reformulation that constructs a partial convex hull representation that subsumes an entire class of valid inequalities via its linear programming relaxation. We also propose suitable heuristic schemes for solving this problem, based on sequentially rounding the continuous relaxation solutions obtained for the various equivalent formulations of the problem. Extensive computational results are provided to demonstrate the effectiveness of the proposed valid inequalities, enhanced formulations, and heuristic schemes. The results indicate that the proposed schemes for tightening the underlying relaxations play a significant role in enhancing the performance of both exact and heuristic solution methods for solving this class of problems. For the estimation of dynamic path ows in a general network, we propose a parametric optimization approach to estimate time-dependent path ows, or origin-destination trip tables, using available data on link traffic volumes for a general road network. Our model assumes knowledge of certain time-dependent link ow contribution factors that are a dynamic generalization of the path-link incidence matrix for the static case. We propose a column generation approach that uses a sequence of dynamic shortest path subproblems in order to solve this problem. Computational results are presented on several variants of two sample test networks from the literature. These results indicate the viability of the proposed approach for use in an on-line mode in practice. Finally, we present a summary of our developments and results, and offer several related recommendations for future research. / Ph. D.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24040号 / 情博第796号 / 新制||情||135(附属図書館) / 京都大学大学院情報学研究科システム科学専攻 / (主査)教授 加納 学, 教授 大塚 敏之, 教授 下平 英寿 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DGAM

This thesis considers two kinds of problems, motivated by practical applications in data center operations and maintenance. Data centers are the brain of the internet, each hosting as many as tens of thousands of IT devices, making them a considerable global energy consumption contributor (more than 1 percent of global power consumption). There is a large body of work at different layers aimed at reducing the total power consumption for data centers. One of the key places to save power is addressing the thermal heterogeneity in data centers by thermal-aware workload distribution. The corresponding optimization problem is challenging due to its combinatorial nature and the computational complexity of thermal models. In this thesis, a holistic theoretical approach is proposed for thermal-aware workload distribution which uses linearization to make the problem model-independent and easier to study. Two general optimization problems are defined. In the first problem, several cooling parameters and heat recirculation effects are considered, where two red-line temperatures are defined for idle and fully utilized servers to allow the cooling effort to be reduced. The resulting problem is a mixed integer linear programming problem which is solved approximately using a proposed heuristic. Numerical results confirm that the proposed approach outperforms commonly considered baseline algorithms and commercial solvers (MATLAB) and can reduce the power consumption by more than 10 percent. In the next problem, additional operational costs related to reliability of the servers are considered. The resulting problem is solved by a generalization of the proposed heuristics integrated with a Model Predictive Control (MPC) approach, where demand predictions are available. Finally, in the second type of problems, we address a problem in inventory management related to data center maintenance, where we develop an efficient dynamic programming algorithm to solve a lot-sizing problem. The algorithm is based on a key structural property that may be of more general interest, that of a just-in-time ordering policy. / Thesis / Doctor of Philosophy (PhD) / Data centers, each hosting as many as tens of thousands of IT devices, contribute to a considerable portion of energy usage worldwide (more than 1 percent of global power consumption). They also encounter other operational costs mostly related to reliability of devices and maintenance. One of the key places to reduce energy consumption is through addressing the thermal heterogeneity in data centers by thermal-aware work load distribution for the servers. This prevents hot spot generation and addresses the trade-off between IT and cooling power consumption, the two main power consump tion contributors. The corresponding optimization problem is challenging due to its combinatorial nature and the complexity of thermal models. In this thesis, we present a holistic approach for thermal-aware workload distribution in data centers, using lin earization to make the problem model-independent and simpler to study. Two quite general nonlinear optimization problems are defined. The results confirm that the proposed approach completed by a proposed heuristic solves the problems efficiently and with high precision. Finally, we address a problem in inventory management related to data center maintenance, where we develop an efficient algorithm to solve a lot-sizing problem that has a goal of reducing data center operational costs.

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