Esta dissertação de mestrado aborda o problema de regulação robusta recursiva para sistemas lineares discretos sujeitos a incertezas paramétricas. Um novo funcional quadrático, baseado na combinação de função penalidade e função custo do tipo jogos, é projetado para lidar com este problema. Uma característica interessante desta abordagem é que a recursividade pode ser realizada sem a necessidade do ajuste de parâmetros auxiliares. Bastante útil para aplicações online. A solução proposta é baseada numa equação recursiva de Riccati. Também, a convergência e a estabilidade do regulador para o sistema linear incerto invariante no tempo são garantidas. / This dissertation deals with robust recursive regulators for discrete-time systems subject to parametric uncertainties. A new quadratic functional based on the combination of penalty functions and game theory is proposed to solve this class of problems. An important issue of this approach is that the recursiveness can be performed without the need of adjusting auxiliary parameters. It is useful for online applications. The solution proposed is based on Riccati equation which guarantees the convergence and stability of the time-invariant system.

本論文比較了幾種估計線性模型係數的方法，包括LASSO、Elastic Net、LAD-LASSO、EBLASSO和EBENet。有別於普通最小平方法，這些方法在估計模型係數的同時，能夠達到變數篩選，也就是刪除不重要的解釋變數，只將重要的變數保留在模型中。在現今大數據的時代，資料量有著愈來愈龐大的趨勢，其中不乏上百個甚至上千個解釋變數的資料，對於這樣的資料，變數篩選就顯得更加重要。本文主要目的為評估各種估計模型係數方法的特性與優劣，當中包含了兩種模擬研究與兩筆實際資料應用。由模擬的分析結果來看，每種估計方法都有不同的特性，沒有一種方法使用在所有資料都是最好的。 / In this study, we compare several methods for estimating coefficients of linear models, including LASSO, Elastic Net, LAD-LASSO, EBLASSO and EBENet. These methods are different from Ordinary Least Square (OLS) because they allow estimation of coefficients and variable selection simultaneously. In other words, these methods eliminate non-important predictors and only important predictors remain in the model. In the age of big data, quantity of data has become larger and larger. A datum with hundreds of or thousands of predictors is also common. For this type of data, variable selection is apparently more essential. The primary goal of this article is to compare properties of different variable selection methods as well as to find which method best fits a large number of data. Two simulation scenarios and two real data applications are included in this study. By analyzing results from the simulation study, we can find that every method enjoys different characteristics, and no standard method can handle all kinds of data.

Esta dissertação de mestrado aborda o problema de regulação robusta recursiva para sistemas lineares discretos sujeitos a incertezas paramétricas. Um novo funcional quadrático, baseado na combinação de função penalidade e função custo do tipo jogos, é projetado para lidar com este problema. Uma característica interessante desta abordagem é que a recursividade pode ser realizada sem a necessidade do ajuste de parâmetros auxiliares. Bastante útil para aplicações online. A solução proposta é baseada numa equação recursiva de Riccati. Também, a convergência e a estabilidade do regulador para o sistema linear incerto invariante no tempo são garantidas. / This dissertation deals with robust recursive regulators for discrete-time systems subject to parametric uncertainties. A new quadratic functional based on the combination of penalty functions and game theory is proposed to solve this class of problems. An important issue of this approach is that the recursiveness can be performed without the need of adjusting auxiliary parameters. It is useful for online applications. The solution proposed is based on Riccati equation which guarantees the convergence and stability of the time-invariant system.

The main area of emphasis in this study is to investigate the methods and technology for aerodynamic configuration sizing of missiles and to develop a software platform in MATLAB&reg / environment as a design tool which has an ability of optimizing the external configuration of missiles for a set of flight requirements specified by the user through a graphical user interface. A genetic algorithm based optimization tool is prepared by MATLAB is expected to help the designer to find out the best external geometry candidates in the conceptual design stage. Missile DATCOM software package is employed to predict the aerodynamic coefficients needed in finding the performance merits of a missile for each external geometry candidate by integrating its dynamic equations of motion. Numerous external geometry candidates are rapidly eliminated according to objectives and constraints specified by designers, which provide necessary information in preliminary design. In this elimination, the external geometry candidates are graded according to their flight performances in order to discover an optimum solution. In the conceptual design, the most important performance objectives related to the external geometry of a missile are range, speed, maneuverability, and control effectiveness. These objectives are directly related to the equations of motion of the missile, concluding that the speed and flight range are related to the total mass and the drag-to-lift ratio acting on missile. Also, maneuverability depends on the normal force acting on missile body and mass whereas the control effectiveness is affected by pitching moment and mass moment of inertia of missile. All of the flight performance data are obtained by running a two degree-of-freedom simulation. In order to solve the resulting multi-objective optimization problem with a set of constraint of linear and nonlinear nature and in equality and inequality forms, genetic-algorithm-based methods are applied. Hybrid encoding methods in which the integer configuration variables (i.e., nose shape and control type) and real-valued geometrical dimension (i.e., diameter, length) parameters are encoded in the same individual chromosome. An external configuration design tool (EXCON) is developed as a synthesis and external sizing tool for the subsonic cruise missiles. A graphical user interface (GUI), a flight simulator and optimization modules are embedded into the tool. A numerical example, the re-configuration problem of an anti-ship cruise missile Harpoon, is presented to demonstrate the accuracy and feasibility of the conceptual design tool. The optimum external geometries found for different penalty weights of penalty terms in the cost function are compared according to their constraint violations and launch mass values. By means of using EXCON, the launch mass original baseline Harpoon is reduced by approximately 30% without deteriorating the other flight performance characteristics of the original Harpoon.

Darbe apskaičiuotas Gerber-Shiu diskontuotos baudos funkcijos pagrindinis narys klasikiniame kolektyvinės rizikos modelyje, kai draudimo kompanijos žalos pasiskirsčiusios pagal Veibulo skirstinį su parametrais &#951; = const, 0< &#951; <1 ir &#963; = 1, o pradinis kompanijos turtas . Minėtojo nario asimptotika gauta pasinaudojus subeksponentinių pasiskirstymo funkcijų savybėmis. Darbe pateiktuose grafikuose pavaizduota diskontuotos baudos funkcijos pagrindinio nario priklausomybė nuo įvairių klasikinio kolektyvinės rizikos modelio parametrų. / In this work the main member of the Gerber-Shiu discounted penalty function in a classic collective risk model with Weibull distribution (parameters &#951; = const, 0< &#951; <1 and &#963; = 1) is calculated. The expression of the main member is obtained by making use of properties of subexponential distribution functions. In the graphs a dependence of the main member of the Gerber-Shiu discounted penalty function on various parameters of classic collective risk model is represented.

Neste trabalho são estudadas três metodologias de otimização não-linear: o Método da Função Lagrangeana, o Método da Função Penalidade e o Método da Função Lagrangeana Aumentada. Com o estudo da Função Lagrangeana e do Método da Função Penalidade, foi possível alcançar a formulação da Função Lagrangeana Aumentada com o objetivo de resolver problemas de programação não-linear não-convexos. Testes numéricos são apresentados para o problema não-convexo de programação não-linear conhecido como Fluxo de Potência Ótimo. / In this dissertation, three nonlinear optimization methodologies are studied: the Lagrangian Function Method, the Penalty Function Method and Augmented Lagrangian Function Method. Through the studies ofthe Lagrangian Function and the Penalty function Method, it was possible to reach the formulation of the Augmented Lagrangian Function aiming to solve nonlinear nonconvex programming problems. Numerical tests are presented for the nonconvex nonlinear programming problem known as optimal power flow.

No contexto do mundo contemporâneo, os veículos automotores estão cada vez mais integrados ao cotidiano das pessoas, sendo mais de 1 bilhão deles circulando pelo mundo. Por serem controlados por motoristas, estão sujeitos a falhas decorrentes da inerente condição humana, ocasionando acidentes, mortes e outros prejuízos. O controle autônomo de veículos tem se apresentado como alternativa na busca de redução desses prejuízos, sendo utilizado nas mais diferentes abordagens, por distintas instituições ao redor do planeta. Deste modo, torna-se uma pauta fundamental para o estudo de sistemas de controle. Este trabalho, valendo-se da descrição matemática do comportamento veicular, busca o desenvolvimento e a implementação de um método eficiente de controle autônomo de veículos voltado, principalmente, para a modelagem em espaço de estados. Considerando que mudanças de marchas, principalmente em um cenário de dirigibilidade autônoma, são ações aleatórias, o objetivo desta dissertação é utilizar estratégias de controle baseadas em sistemas lineares sujeitos a saltos Markovianos. / In nowadays society, automobile vehicles are getting more and more integrated to people\'s daily activities, as there are more than 1 billion of them on the streets around the world. As they are controlled by drivers, vehicles are subjected to failures caused by human mistakes that lead to accidents, injuries and others. Autonomous vehicle control has shown itself to be an alternative in the pursuit of damage reduction, and it is applied by different institutions in many countries. Therefore, it is a main subject in the area of control systems. This paper, relying on mathematical descriptions of vehicle behavior, aims to develop and apply an efficient autonomous control method that takes into account state-space formulation. This goal will be achieved by the use of control strategies based on Markovian Jump Linear Systems that will describe the highly non-linear dynamics of the vehicle in different operation points.

The theme of my diploma thesis is mentally disabled people in prison. The aim of this work is to map methods of social work and functioning of a specialized department for mentally disabled people. The theoretical part focuses on legislation regulating this area. Moreover, there is a characteristic of particular types of prisons and a description of rights and obligations of the convicted persons and disciplinary punishments. Another topic of the work is the function of the sentence, characteristic of the specialized department and brief characteristic of particular disabilities. The practical part includes an interview with workers in this department. I found out the methods of work they use and how much different the work with these convicted persons is. Fort better understanding of this topic there are also case studies of convicted persons from the specialized department.

Orientador: Edméa Cássia Baptista / Resumo: O problema de fluxo de potência ótimo reativo é representado matematicamente por um problema de otimização não linear, restrito, não convexo, de grande porte e com variáveis de controle contínuas e discretas. A representação dos taps dos transformadores em fase e das susceptâncias shunt dos bancos de capacitores/reatores do sistema como variáveis discretas, torna o problema mais próximo da realidade. Entretanto, problemas de otimização não linear com variáveis discretas apresentam dificuldades em sua resolução, as quais são impostas pelas variáveis discretas. Uma das técnicas para sua resolução consiste em utilizar funções penalidades para tratar as variáveis discretas. Desta forma, transforma-se o problema discreto em uma sequência de problemas contínuos, e o método primal-dual barreira logarítmica pode ser utilizado para resolver esses problemas. Neste trabalho o objetivo é analisar a convergência do método de penalidade para variáveis discretas aplicado ao problema de fluxo de potência ótimo reativo, ao se utilizar diferentes funções penalidade e a combinação delas. Testes computacionais foram realizados com um exemplo númérico e com os sistemas elétricos IEEE 14, 30 e 118 barras, utilizando o pacote de otimização KNITRO em interface com o software GAMS. Os resultados demonstram que a combinação de diferentes funções penalidade para o tratamento das variáveis discretas é promissora. / Abstract: The reactive optimal power flow problem is mathematically represented by a nonlinear, constrained, nonconvex, large scale optimization problem with continuous and discrete control variables. The representation of the in-phase transformers taps and/or the shunt susceptances of capacitor/reactor Banks of the system, as discrete variables, make the problem closer to reality. Nonlinear optimization problems with discrete variables are difficulty to solve, due to the discrete variables. One of the soluction techniques consist in using penalty functions to treat the discrete variables. Thus, the discrete problem is transformed in a sequence of continuous problems, and the primal dual logarithmic barrier method can be used to solve these problems. In this work the objective is to analyze the convergence of the penalty method for discrete variables applied to the reactive optimal power flow problem, by using different penalty functions and the mixture of them. Computational tests have been carried out with a numerical example and with the IEEE 14, 30 and 118 buses electrical systems, using the KNITRO optimization package in interface with the GAMS software. The results show that a mixture of different penalty functions for treatment of discrete variable is advantageous. / Mestre

The diploma thesis "The Problems of Social Integration after Serving a Prison Sentence"deals in theoretical part with theories of punishment and function and aim of prison sentence. In more detail attention is paid to serving a prison sentence especially programmes of treatment in theoretical part. The corrective function of imprisonment is not in the long term accomplished and there is necessity to improve the system of care for person released from prison. Thesis tries to show necessity of continuity and deepening penitentiary with post- penitentiary care. Opinions of prisoners on the life reality after release are noticed in research part of this work.