Orientador: Edvaldo Assunção / Banca: Marcelo Carvalho Minhoto Teixeira / Banca: Rodrigo Cardim / Banca: Marcio Roberto Covacic / Banca: Eduardo Fontoura Costa / Resumo: Nesta tese apresentam-se resultados para a estabilidade robusta de sistemas lineares sujeitos a incertezas paramétricas do tipo politópicas, variantes no tempo (do inglês Linear Parameter Varying - LPV). De início, expõe-se um método aprimorado para o projeto com otimização da norma de controladores robustos via desigualdades matriciais lineares (do inglês Linear Matrix Inequalitites - LMIs), com base na teoria de estabilidade segundo Lyapunov. Esta nova formulação foi manipulada utilizando o lema de Finsler, e permitiu encontrar melhores resultados de factibilidade com o acréscimo de matrizes extras e redução do número de LMIs. Neste novo equacionamento houve a inclusão do índice de desempenho da taxa de decaimento, responsável por diminuir o tempo de duração do período transitório, e também da otimização da norma dos controladores, responsável por menores ganhos mantendo a mesma eficiência dos requisitos de projeto. Devido a importantes resultados da literatura para o projeto de controladores robustos com incertezas variantes no tempo, optou-se por explorar o projeto de controladores dinâmicos chaveados, inovando-se no tocante ao acréscimo da taxa de decaimento e à otimização da norma dos controladores chaveados, o que possibilitou encontrar melhores resultados de implementação. Por fim, foram propostos critérios menos conservadores para a análise de estabilidade e projeto de controladores chaveados, utilizando funções de Lyapunov quadráticas por partes do tipo mínimo. A vantagem desse procedimento está no aumento dos parâmetros de relaxação porém, concebido através de formulações baseadas em desigualdades matriciais bilineares (do inglês Bilinear Matrix Inequalitites - BMIs), nos quais os termos e se encontram no produto entre variáveis escalares de otimização e matrizes, que também são variáveis do procedimento de otimização. Apresentam-se, no corpo do texto, exemplos numéricos e ... / Abstract: This thesis presents results for robust stability of linear systems subject to polytopic timevarying parametric uncertainties (LPV). To start with, an improved method for the optimal gain design of robust controllers via Linear Matrix Inequalities (LMI), based on Lyapunov stability theory is presented. This new formulation was manipulated using the Finsler lemma, which enabled finding better feasibility results with the addition of extra matrices and reducing the number of LMIs. In this new equation it was included the decay rate performance index, responsible for reducing the transitional period time, as well as the controllers norm optimization, responsible for lower gains while maintaining the same project requirements efficiency. Then, due to important results in literature regarding the design of robust controllers with time-varying uncertainties, the design of switched dynamic controllers was explored by including the decay rate index and the optimization of the switched controllers norm in the equation, which allowed finding better implementation results. Finally, less conservative criteria were proposed for stability analysis and design of switched controllers using minimum-type piecewise quadratic Lyapunov functions. The advantage of this procedure lies in the increase of relaxation parameters, however, designed through formulations based on Bilinear Matrix Inequalities (BMIs), where the bilinear terms are in the product between optimization scalar variables and matrices, which are also variables on the optimization procedure. Numerical examples are presented and simulated to illustrate the efficiency of the proposed methodologies in relation to other existing throughout the text. The designed controllers were implemented using these new proposals in a Three Degrees Of Freedom (3-DOF) helicopter or in the Shake Table II (STII) + Active Mass Dumper - One Floor (AMD-1) system, in order to validate in practice the proposed theories / Doutor

O setor sucroalcooleiro vem ganhando cada vez mais destaque no agronegócio brasileiro. O Produto Interno Bruto (PIB) do setor na safra de 2015 gerou mais de US$113 bilhões ao longo de toda cadeia produtiva (UNICA, 2016). Esse período de ascensão é acompanhado de novos desafios e oportunidades, o que torna o setor um tema fértil para a pesquisa acadêmica, teórica e aplicada. Dada à pluralidade do setor que hoje extravasa seu nicho tradicional, álcool e açúcar, e atua cada vez mais intensamente nos setores energéticos, eletricidade e combustíveis renováveis, faz-se necessário a incorporação da nova dinâmica de produção que esses produtos trazem à realidade administrativa do setor. Assim, além de discutir teoria e metodologia correlatas à modelagem matemática empregada no auxilio à gestão do setor, esse trabalho visa contribuir com a literatura, incorporando e discutindo as novas possibilidades produtivas que a produção de biogás trás ao mix de produção tradicional. As principais ferramentas utilizadas nessa análise são a teoria de portfólios e o arcabouço teórico da otimização robusta. A partir dessas técnicas construiu-se um modelo de otimização onde se busca a minimização do risco para um dado retorno, princípio da teoria de portfólios, avaliando o risco com o CVaR, uma medida de risco mais adequada do que a tradicional variância. Construído esse modelo, analisa-se o papel do biogás, um produto ainda pouco usual nas usinas brasileiras, no portfólio produtivo de uma usina hipotética. Com base nesse modelo implementou-se as técnicas de otimização robusta com o intuito de aferir se os resultados verificados no modelo determinístico se mantém no caso robusto. / The sugarcane sector is gaining a huge prominence in the Brazilian agribusiness. The GDP of the sector in 2015 crop was over then US$ 113 billion along the entire production chain (UNICA, 2016). This auspicious period is accompanied by new challenges and opportunities, which makes the sector a hot field for academic research, theoretical and applied. Given the industry plurality which today goes beyond its traditional niche, alcohol and sugar, the sector is increasingly strongly its share in the energy sector, electricity and renewable fuels. Thus it is necessary to incorporate the new dynamic of production that these products bring to the administrative reality of the sector. Therefore, in addition to discussing theory and methodology related to the mathematical modeling used as a support to sector management, this work aims to contribute to the literature by incorporating and discussing the new production possibilities that biogas production brings to the traditional production mix. The main tools used in this analysis are the portfolio theory and the theoretical and applied framework of robust optimization. From these techniques it is built up an optimization model where one seeks to minimize risk for a given return, the principle of portfolio theory, assessing the risk with CVaR, a better measure of risk than traditional variance. Through this model, the role of biogas, an unusual product in the Brazilian plants, is analyzed considering a hypothetical plant. Based on this model it is implemented robust optimization techniques in order to assess whether the results observed in the deterministic model remains in the case robust.

Este trabalho tem como objetivo avaliar a viabilidade da aplicação de técnicas de otimização robusta (OR) no planejamento da operação de reservatórios para geração de energia hidrelétrica. A OR é uma técnica de otimização que visa encontrar resultados que sejam menos sensíveis às incertezas nas variáveis do modelo através da minimização da variância da função objetivo para diferentes cenários. Desta forma foi desenvolvido um modelo de otimização robusta aplicado à operação de reservatórios para a geração de energia hidrelétrica, chamado HIDRO-OR, utilizando o software General Algebraic Modeling System (GAMS). Para estudo de caso foram utilizados os dados da UHE Sinop, a ser instalada no rio Teles Pires MT. Inicialmente foi realizada uma análise de sensibilidade utilizando diferentes combinações dos coeficientes de ponderação da função objetivo e três conjuntos de cenários. Nesta abordagem, o modelo resultou em vertimentos indesejados para realizar a diminuição do desvio padrão dos resultados entre os diferentes cenários. Uma solução encontrada para o problema foi realizar a otimização em duas etapas. Na primeira etapa ocorre a otimização robusta propriamente dita e são fixados os resultados para o primeiro mês de operação. Na segunda etapa, apenas a função objetivo principal é otimizada e, assim, são corrigidos os vertimentos indesejados. No entanto, com a otimização em duas etapas, não ocorreram mudanças na operação do reservatório para os diferentes coeficientes de ponderação. Ao final do trabalho conclui-se que, apesar dos resultados da análise de sensibilidade terem sido praticamente iguais com a otimização em duas etapas, estes podem ser considerados robustos pois são factíveis para todos os cenários. Por fim, são realizadas sugestões para a continuidade das pesquisas utilizando as técnicas de OR para a operação de usinas hidrelétricas. / This work aims to evaluate the feasibility of robust optimization techniques (OR) for reservoir management for hydropower production. The OR is an optimization technique which aims to find results that are less sensitive to the randomness of variables in the model by minimizing the variance of the objective function for different scenarios. One OR model was developed to the operation of reservoirs for hydropower production, called HYDRO-OR, using the software General Algebraic Modeling System (GAMS). As study case, data from the Sinop hydropower plant were used, which will be constructed in the Teles Pires river - MT. First, a sensitivity analysis was performed using different combinations of weigh coefficients of the objective function with three sets of scenarios. Preliminary results in this approach showed that the model resulted in unwanted spills to force the reduction of the standard deviation of the results from different scenarios. To correct this, the model was reconfigured to perform the optimization in two stages, the first one being the OR itself in which the results were obtained for the first month of planning. In the second step, the model was optimized again for subsequent months. In this case the model corrected the unnecessary spills but the results were quite similar for the three combinations of the weight coefficients. However the results can be considered robust because it is feasible for all scenarios. Finally, suggestions are made for further studies using the techniques of OR for the operation of hydropower plants.

Este trabalho apresenta os resultados da aplicação de três técnicas de controle utilizadas no projeto e implementação do controle de um manipulador subatuado planar de três juntas em série e de elos rígidos, projetado e construído pela Universidade Carnegie Mellon, EUA. Devido ao alto grau de não-linearidade deste sistema, seria muito difícil implementar um controlador H2, H&#8734 ou H2/H&#8734 que atuasse sozinho. Assim, propõe-se a utilização de um método de controle combinado: torque computado/H2, H&#8734 ou H2/H&#8734. No controle combinado, a porção correspondente ao torque computado lineariza e pré-compensa a dinâmica do modelo da planta nominal, enquanto a porção correspondente ao controle H2, H&#8734 ou H2/H&#8734 realiza uma pós-compensação dos erros residuais, que não foram completamente eliminados pelo método torque computado. Testes de acompanhamento de trajetória e testes de robustez são realizados aqui para comprovar a eficiência destes controladores, com resultados de implementação bastante satisfatórios. / This work presents the application results of three control techniques used for the control design and implementation of a serial planar underactuated manipulator with three joints and rigid links, designed and built by the Carnegie Mellon University, USA. Due to the high non-linearity degree of this system, it would be very difficult to implement an H2, H&#8734 or H2/ H&#8734 control which would actuate on the system by itself. Therefore, it is proposed a combined control method: computed torque/ H2, H&#8734 or H2/H&#8734. In the combined control, the portion corresponding to the computed torque linearizes and pre-compensates the dynamics of the nominal model, while the portion corresponding to the H2, H&#8734 or H2/H&#8734 control realizes a pos-compensation of the residual errors, not completely removed by the computed torque method. Trajetory tracking and robustness tests are performed here to demonstrate the efficiency of these controllers, with very satisfatory implementation results.

This thesis presents alternative methods for designing a speed controller for a hydrostatic power transmission system. Recognising that such a system, comprising a valve controlled motor supplied by the laboratory ring main and driving a hydraulic pump as a load, contains significant non-linearities, the thesis shows that robust 'modern control' approaches may be applied to produce viable controllers without recourse to the use of a detailed model of the system. In its introduction, it considers why similar approaches to the design of fluid power systems have not been applied hitherto. It then sets out the design and test, in simulation and on a physical rig, of two alternative linear controllers using H∞ based methods and a 'self organising fuzzy logic' controller (SOFLC). In the linear approaches, differences between the characteristics of the system and the simple models of it are accommodated in the controller design route as 'perturbations' or 'uncertainties'. The H∞ based optimisation methods allow these to be recognised in the design. “Mixed sensitivity” and “Loop shaping” methods are each applied to design controllers which are tested successfully on the laboratory rig. The SOFLC in operation does not rely on a model, but instead allows fuzzy control rules to evolve. In the practical tests, the system is subjected to a range of disturbances in the form of supply pressure fluctuations and load torque changes. Also presented are test results for proportional and proportional plus integral (PI) controllers, to provide a reference. It is demonstrated qualitatively that performance using the linear controllers is superior to that using proportional and PI controllers. An increased range of stable operation is achieved by the controller designed using “loop shaping” – performance is enhanced by the use of two controllers selected automatically according to the operating speed, using a “bumpless” transfer routine. The SOFLC proved difficult to tune. However, stable operation was achieved.

"As a part of an effective SETAR (self-exciting threshold autoregressive) mod- eling methodology, it is important to identify processes exhibiting SETAR-type non- linearity. A number of tests of nonlinearity have been developed in the literature, including those of Keenan (1985), Petruccelli and Davies (1986), Tsay (1986, 1989), Luukkonen (1988), and Chan and Tong (1990). However, it has recently been shown that all these tests perform poorly for SETAR-type nonlinearity detection in the presence of outliers. In this project we develop an improved test for SETAR-type nonlinearity in time series. The test is an outlier-robust variant of the Petruccelli and Davies (1986) test based on the cumulative sums of ordered weighted residuals from generalized maximum likelihood fits (which we call CUSUM-GM). The properties of the proposed CUSUM-GM test are illustrated by means of Monte Carlo simulations. The merits, in terms of size and power, of the proposed test are evaluated relative to the test based on ordered residuals from the ordinary least squares fit (which we call CUSUM-LS) and also to that of other tests for nonlinearity developed in literature. The simulations are run for uncontaminated data and for data contaminated with additive and innovational outliers. The simulation study strongly supports the validity of the proposed robust CUSUM-GM test, particularly in situations in which outliers might be a problem."

by Ho, Kei Shiu Edward. / "June 1996." / Thesis (Ph.D.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (p. 186-193). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web.

Liu Lu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 65-70). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Output Regulation Problem --- p.1 / Chapter 1.2 --- Control Design with Unknown High-frequency Gain Sign --- p.3 / Chapter 1.3 --- Contribution of the Thesis --- p.4 / Chapter 1.4 --- Thesis Outline --- p.5 / Chapter 2 --- Global Robust Stabilization of a Class of Nonlinear Systems --- p.6 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Problem Formulation and Preliminaries --- p.8 / Chapter 2.3 --- Main Result --- p.11 / Chapter 2.4 --- An Example --- p.20 / Chapter 2.5 --- Application of Theorem 2.1 --- p.26 / Chapter 2.5.1 --- Chua's Circuit and Control Problem --- p.26 / Chapter 2.5.2 --- Solvability of the Control Problem --- p.28 / Chapter 2.5.3 --- Simulation Results --- p.32 / Chapter 2.5.4 --- Conclusion --- p.33 / Chapter 2.6 --- Conclusion --- p.36 / Chapter 3 --- Global Robust Output Regulation of Nonlinear Systems in Output Feedback Form --- p.39 / Chapter 3.1 --- Introduction --- p.40 / Chapter 3.2 --- Output Regulation Converted to Stabilization --- p.42 / Chapter 3.3 --- Main Result --- p.49 / Chapter 3.4 --- An Example --- p.55 / Chapter 3.5 --- Conclusion --- p.58 / Chapter 4 --- Conclusions --- p.62 / List of Figures --- p.64 / Bibliography --- p.65 / Biography

Chen Zhiyong. / "April 2005." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 205-215) / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Another important contribution of this thesis is that we propose another novel and highly robust estimator: Kernel Density Estimation Sample Consensus (KDESAC) which employs Random Sample Consensus algorithm combined with Kernel Density Estimation (KDE). The main advantage of KDESAC is that no prior information and no scale estimators are required in the estimation of the parameters. The computational load of KDESAC is much lower than the robust algorithms which estimate the scale in every sample loop. The experiments on synthetic data show that the proposed method is more robust to the heavily corrupted data than other algorithms. KDESAC can tolerate more than 80% outliers and multiple structures. Although Adaptive Scale Sample Consensus (ASSC) can obtain such good performance as KDESAC, ASSC is much slower than KDESAC. KDESAC is also applied to SFM problem and multi-motion estimation with real data. The experiments demonstrate that KDESAC is robust and efficient. / Structure from motion (SFM), the problem of estimating 3D structure from 2D images hereof, is one of the most popular and well studied problems within computer vision. This thesis is a study within the area of SFM. The main objective of this work is to improve the robustness of the SFM algorithm so as to make it capable of tolerating a great number of outliers in the correspondences. For improving the robustness, a stereo image sequence is processed, so the random sampling algorithms can be employed in the structure and motion estimation. With this strategy, we employ Random Sample Consensus (RANSAC) in motion and structure estimation to exclude outliers. Since the RANSAC method needs the prior information about the scale of the inliers, we proposed an auto-scale RANSAC algorithm which determines the inliers by analyzing the probability density of the residuals. The experimental results demonstrate that SFM by the proposed auto-scale RANSAC is more robust and accurate than that by RANSAC. / Chan Tai. / "September 2006." / Adviser: Yun Hui Liu. / Source: Dissertation Abstracts International, Volume: 68-03, Section: B, page: 1716. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (p. 113-120). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.