The Generalized Minimal Residual method (GMRES) is often used to solve a nonsymmetric linear system Ax = b. But its convergence analysis is a rather difficult task in general. A commonly used approach is to diagonalize A = XΛX-1 and then separate the study of GMRES convergence behavior into optimizing the condition number of X and a polynomial minimization problem over As spectrum. This artificial separation could greatly overestimate GMRES residuals and likely yields error bounds that are too far from the actual ones. On the other hand, considering the effects of both As spectrum and the conditioning of X at the same time poses a difficult challenge, perhaps impossible to deal with in general but only possible for certain particular linear systems. This thesis will do so for a (nonsymmetric) tridiagonal Toeplitz system. Sharp error bounds on and sometimes exact expressions for residuals are obtained. These expressions and/or bounds are in terms of the three parameters that define A and Chebyshev polynomials of the first kind or the second kind.

Abstract Non-linear methods have been utilised in modelling the processes on a flue-gas oxygen-content control system of a power plant. The ultimate objective is to reduce NOx and CO emissions by enhancing the control system. By investigating the flue-gas emission control strategy, the major factors affecting the flue-gas emissions have been determined. A simulator has been constructed, and it emulates a real process automation system and its physical processes. The process models of the simulator are: a flue-gas oxygen-content model, a secondary air flow model, a primary air flow model and a fuel feeding screw model (a fuel flow). The effort has been focused on two plant models: the flue-gas oxygen-content model and the secondary air flow model. Combustion is a non-linear, timevariant, multi-variable process with a variable delay. The secondary air model is a non-linear, timeinvariant (in principle), multi-variable system. Both phenomenological modelling (mass and energy calculations) and black-box modelling (neural networks) have been utilised in the Wiener/Hammerstein structures. It is possible to use a priori knowledge in model modifying, and therefore the model of flue-gas oxygen-content can be tuned on site. The simulator with precalculated parameters was tested in a full-scale power plant and a pilot-scale circulating fluidised bed boiler. The results in the power plant were remarkable since NOx emissions decreased significantly without increasing CO emissions.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第17889号 / 工博第3798号 / 新制||工||1581(附属図書館) / 30709 / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 萩原 朋道, 教授 土居 伸二, 准教授 久門 尚史 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

SPIKE is a parallel algorithm to solve block tridiagonal matrices. In this work, two useful improvements to the algorithm are proposed. A flexible threading strategy is developed, to overcome limitations of the recursive reduced system method. Allo- cating multiple threads to some tasks created by the SPIKE algorithm removes the previous restriction that recursive SPIKE may only use a number of threads equal to a power of two. Additionally, a method of solving transpose problems is shown. This method matches the performance of the non-transpose solve while reusing the original factorization.

The Sherman Morrison iteration method is developed to solve regularized least squares problems. Notions of pivoting and splitting are deliberated on to make the method more robust. The Sherman Morrison iteration method is shown to be effective when dealing with an extremely underdetermined least squares problem. The performance of the Sherman Morrison iteration is compared to classic direct methods, as well as iterative methods, in a number of experiments. Specific Matlab implementation of the Sherman Morrison iteration is discussed, with Matlab codes for the method available in the appendix. / Master of Science

With the rapid development of optical communications and the increasing amount of data exchanged, it has become utterly important to provide effective architectures to protect sensitive data. The use of chaotic optoelectronic devices has already demonstrated great potential in terms of additional computational security at the physical layer of the optical network. However, the determination of the security level and the lack of a multi-user framework are two hurdles which have prevented their deployment on a large scale. In this thesis, we propose to address these two issues. First, we investigate the security of a widely used chaotic generator, the external cavity semiconductor laser (ECSL). This is a time-delay system known for providing complex and high-dimensional chaos, but with a low level of security regarding the identification of its most critical parameter, the time delay. We perform a detailed analysis of the influence of the ECSL parameters to devise how higher levels of security can be achieved and provide a physical interpretation of their origin. Second, we devise new architectures to multiplex optical chaotic signals and realize multi-user communications at high bit rates. We propose two different approaches exploiting known chaotic optoelectronic devices. The first one uses mutually coupled ECSL and extends typical chaos-based encryption strategies, such as chaos-shift keying (CSK) and chaos modulation (CMo). The second one uses an electro-optical oscillator (EOO) with multiple delayed feedback loops and aims first at transposing coded-division multiple access (CDMA) and then at developing novel strategies of encryption and decryption, when the time-delays of each feedback loop are time- dependent.

<p>Certification of energy wheel effectiveness by a selected international laboratory for many types and sizes of wheel produced by each manufacturer has proven to be very expensive and has been prone to large uncertainties. This research uses a new, low-cost, transient method to predict the effectiveness using only data obtained from transient measurements.</p><p>In this thesis, an analytical model is presented for predicting the effectiveness of rotating energy wheels using only the characteristics measured on the same non-rotating wheels exposed to a step change in temperature and humidity. A relationship between the step response and the periodic response of an energy wheel is developed using first order linear system design theory. This allows the effectiveness of an energy wheel to be predicted when the characteristics of a step response are known. The effectiveness correlations and uncertainty bounds for sensible and latent effectiveness of energy wheels determined from transient measurements are thus presented.</p><p>The experimental transient testing method and experimental verification of the effectiveness model for several different wheels are also presented in this thesis. The results obtained from the new effectiveness model are shown to agree, within uncertainty bounds, with the results obtained from the standard steady state experimental testing method and numerical simulations.</p>

<p>Certification of energy wheel effectiveness by a selected international laboratory for many types and sizes of wheel produced by each manufacturer has proven to be very expensive and has been prone to large uncertainties. This research uses a new, low-cost, transient method to predict the effectiveness using only data obtained from transient measurements.</p><p>In this thesis, an analytical model is presented for predicting the effectiveness of rotating energy wheels using only the characteristics measured on the same non-rotating wheels exposed to a step change in temperature and humidity. A relationship between the step response and the periodic response of an energy wheel is developed using first order linear system design theory. This allows the effectiveness of an energy wheel to be predicted when the characteristics of a step response are known. The effectiveness correlations and uncertainty bounds for sensible and latent effectiveness of energy wheels determined from transient measurements are thus presented.</p><p>The experimental transient testing method and experimental verification of the effectiveness model for several different wheels are also presented in this thesis. The results obtained from the new effectiveness model are shown to agree, within uncertainty bounds, with the results obtained from the standard steady state experimental testing method and numerical simulations.</p>

Spectral graph theory is the interplay between linear algebra and combinatorial graph theory. Laplace’s equation and its discrete form, the Laplacian matrix, appear ubiquitously in mathematical physics. Due to the recent discovery of very fast solvers for these equations, they are also becoming increasingly useful in combinatorial optimization, computer vision, computer graphics, and machine learning. In this thesis, we develop highly efficient and parallelizable algorithms for solving linear systems involving graph Laplacian matrices. These solvers can also be extended to symmetric diagonally dominant matrices and M-matrices, both of which are closely related to graph Laplacians. Our algorithms build upon two decades of progress on combinatorial preconditioning, which connects numerical and combinatorial algorithms through spectral graph theory. They in turn rely on tools from numerical analysis, metric embeddings, and random matrix theory. We give two solver algorithms that take diametrically opposite approaches. The first is motivated by combinatorial algorithms, and aims to gradually break the problem into several smaller ones. It represents major simplifications over previous solver constructions, and has theoretical running time comparable to sorting. The second is motivated by numerical analysis, and aims to rapidly improve the algebraic connectivity of the graph. It is the first highly efficient solver for Laplacian linear systems that parallelizes almost completely. Our results improve the performances of applications of fast linear system solvers ranging from scientific computing to algorithmic graph theory. We also show that these solvers can be used to address broad classes of image processing tasks, and give some preliminary experimental results.

[pt] Nesta tese é feito um estudo sobre os Sistemas estritamente reais Positivos e suas aplicações no controle de sistemas com incertezas, tais como adaptativo com memória e o controle com estrutura variável e modos deslizantes. Os resultados obtidos ampliam o conhecimento sobre os sistemas estritamente reais Positivos e o seu emprego em sistemas de controle, e apresentam novas leis de controle que melhoram as configurações existentes em aspectos tais como a estabilidade, a estimação de transitórios, a necessidade do acesso às variáveis de estado e detalhes práticos de implementação. Este trabalho aborda e fornece contribuições a alguns problemas de controle, tais como o controle adaptativo com modelo de referência, a estabilização de sistemas com incertezas e o problema do servomecanismo com referência parcialmente conhecida. São obtidos também alguns resultados sobre os sistemas estritamente reais positivos: definições equivalentes, condições para tornar um sistema estritamente real positivo e relações entre os sistemas de controle com estrutura variável e modos deslizantes e os sistemas com alto ganho, com os sistemas estritamente reais positivos. Uma parte dos resultados acima, desenvolvidos inicialmente para sistemas lineares e invariantes no tempo, é generalizada para uma classe de sistemas lineares variantes no tempo. / [en] This thesis addresses strictly positive real systems and their application in the control of uncertain dynamical systems, as for exemplare, in adaptative control with memory and in variable structure systems with sliding motions. The results of this work extend the knowledge about strictly positive real systems and their application in control systems, and offer new control laws that improve the existing configurations, as for example in transient estimation, state variable access and practical details of implementation. The model reference adaptive control, the stabilization of uncertain dynamical systems and the servo system problem are considerad new results are obtained. For the strictly positive real systems, equivalent definitions, conditions to turn a transfer matrix into a strictly positive real and relations of the variable structure systems with sliding motions and high gain system with the strictly positive real systems are presented. Some of the results above are extended for the linear time varying sytems.