In this paper we deal with the `strength' of ill-posedness for ill-posed linear operator equations Ax = y in Hilbert spaces, where we distinguish according_to_M. Z. Nashed [15] the ill-posedness of type I if A is not compact, but we have R(A) 6= R(A) for the range R(A) of A; and the ill-posedness of type II for compact operators A: From our considerations it seems to follow that the problems with noncompact operators A are not in general `less' ill-posed than the problems with compact operators. We motivate this statement by comparing the approximation and stability behaviour of discrete least-squares solutions and the growth rate of Galerkin matrices in both cases. Ill-posedness measures for compact operators A as discussed in [10] are derived from the decay rate of the nonincreasing sequence of singular values of A. Since singular values do not exist for noncompact operators A; we introduce stability rates in order to have a common measure for the compact and noncompact cases. Properties of these rates are illustrated by means of convolution equations in the compact case and by means of equations with multiplication operators in the noncompact case. Moreover using increasing rearrangements of the multiplier functions specific measures of ill-posedness called ill-posedness rates are considered for the multiplication operators. In this context, the character of sufficient conditions providing convergence rates of Tikhonov regularization are compared for compact operators and multiplication operators.

Made available in DSpace on 2016-06-02T20:06:02Z (GMT). No. of bitstreams: 1 2567.pdf: 3332442 bytes, checksum: 1e03b44e1c1f61f90b947fdca5682355 (MD5) Previous issue date: 2009-03-06 / Financiadora de Estudos e Projetos / Several techniques are proposed to determine the lag length of a dynamic regression model. However, none of them is completely satisfactory and a wrong choice could imply serious problems in the estimation of the parameters. This dissertation presents a review of the main criteria for models selection used in the classical methodology and presents a way for determining the lag length from the perspective Bayesian. A Monte Carlo simulation study is conducted to compare the performance of the significance tests, R2 adjusted, final prediction error, Akaike information criterion, Schwarz information criterion, Hannan-Quinn criterion, corrected Akaike information criterion and fractional Bayesian approach. Two estimation methods are also compared, the ordinary least squares and the Almon approach. / Na literatura, muitas técnicas são propostas para determinar o tamanho da defasagem de um modelo de regressão dinâmico. Entretanto, nenhuma delas é completamente satisfatória e escolhas erradas implicam em sérios problemas na estimação dos parâmetros. Este trabalho apresenta uma revisão dos principais critérios de seleção de modelos disponíveis na metodologia clássica, assim como aborda uma maneira de determinar o tamanho da defasagem sob a perspectiva Bayesiana. Um estudo de simulação Monte Carlo é conduzido para comparar a performance dos testes de significância, do R2 ajustado, do erro de predição final, dos critérios de informação de Akaike, Schwarz, Hannan-Quinn e Akaike corrigido e da aproximação Bayesiana fracionada. Também serão comparados os métodos de estimação de Mínimos Quadrados Ordinários e de Almon.

This diploma thesis deal with analysis of current surveying methods of railway track spatial position of the track section located between Břeclav and Znojmo. At the beginning of the work there is described historical development of railway geodesy in our country and conditions of railway geodetic points field abroad. Further there are mentioned rules for measurement of railway point fields in the Czech Republic. In the following chapter you will find sub-stages of building railway point fields in track section with analysis of accuracy measurement and a proposal of prior accuracy of measurement for computing with the least square method. In the end of the thesis there is described a calculation of parameters spatial track geometry with the suggestion of computing service for uniform way of calculating partial stages of railway geodetic point field.

Diploma thesis describes the measurement and evaluation of displacements and deformations of the wooden roof structure of the aquapark hall in Brno – Kohoutovice. Part of the work is devoted to the preparation and testing of used devices and tools. The main part of the work consists of performing one stage of measurement using the polar method and the laser scanning method. The polar method measurement is compared with the results of the polar method of the previous stage. The next part of the work deals with the comparison of the polar method and the laser scanning method measured in the last stage. The results achieved are interpreted in the final part of the work.

The diploma thesis is focused on an adaptive control, especially in a self-tuning controller area. The thesis is divided into two main parts. The first part deals with identification methods of the adaptive control. The recursive least squares algorithm and the neural network method are the most popular identification methods. These methods are contrasted and the identification quality evaluation is done. The second part compares various types of the adaptive controllers with a non-adjustable PSD controller. The adaptive controllers are investigated from the various identification method point of view. The user graphic interface was realized for the identification and regulatory part. The time behavior of system responses after incoming disturbance and dynamic process changes during simulation systems control is compared with a physical model connected to B&R PLC. The comparison is done with the application of Matlab/Simulink program.

This thesis deals with implementation of industrial used controlling block into Power Panel equipment of B&R in integrated development environment Automation Studio 3.0.71. It is PID controller with autotuner and visualization, which allowed bumpless transfer among controlling algorithms and manual control. PID and I-PD controllers with filtering of derivative action and dynamic antiwindup were implemented. Parameters of PID controller is possible to tune with the aid of ultimate gain and ultimate period according rules of Ziegler-Nichols. Ultimate parameters of controlled plant is possible to acquire with the aid of two identification methods, recursive least squares method and relay feedback. Recursive least squares method was implemented with directional forgetting. For relay feedback were used two types of relays: ideal and saturation relay for improving accuracy of searched ultimate values. The whole solution is programmed in ANSI C which Automation Studio supports. Created controller is control with the aid of touchscreen which is integrated in Power Panel. Trends of process values are viewed on the screen too. For comparison adaptive controller by B&R was implemented. This contoller is standardly supplied with Automation Studio in LoopConR library. All created algorithms were first validated on mathematical model of plant and then on real model in laboratory. The first part of thesis deals with theoretic analysis of used methods. The practical realization is described in the second part of this diploma thesis.

The electrical motors parameters identification is solved in this master’s thesis using subspace based methods. Electrical motors are simulated in Matlab/Simulink interactive environment, specifically permanent magnet DC motor and permanent magnet synchronous motor. Identification is developed in Matlab interactive environment. Different types of subspace algorithms are used for the estimation of parameters. Results of subspace parameters estimation are compared with least squares parameters estimation. The thesis describes subspace method, types of subspace algorithms, used electrical motors, nonlinear approach of identification and comparation of parameters identification.

This master‘s thesis deals with the design of modern process control algorithms suitable for SISO industrial control equipments. In this thesis the analysis of the controller design methodology using Mixed-sensitivity function is described. This method consists in shaping frequency characteristics of the sensitivity function and complementary sensitivity fiction using the weighting functions. The proposed H controllers are compared with the classical structure of a discrete PID controller with filtered derivative part. The proposed controllers are compared in terms of robustness, performance, complexity of the design and requirements necessary for their practical application (anti-windup, smooth switchover). Robustness of the controller is evaluated on the basis of modulus stability margin. Estimation of model´s parameters is solved least-square method. The proposed control system consists of an industrial PC and Automation Panel from the company B&R, decentralized system I/O and the real plant. Visualization for control workplace was created in the program Automation studio. This visualization is used to the easy transfer of information from a controlled process.

This final thesis deals with adaptive control of small brewery. Contains a short description of brewing technology and adaptive control. Includes design of small brawery and control system based on STM32F407 Cortex-M4 microcontroller. For online identification is used Recursive Least Squares Method. The controller function perform a modified PSD controller with filtered derivative component, reducing the first overshot and dynamic antiwindup. The proposed adaptive controller is implemented into microcontroller. Created device i used for semi-automatic beer production.

Tato diplomová práce nastiňuje teoretické základy potřebné pro návrh algoritmu rekurzivní metody nejmenších čtverců a následně jeho aplikaci na experimentální data naměřená při testovacím manévru uskutečněném v roce 2001. Analyzována byla příčná dynamika jednostopého rovinného modelu vozidla. Práce také obsahuje srovnání výsledků získaných jednak rekurzivním algoritmem a dále i algoritmem Kalmanova filtru.